Download INTRODUCTION TO SPSS FOR WINDOWS

INTRODUCTION TO SPSS
FOR WINDOWS
Version 15.0
Summer 2007
Contents
Purpose of handout & Compatibility between different versions of SPSS……………….. 1
SPSS window & menus…………………………………………………………………… 1
Getting data into SPSS & Editing data…………………………………………………….. 3
Reading an SPSS viewer/output (.spo) file & Editing your pout…………………………. 7
Saving data as an SPSS data (.sav) file…..………………………………………………... 8
Saving your output (statistical results and graphs)………………………………………… 9
Exporting SPSS Output……………………………………………………………………. 10
Printing your work & Exiting SPSS……………………………………………………….. 12
Running SPSS using syntax or command language (.sps files)….…………………………13
Creating a new variable……………………………………………………………………. 14
Recoding or combining categories of a variable……………………………………………15
Summarizing your data
Frequency tables (& bar charts) for categorical variables…………………………………. 20
Contingency tables for categorical variables………………………………………………. 21
Descriptive statistics (& histograms) for numerical variables…………………………….. 22
Descriptive statistics (& boxplots) by groups for numerical variables……………………. 24
Using the Split File option for summaries by groups……………………………………… 26
Using the Select Cases option for summaries for a subgroup of subjects/observations…… 27
Graphing your data
Bar chart…………………………………………………………………………………… 28
Histogram & Boxplot……………………………………………………………………… 29
Normal probability plot……………………………………………………………………. 30
Error bar plot……………………………………………………………………………….. 31
Scatter plot…………………………………………………………………………………. 32
Adding a line or loess smooth to a scatter plot…………………………………………….. 32
Stem-and-leaf plot………………………………………………………………………….. 33
Hypothesis tests & Confidence intervals
One sample t test & Confidence interval for a mean………………………………………. 34
Paired t test & Confidence interval for the difference between means……………………. 37
Two sample t test & Confidence interval for the difference between means……………… 39
Sign test and Wilcoxon signed rank test………………………………………………....... 42
Mann Whitney U test (or Wilcoxon rank sum test)……………………………….............. 45
One-way ANOVA (Analysis of variance) & Post-hoc tests…………………………......... 47
Kruskal-Wallis test……………………………………………………………………….....50
One-sample binomial test………………………………………………………………...... 52
McNemar’s test……………………………………………………………………………..53
Chi-square test for contingency tables………………..…………………………………….55
Fisher’s exact test………………………………………………………………………....... 55
Trend test for contingency tables/ordinal variables……………………………………....... 55
Binomial, McNemar’s, Chi-square and Fisher’s exact tests using summary data……….... 59
Confidence interval for a proportion………………………………………………………. 63
Correlation & Regression
Pearson and spearman rank correlation coefficient……………………………………....... 65
Linear regression………………………………………………………………………........ 68
Liner regression via ANOVA commands………………………………………………….. 76
Logistic regression………………………………………………………………………… 80
1
Purpose of handout
SPSS for Windows provides a powerful statistical and data management system in a graphical
environment. The user interfaces make statistical analysis more accessible for casual users and
more convenient for experienced users. Most tasks can be accomplished simply by pointing and
clicking the mouse.
The objective of this handout is to get you oriented with SPSS for Windows. It teaches you how
to enter and save data in SPSS, how to edit and transform data, how to explore your data by
producing graphics and summary descriptives, and how to use pointing and clicking to run
statistical procedures. It is also intended to serve as a reference guide for SPSS procedures that
you will need to know to do your homework assignments.
Compatibility between different versions of SPSS
SPSS for Windows data files (files ending in .sav) and syntax (command) files (files ending in
.sps) are compatible between different versions of SPSS (at least, versions 11.0 or newer).
However, SPSS output/viewer files (files ending .spo) are NOT always compatible between
different versions. Usually SPSS output files created with an old version and can be read by a
new version, but an output file created using a new version can not be read by an old version.
One option for avoiding compatibility problems between different versions of SPSS is to export
your output in html or MS Word format. The compatibility between Window and Mac versions
of SPSS is limited.
SPSS Windows & Menus
An overview of the SPSS windows, menus, toolbars, and dialog boxes is given in the SPSS
Tutorials under Help. You can also find information under Topics, Case Studies, Statistics
Coach, and Command & Syntax (if you are using syntax commands.)
Window Types
SPSS Data Editor. When you start an SPSS session, you usually see the Data Editor window
(otherwise you will see a Viewer window). The Data Editor displays the contents of the working
data file. There a two views in the data editor window: 1) Data View displays the data in a
spreadsheet format with variable names listed for column headings, and 2) Variable View which
displays information about the variables in your data set. In the Data View you can edit or enter
data, and in the Variable View you can change the format of a variable, add format and variable
labels, etc.
SPSS Viewer/Output. Statistical results and graphs are displayed in the Viewer window. The
(output) Viewer window is divided into two panes. The right-hand pane contains the all the
output and the left-hand pane contains a tree-structure of the results. You can use the left-hand
pane for navigating through, editing and printing your results.
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Chart Editor. The chart editor is used to edit graphs. When you double-click on figure or
graph, it will reappear in a chart editor window.
SPSS Syntax Editor. The Syntax Editor is used to create SPSS command syntax for using the
SPSS production facility. Usually you will be using the point and click facilities of SPSS, and
hence, you will not need to use the Syntax Editor. More information about the Syntax Editor and
using the SPSS syntax is given in the SPSS Help Tutorials under Working with Syntax. A few
instructions to get you started are given later in the handout in the section Running SPSS using
the Syntax Editor (or Command Language)
Menus
Data Editor Menu:
File. Use the File menu to create a new SPSS file, open an existing file, or read in spreadsheet or
database files created by other software programs (e.g., Excel).
Edit. Use the Edit menu to modify or copy data and output files.
View. Choose which buttons are available in the window or how the window should look.
Data. Use the Data menu to make changes to SPSS data files, such as merging files, transposing
variables, or creating subsets of cases for subset analysis.
Transform. Use the Transform menu to make changes to selected variables in the data file (e.g.,
to recode a variable) and to compute new variables based on existing variables.
Analyze. Use the Analyze menu to select the various statistical procedures you want to use, such
as descriptive statistics, cross-tabulation, hypothesis testing and regression analysis.
Graphs. Use the Graphs menu to display the data using bar charts, histograms, scatterplots,
boxplots, or other graphical displays . All graphs can be customized with the Chart Editor.
Utilities. Use the Utilities menu to view variable labels for each variable.
Add-ons. Information about other SPSS software.
Window. Choose which window you want to view.
Help. Index of help topics, tutorials, SPSS home page, Statistics coach, and version of SPSS.
Viewer Menu: Menu is similar to Data Editor menu, but has two additional options:
Insert. Use the insert menu to edit your output
Format. Use the format menu to change the format of your output.
Chart Editor Menu: Use SPSS Help to learn more about the Chart Editor.
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Toolbars
Most Windows applications provide buttons arranged along the top of a window that act as
shortcuts to executing various functions. In SPSS, you will find such buttons (icons) at the top
the of the Data Editor, Viewer, Chart Editor, and Syntax windows. The icons are usually
symbolic representations of the procedure they execute when pushed, unfortunately their
meanings are not intuitively obvious until one has already used them. Hence, the best way to
learn these buttons is to use them and note what happens.
The Status Bar The Status Bar runs along the bottom of a window and alerts the user to the status
of the system. Typical messages one will see are “SPSS Processor is ready”,
“Running procedure…”. The Status Bar will also provide up-to-date information concerning
special manipulations of the data file like whether only certain cases are being used in an
analysis or if the data has been weighted according to the value of some variable.
File Types
Data Files. A file with an extension of .sav is assumed to be a data file in SPSS for Windows
format. A file with an extension of .por is a portable SPSS data file. The contents of a data file
are displayed in the Data Editor window.
Viewer (Output) Files. A file with an extension of .spo is assumed to be a Viewer file
containing statistical results and graphs.
Syntax (Command) Files. A file witn an extension of .sps is assumed to be a Syntax file
containing spss syntax and commands.
Getting Data into SPSS & Editing Data
When reading and editing data into SPSS the data will be displayed in the Data Editor Window.
An overview of the basic structure of an SPSS data file is given in the SPSS Help Tutorials:
1. Choose Help on the menu bar
2. Choose Tutorial
3. Choose Reading Data
Reading Data from a SPSS Data (.sav) File
To read a data file from your computer/floppy disk/flash drive that was created and saved using
SPSS. The filename should end with the suffix .sav.
1. Choose Open an existing data source
2. Double click on the filename or
3. Single click on the filename and choose OK
Or
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1.
2.
3.
4.
5.
6.
7.
Choose Cancel
Choose File on the menu bar
Choose Open
Choose Data...
Edit the directory or disk drive to indicate where the data is located.
Double click on the filename or
Single click on the filename and choose Open
Reading Data from an Text Data File
To read an raw/text (ascii) data file from your computer/floppy disk/flash drive, where the data
for each observation is on a separate line and a space is used to separate variables on the same
line (i.e., the file format is freefield). The filename should end with the suffix .dat.
1.
2.
3.
4.
5.
6.
7.
Choose File on the menu bar
Choose Read Text Data
Choose Files of Type *.dat
Edit the directory or disk drive to indicate where the data is located
Double click on the filename or
Single click on the filename and choose Open
Follow the Import Wizard Instructions.
You can also get to the Import Wizard as follows:
1.
2.
3.
4.
5.
6.
7.
8.
Choose File on the menu bar
Choose Open
Choose Data...
Choose Files of Type *.dat
Edit the directory or disk drive to indicate where the data is located
Double click on the filename or
Single click on the filename and choose Open
Follow the Import Wizard Instructions.
Instructions on how to read a text data file in fixed format are located in SPSS Help Tutorials
under Reading Data from a Text File.
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Reading Data from Other Types of External Files
SPSS allows you to read a variety of other types of external files, such as Excel spreadsheet files,
SAS data files, Lotus 1-2-3 spreadsheet files, and dBASE database files. To read data from other
types of external files, you follow the same steps as you would for reading an SPSS save file,
except that you specify the file type according to what package was used to create the save file.
For further instruction on how to read data from other types of external files, see the SPSS for
Windows Base System User's Guide on data files or the SPSS Help Tutorials.
Entering and Editing Data Using the Data Editor
The Data Editor provides a convenient spreadsheet-like facility for entering, editing, and
displaying the contents of your data file. A Data Editor window opens automatically when you
start an SPSS session. Instruction on Using the Data Editor to enter data is given in the SPSS
Help Tutorials. Note that if you are already familiar with entering data into a different
spreadsheet program (e.g., MS Excel), you might find it easy to enter your data in the program
your are familiar with and then read the data into SPSS.
Entering Data. Basic data entry in the Data Editor is simple:
Step 1. Create a new (empty) Data Editor window. At the start of an SPSS session a new
(empty) Data Editor window opens automatically. During an SPSS session you can create a new
Data Editor window by
1. Choose File
2. Choose New
3. Choose Data
Step 2. Move the cursor to the first empty column.
Step 3. Type a value into the cell. As you type, the value appears in the cell editor at the top of
the Data Editor window. Each time you press the Enter key, the value is entered in the cell and
you move down to the next row. By entering data in a column, you automatically create a
variable and SPSS gives it the default variable name var00001.
Step 4. Choose the first cell in the next column. You can use the mouse to click on the cell or use
the arrow keys on the keyboard to move to the cell. By default, SPSS names the data in the
second column var00002.
Step 5. Repeat step 4 until you have entered all the data. If you entered an incorrect value(s) you
will need to edit your data. See the following section on Editing Data.
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Editing Data. With the Data Editor, you can modify a data file in many ways. For example you
can change values or cut, copy, and paste values, or add and delete cases.
To Change a Data Value:
1. Click on a data cell. The cell value is displayed in the cell editor.
2. Type the new value. It replaces the old value in the cell editor.
3. Press then Enter key. The new value appears in the data cell.
To Cut, Copy, and Paste Data Values
1. Select (highlight) the cell value(s) you want to cut or copy.
2. Pull down the Edit box on the main menu bar.
3. Choose Cut. The selected cell values will be copied, then deleted. Or
4. Choose Copy. The selected cell values will be copied, but not deleted.
5. Select the target cell(s) (where you want to put the cut or copy values).
6. Pull down the Edit box on the main menu bar.
7. Choose Paste. The cut or copy values will be ``pasted'' in the target cells.
To Delete a Case (i.e., a Row of Data)
1. Click on the case number on the left side of the row. The whole row will be highlighted.
2. Pull down the Edit box on the main menu bar.
3. Choose Clear.
To Add a Case (i.e., a Row of Data)
1. Select any cell in the case from the row below where you want to insert the new case.
2. Pull down the Data box on the main menu bar.
3. Choose Insert.
Defining Variables. The default name for new variables is the prefix var and a sequential fivedigit number (e.g., var00001, var00002, var00003). To change the name, format and other
attributes of a variable.
1. Double click on the variable name at the top of a column or,
2. Click on the Variable View tab at the bottom of Data Editor Window.
3. Edit the variable name under column labeled Name. The variable name must be eight
characters or less in length. You can also specify the number of decimal places (under
Decimals), assign a descriptive name (under Label), define missing values (under
Missing), define the type of variable (under Measure; e.g., scale, ordinal, nominal), and
define the values for nominal variables (under Values).
After the data is entered (or several times during data entering), you will want to save it as an
SPSS save file. See the section on Saving Data As An SPSS Save File.
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Reading an SPSS Viewer/Output (.spo) File
Statistical results and graphs are displayed in the Viewer window. An overview of how to use
the Viewer is given in the SPSS Help Tutorials under Working with Output.
If you saved the results of Viewer window during an earlier SPSS session, you can use the
following commands to display the Viewer (output) results in a current SPSS session. However,
SPSS output/viewer files (files ending .spo) are NOT always compatible between different
versions. Usually SPSS output files created with an older version and can be read by a new
version, but an output file created using a new version can not be read by an older version. One
option for avoiding compatibility problems between different versions of SPSS is to export your
output in html or MS Word format. The compatibility between Window and Mac versions of
SPSS is limited.
To read a Viewer file from your computer\floppy disk\flashdrive that was created and saved
using SPSS. The filename should end with the suffix spo.
1.
2.
3.
4.
5.
6.
Choose File on the menu bar
Choose Open
Choose Output...
Edit the directory or disk drive to indicate where the data is located
Double click on the filename or
Single click on the filename and choose Open
Editing Your Output
Editing the statistical results and graphs in the Viewer window is beyond the scope of this
handout. Instructions on how to edit your output is given in the SPSS Help Tutorials under
Working with Output and Creating and Editing Charts.
 You can use either the tree-structure in the left hand pane or the results displayed in the right
hand pane to select, move or delete parts of the output.
 To edit a table or object (an object is a group of results) you first need to double click on the
table/object so an “editing” box appears around the table/object, and then select the value you
want to modify. An “editing box'” will be a ragged box outlining the table. If you only do a
single click you will get a box with straight/plain lines outlining the table. In general, to create
“nice looking” tables of your results it is often easier to hand enter the values into a blank MS
Word table than to edit a SPSS table/object (either in SPSS or MS Word).
 To edit a chart you first need to double click on the chart so it appears in a new Chart Editor
window. After you are done editing the chart, close the window and then export the chart, for
example to a windows metafile and then into a MS Word file.
 By default in SPSS a P-value is displayed as .000 if the P-value is less than .001. You can
report the P-value as <.001 or to have SPSS display more significant digits:
8
1. In a SPSS (output) Viewer window double click (with the left mouse button) on the table
containing the p-value you want to display differently A ``editing box'' should appear
around the table.
2. Click on the p-value using the right mouse button.
3. Choose Cell Properties. (If you do not get this option, you need to double click on the table
to get the ragged box.)
4. Change the number of decimals to the desired number (default is 3).
5. Choose OK or
6. Double click on the p-value with the left mouse button and SPSS will display the p-value
with more significant digits. If the p-value is very small, the p-value will be displayed in
scientific notation (e.g., 1.745E-10 = 0.0000000001745).
Saving Data as an SPSS Data (.sav) File
To save data as a new SPSS Data file onto your computer/floppy disk/flashdrive:
1. Display the Data Editor window (i.e., execute the following commands while in the Data
Editor window displaying the data you want to save.)
2. Choose File on the menu bar.
3. Choose Save As...
4. Edit the directory or disk drive to indicate where the data should be saved. SPSS will
automatically add the .sav suffix to the filename.
5. Choose Save
To save data changes in an existing SPSS Save: file.
1. Display the Data Editor window (i.e., execute the following commands while in the Data
Editor window displaying the data you want to save.)
2. Choose File box on the menu bar
3. Choose Save
Caution. The Save command saves the modified data by overwriting the previous version of the
file.
You can save your data in other formats besides an SPSS save file (e.g., as an ASCII file, Excel
file, SAS data set). To save your data with a given format you follow the same steps as saving
data in a new SPSS Save file, except that you specify the Save as Type as the desired format.
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Saving Your Output (Statistical Results and Graphs)
To save the statistical results and graphs displayed in the Viewer window as a new SPSS Output
file:
1. Display the Viewer window (i.e., execute the following commands while in the Viewer
window displaying the results you want to save.)
2. Choose File on the menu bar.
3. Choose Save As...
4. Edit the directory or disk drive to indicate where the output should be saved. SPSS will
automatically add the .spo suffix to the filename.
5. Choose Save
To save Viewer changes in an existing SPSS Output file.
1. Display the Viewer window (i.e., execute the following commands while in the Viewer
window displaying the results you want to save.)
2. Choose File on the menu bar.
3. Choose Save.
Caution. The Save command saves the modified Viewer window by overwriting the previous
version of the file.
Note that you will not be able to open SPSS output that was created with a newer version than
the version of SPSS that you are using to open the output. Hence, you may want to avoid this
problem you by exporting your output in html or MS word format. Also, charts often do not
export properly into a Html or Word file. Usually you need to export charts separately into a
window metafile file (.wmf). Sometimes the output, including charts, and be copied and pasted
directly into a Word file.
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Exporting SPSS Output
Sometimes you will want to save your SPSS output in a different file format than a SPSS output
file, because you want to avoid compatibility problems between different versions of SPSS, you
want to further edit your output in a Word document, or you want include graphs or figures in
another document file. The basic steps in exporting SPSS output to another file type are, while
in a SPSS (output) Viewer window:
1. Choose File
2. Choose Export
3. Choose what you want to export:
Output Document – exports all the output
Output Document (No Charts) – exports
only the numerical results
Charts Only – exports only charts (i.e., graphs
& figures)
Note that charts often do not export properly into
a Html or Word file. Usually you need to export
charts separately into a window metafile file
(.wmf).
4. Define further what you want to export:
All Objects – this option also exports
other extraneous information (rarely
useful)
All Visible Objects – use this option to
export all the output.
Selected Objects – this allows you to
export only the objects you have selected
in the Viewer window.
11
5. Choose the file type
HTML and Word/RTF a good file
types for numerical results (no
charts).
Windows Metafile (.WMF) is a good
file type for charts in you want to
include figures in a MS Word
document.
Note that the file type options are
dependent on what you are exporting.
6. Choose the location and file name for the
output you want to export.
7. Choose OK
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Printing Your Work in SPSS
To print statistical results and graphs in the Viewer window or data in the Data Editor window:
1. Display the output or data you want to
print (i.e., execute the following
commands while in a output or data
window)
2. Choose File on the menu bar.
3. Choose Print...
4. Choose All visible output or Selection (if
you have selected parts of the output).
When printing from a data file, the
options are All, Selection and Page # to
Page #.
5. Choose OK
Exiting SPSS
To exit SPSS:
1. Choose File on the menu bar
2. Choose Exit SPSS
If you have made changes to the data file or the output file since the last time you saved these
files, before exiting SPSS you will be asked whether you want to save the contents of the Data
Editor window and Viewer window. If you are unsure as to whether you want to save the
contents of the data or output window, choose Cancel, then display the window(s) and if you
want to save the contents of the window, follow the instructions in this handout for saving data
or output windows. SPSS will use the overwrite method when saving the contents of the
window.
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Running SPSS using Syntax (or Command Language)
This handout describes how to the run various statistical summaries and procedures using the
point-and-click menus in SPSS. However, it is possible run SPSS commands using SPSS
syntax/command language. If you are running similar analyses repeatedly, it can be more
efficient to run your analysis using SPSS syntax. How to run SPSS using the syntax/command
language is beyond the scope of this handout. Help on running SPSS using the syntax/command
language can be found in the SPSS Tutorials under Working with Syntax.
To get you started using SPSS syntax, follow the point-and-click instructions for running a
particular analysis, but select Paste instead of OK at the last step. A SPSS Syntax Editor window
will open containing the SPSS syntax for running the analysis. To run the analysis you can
choose Run on the menu bar or you can highlight the syntax you want to run, click the right
mouse button, and select Run Current. You can add more syntax to the Syntax Editor window
by using the point-and-click method, selecting Paste instead of OK at the last step. The
additional syntax will be added at the bottom of the Syntax Editor window. You can also write
syntax directly into the syntax file and/or use copy, paste and editing commands to modify the
syntax. Remember to save you syntax file before exiting SPSS. The file should end in .sps.
You can open a syntax file by selecting File on the menu bar, Open, and the Syntax…
Here’s an example of SPSS syntax.
This syntax runs a two sample test
comparing HDL cholesterol (hdl) for
subjects without and with a family
history of heart attack (fhha, coded 0
for no and 1 for yes).
This syntax creates 3 indicators
variables, neversmoke, formersmoke,
and currentsmoke for smoking status
(smoke).
Note that a period (.) is used to denote
the end of a string of syntax and
Execute. is sometimes required to run
the syntax.
14
Creating a New Variable
To create a new variable:
1. Display the Data Editor window (i.e., execute the following commands while in the Data
Editor window displaying the data file you want to use to create a new variable).
2. Choose Transform on the menu bar
3. Choose Compute...
4. Enter the new variable name in the Target Variable box.
5. Enter the definition of the new variable in the Numeric Expression box (e.g., SQRT(visan),
LN(age), or MEAN(age)) or
6. Select variable(s) and combine with desired arithmetic operations and/or functions.
7. Choose OK
After creating a new variable(s), you will probably want to save the new variable(s) by re-saving
your data using the Save command under File on the menu bar (See Saving Data as an SPSS
Save File). Further instructions on creating a new variable are given in the SPSS Help Tutorials
under Modifying Data Values.
Example: Creating a (New) Transformed Variable
You can use the SPSS commands for creating a new variable to create a transformed
variable. Suppose you have a variable indicating triglyceride level, trig, and you want to
transform this variable using the natural logarithm to make the distribution less skewed
(i.e., you want to create a new variable which is natural logarithm of triglyceride levels).
1. Display the Data Editor
window
2. Choose Transform on the
menu bar
3. Choose Compute...
4. Enter, say, lntrig, in the
Target Variable box.
5. Enter Ln(trig) in the Numeric
Expression box.
6. Choose OK
Now, a new variable, lntrig, which is the natural logarithm of trig, will be added to your
data set. Remember to save your data set before exiting SPSS (e.g., while in the SPSS
Data window, choose Save under File or click on the floppy disk icon).
15
Recoding or Combining Categories of a Variable
To recode or combine categories of a variable:
1.
Display the Data Editor window (i.e., execute the following commands while in the Data
Editor window displaying the data file you want to use to recode variables).
2. Choose Transform on the menu bar
3. Choose Recode
4. Choose Into Same Variable... or Into Different Variable...
5. Select a variable to recode from the variable list on the left and then click on the arrow
located in the middle of the window. This defines the input variable.
6. If recoding into a different variable, enter the new variable name in the box under Name:,
then choose Change. This defines the output variable.
7. Choose Old and New Values...
8. Choose Value or Range under Old Value and enter old value(s).
9. Choose New Value and enter new value, then choose Add.
10. Repeat the process until all old values have been redefined.
11. Choose Continue
12. Choose OK
After creating a new variable(s), you will probably want to save the new variable(s) by re-saving
your data using the Save command under File box on the menu bar (See Saving Data as an SPSS
Save File).
Example: Recoding a Categorical Variable
You can use the commands for recoding a variable to change the coding values of a
categorical variable. You may want to change a coding value for a particular category to
modify which category SPSS uses as the referent category in a statistical procedure. For
example, suppose you want to perform linear regression using the ANOVA (or General
Linear Model) commands, and one of your independent variables is smoking status, smoke,
that is coded 1 for never smoked, 2 for former smoker and 3 for current smoker. By
default SPSS will use current smoker as the referent category because current smoker
has the largest numerical (code) value. If you want never smoked to be the referent
category you need to recode the value for never smoked to a value larger than 3.
Although you can recode the smoking status into the same variable, it is better to recode
the variable into a new/different variable, newsmoke, so you do not lose your original data
if you make an error while recoding.
16
1. Display the Data Editor
window
2. Choose Transform
3. Choose Recode
4. Choose Into Different
Variables...
5. Select the variable smoke as
the Input variable
6. Enter newsmoke as the name
of the Output variable, and
then choose Change.
7. Choose Old and New
Values...
8. Choose Value under Old
Value. (It may already be
selected.)
9. Enter 1 (code for never
smoker)
10. Choose Value under New
Value. (It may already be
selected.)
11. Enter 4 (or any value greater
than 3)
12. Choose Add
13. Choose All Other Values
under Old Value.
14. Choose Copy Old Value(s)
under New Value.
15. Choose Add
16. Choose Continue
17. Choose OK
Remember to save your data set before exiting SPSS.
17
Example: Creating Indicator or Dummy Variables
You can use the commands for recoding a variable to create indicator or dummy variables
in SPSS. Suppose you have a variable indicating smoking status, smoke, that is coded 1 for
never smoked, 2 for former smoker and 3 for current smoker. To create three new
indicator or dummy variables for never, former and current smoking:
1. Display the Data Editor
window
2. Choose Transform
3. Choose Recode
4. Choose Into Different
Variables...
5. Select the variable smoke
as the Input variable
6. Enter neversmoke as the
name of the Output
variable, and then choose
Change.
7. Choose Old and New
Values...
8. Choose Value under Old
Value. (It may already be
selected.)
9. Enter 1 (code value for
never smoker)
10. Choose Value under New
Value. (It may already be
selected.)
11. Enter 1 (to indicate never
smoker)
12. Choose Add
13. Choose All Other Values
under Old Value.
14. Choose Value under New
Value.
15. Enter 0
16. Choose Add
17. Choose Continue
18. Choose OK
Now, you have created a binary indicator variable for never smoker (coded 1 if never
smoker, 0 if former or current smoker). Next, create a binary indicator variable for
former smoker.
18
1. Display the Data Editor
window
2. Choose Transform
3. Choose Recode
4. Choose Into Different
Variables...
5. Select the variable smoke
as the Input variable
6. Enter formersmoke as the
name of the Output
variable, and then choose
Change. (Or change (edit)
never to former, and then
choose Change).
7. Choose Old and New
Values...
8. Choose 1→1 under
Old→New and then
choose Remove.
9. Choose Value under Old
Value.
10. Enter 2 (code value for
former smoker)
11. Choose Value under New
Value.
12. Enter 1 (to indicate former
smoker)
13. Choose Add
14. Choose Continue
15. Choose OK
Now, you have a created a binary indicator variable for former smoker (coded 1 if former
smoker, 0 if never or current smoker). To create a binary indicator variable for current
smoker you would use similar commands to those for creating the indicator variable for
former smoke, except that now the value of 3 for smoke is coded as 1 and all other values
are coded as 0.
19
Example: Creating a Categorical Variable From a Numerical Variable
You can use the commands for recoding a variable to create a categorical variable from a numerical
variable (i.e., group values of the numerical variable into categories). For example, suppose you have
a variable that is the number of pack years smoked, packyrs, and you want to create a categorical
variable with the four categories, 0, >0 to 10, >10 to 30, and >30 pack years smoked .
1.
2.
3.
4.
5.
Display the Data Editor window
Choose Transform
Choose Recode
Choose Into Different Variables...
Select the variable packyrs as the
Input variable
6. Enter a name for the new variable,
packcat, for the Output variable, and
then choose Change.
7. Choose Old and New Values...
8. Choose Value under Old Value. (It
may already be selected.)
9. Enter 0
10. Choose Value under New Value.
11. Enter 0 (to indicate 0 pack years)
12. Choose Add
13. Choose Range under Old Value.
14. Enter 0.01 and 10 in the two blank
boxes.
15. Choose Value under New Value
16. Enter 1 (to indicate >0 to 10 pack
years)
17. Choose Add
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
Choose Range under Old Value.
Enter 10.01 and 30 in the two blank boxes.
Choose Value under New Value
Enter 2 (to indicate >10 to 30 pack years)
Choose Add
Choose Range, value through HIGHEST under Old Value.
Enter 30.01 in the blank box.
Choose Value under New Value
Enter 3 (to indicate >30 pack years)
Choose Add
Choose Continue
Choose OK
Note that if you may want to use different coding values depending on which category you want to
be used as the referent category in certain statistical procedures. Remember to save your data set
before exiting SPSS.
20
Summarizing Your Data
Frequency Tables (& Bar Charts) for Categorical Variables. To produce frequency tables
and bar charts for categorical variables:
1.
2.
3.
4.
5.
6.
7.
8.
Choose Analyze from the menu bar
Choose Descriptive Statistics
Choose Frequencies…
Variable(s): To select the variables you want from the source list on the left, highlight a
variable by pointing and clicking the mouse and then click on the arrow located in the middle
of the window. Repeat the process until you have selected all the variables you want.
Choose Charts (Skip to step 7 if you do not want bar charts.)
Choose Bar Chart(s)
Choose Continue
Choose OK
Example: Frequency table and bar chart for the categorical variable, smoking status.
Smoking
status is the
selected
variable(s) and
Bar charts
under Charts…
has been
selected.
Frequency table and bar chart of smoking status
Smoking status
Smoking status
Percent
Valid
Percent
never
590
59.0
59.0
59.0
former
293
29.3
29.3
88.3
current
117
11.7
11.7
100.0
1000
100.0
100.0
Total
50
40
Percent
Frequency
60
Cumulative
Percent
30
20
10
0
never
former
Smoking status
current
21
Contingency Tables for Categorical Variables. To produce contingency tables for categorical
variables:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Choose Analyze from the menu bar.
Choose Descriptive Statistics
Choose Crosstabs...
Row(s): Select the row variable you want from the source list on the left and then click on the
arrow located next to the Row(s) box. Repeat the process until you have selected all the row
variables you want.
Column(s): Select the column variable you want from the source list on the left and then
click on the arrow located next to the Column(s) box. Repeat the process until you have
selected all the column variables you want.
Choose Cells...
Choose the cell values (e.g., observed counts; row, column, and margin (total) percentages).
Note the option is selected when the little box is not empty.
Choose Continue
Choose OK
Example: Contingency table of smoking status by coronary heart disease (CHD).
Smoking
status is the
row variable
and CHD is
the column
variable.
Observed
counts and
row
percentages
will be
displayed.
Smoking status * Incident CHD Crosstabulation
Incident CHD
Smoking
status
never
former
current
Total
Count
no
537
yes
53
Total
590
% within Smoking status
91.0%
9.0%
100.0%
Count
257
36
293
% within Smoking status
87.7%
12.3%
100.0%
Count
106
11
117
% within Smoking status
90.6%
9.4%
100.0%
Count
900
100
1000
% within Smoking status
90.0%
10.0%
100.0%
22
Descriptive Statistics (& Histograms) for Numerical Variables. To produce descriptive
statistics and histograms for numerical variables:
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Descriptive Statistics
Choose Frequencies...
Variable(s): To select the variables you want from the source list on the left, highlight a
variable by pointing and clicking the mouse and then click on the arrow located in the middle
of the window. Repeat the process until you have selected all the variables you want.
5. Choose Display frequency tables to turn off the option. Note that the option is turned off
when the little box is empty.
6. Choose Statistics
7. Choose summary measures (e.g., mean, median, standard deviation, minimum, maximum,
skewness or kurtosis).
8. Choose Continue
9. Choose Charts (Skip to step 11 if you do not want histograms.)
10. Choose Histograms(s)
11. Choose Continue
12. Choose OK
An alternate way to produce only the descriptive statistics is at step 3 to choose Descriptives...
instead of Frequencies..., then, select the variables you want. By default SPSS computes the
mean, standard deviation, minimum and maximum. Choose Options... to select other summary
measures.
Example: Descriptive summaries and histogram for the numerical variable age.
Age is the variable to summarize. You can
select more than one variable to analyze.
Remember to turn off the Display
frequency tables option.
23
Mean, standard
deviation,
minimum and
maximum were
selected under
Statistics…, and
histogram was
selected under
Charts…
Summaries for Age
Statistics
Age
Valid
N
1000
Missing
0
Mean
72.14
Std. Deviation
5.275
Minimum
65
Maximum
90
Histogram of Age
Histogram
120
Frequency
100
80
60
40
20
Mean =72.14
Std. Dev. =5.275
N =1,000
0
60
65
70
75
80
Age
85
90
95
24
Descriptive Statistics (& Boxplots) by Groups for Numerical Variables. To produce
descriptive statistics and boxplots by groups for numerical variables:
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Descriptive Statistics
Choose Explore...
Dependent List: To select the variables you want to summarize from the source list on the
left, highlight a variable by pointing and clicking the mouse and then click on the arrow
located next to the dependent list box. Repeat the process until you have selected all the
variables you want.
5. Factor List: To select the variables you want to use to define the groups from the source list
on the left, highlight a variable by pointing and clicking the mouse and then click on the
arrow located next to the factor list box.
6. Choose Plots... (If you do not want boxplots, choose Statistics for the Display option and
skip to Step 11.)
7. Choose Factor levels together from the Boxplot box.
8. Select Stem-and-leaf option from the Descriptive box to turn off the option.
9. Choose Continue
10. Choose Both for the Display option
11. Choose OK
Example: Total cholesterol by family history of heart attack (yes or no).
In this example total cholesterol is
the dependent variable. You can
select more than one variable.
Summaries will computed for each
group defined by family history of
heart attack.
Both numerical summaries
(statistics) and plots are selected.
Under Statistics…
Descriptives is usually
selected by default.
Under Plots select
Boxplot option and
unselect stem-andleaf.
25
Descriptives
Statistic
Mean
95% Confidence
Interval for Mean
221.93
Lower Bound
219.15
Upper Bound
224.72
5% Trimmed Mean
221.63
Median
219.76
Variance
Std. Deviation
1.417
36.751
111
Maximum
363
Range
252
49
Skewness
.184
.094
Kurtosis
.363
.188
2.150
Lower Bound
220.53
216.30
Upper Bound
224.76
yes
Mean
95% Confidence
Interval for Mean
Std.
Error
1350.641
Minimum
Interquartile Range
The explore
command by
default
produces a lot
of different
summaries, so
you need to
select what to
report.
All summaries
are shown for
all groups –
the table has
been cropped
in this
example.
Boxplot of Total Cholesterol by Family History of Heart Attack
400
95
812
350
Total cholesterol
Total
cholesterol
Family
history of
heart
attack
no
172
438
875
729
659
300
250
200
150
100
no
yes
Family history of heart attack
26
Using the Split File Option for Summaries by Groups for Categorical and Numerical
Variables. The Split File option in SPSS is a convenient way to produce summaries, graphs, and
run statistical procedures by groups. To activate the option:
1. Choose Data on the menu bar of the Data Editor window
2. Choose Split File
3. Choose Compare groups or Organize output by groups. The two options display the output
differently. Try each option to see which works best for your needs.
4. Choose the variable that defines the groups.
5. Choose OK
Now, all the summaries, graphs, and statistical procedures you request will be done
(automatically) for each group. To turn off this option:
1.
2.
3.
4.
Choose Data on the menu bar of the Data Editor window
Choose Split File
Choose Analyze all cases, do no create groups
Choose OK
Example. Use the Split File option to run summaries by family history of heart attack (yes
or no).
Compare groups option will try to
display the results for each group
side by side when feasible.
Organize output by groups option
will display the results separately
for each group starting with the
group with the lowest numerical
code value.
27
Using the Select Cases Option for Summaries for a subgroup of subjects/observations.
The Select Cases option in SPSS is a convenient way to produced summaries and run statistical
procedures for a subgroup of subjects or to temporary exclude subjects from the analysis. To
activate this option:
1.
2.
3.
4.
5.
6.
7.
Choose Data on the menu bar of the Data Editor window
Choose Select Cases…
Choose If condition is satisfied
Choose If…
Enter the expression that indicates the subjects/observation you want to select.
Choose Continue
Choose OK
Now, all the summaries, graphs, and statistical procedures you request will be done using only
the selected subjects/observations. To turn off this option:
1.
2.
3.
4.
Choose Data on the menu bar of the Data Editor window
Choose Select Cases…
Choose All cases
Choose OK
Example: Select subjects not lipid lowering medications (i.e., subjects with lipid = 0
indicating no medications).
Select the If condition is satisfied and then If…
Caution! Usually you do not want to delete
observations from your dataset, so do not select
this option.
Typical expressions will involve
combinations of the following symbols:
Symbol
=
~=
>=
<=
>
<
&
|
Definition
equal
not equal
greater than or equal
less than or equal
greater than
less than
and
or
28
Graphing Your Data
You can produce very fancy figures and graphs in SPSS. Producing fancy figures and graphs is
beyond the scope of this handout. Instructions on producing figures and graphs can be found in
SPSS Help under Topics → Contents → Chart Galleries, Standard Charts, and Chart Editor, as
well as in the SPSS Tutorials under Creating and Editing Charts. The commands for making
charts are located under Graphs (and then Legacy Dialogs, if using Version 15) on the menu bar,
and the commands for making simple figures and graphs are relatively easy to use and some
instruction is given below. The Interactive option under Graphs is another way to produce charts
in SPSS interactively, as well as fancier versions of the basic charts (e.g., 3-dimensional bar
charts).
Bar Charts
The easiest way to produce simple bar charts is to use the Bar Chart option with the
Frequencies... command. See Frequency Tables (& Bar Charts) for Categorical Variables. You
can only produce only one bar chart at a time using the Bar command.
1.
2.
3.
4.
5.
6.
Choose Graphs (& then Legacy Dialogs, if Version 15) from the menu bar.
Choose Bar...
Choose Simple, Clustered, or Stacked
Choose what the data in the bar chart represent (e.g., summaries for groups of cases).
Choose Define
Select a variable from the variable list on the left and the click on the arrow next to the
Category axis.
7. Choose what the bars represent (e.g., number of cases or percentage of cases)
8. Choose OK
60.0%
Family history of
heart attack
60.0%
50.0%
50.0%
40.0%
40.0%
Percent
Percent
no
yes
30.0%
30.0%
20.0%
20.0%
10.0%
10.0%
0.0%
0.0%
never
former
Smoking status
current
never
former
Smoking status
current
29
Histograms
The easiest way to produce simple histograms is to use the Histogram option with the
Frequencies... command. See Descriptive Statistics (& Histograms) for Numerical Variables.
You can produce only one histogram at a time using the Histogram command.
120
100
80
Frequency
1. Choose Graphs (& then Legacy
Dialogs, if Version 15) from the
menu bar
2. Choose Histogram...
3. Select a variable from the
variable list on the left and then
click on the arrow in the middle of
the window.
4. Choose Display normal Curve if
you want a normal curve
superimposed on the histogram.
5. Choose OK
60
40
20
Mean =26.2366
Std. Dev. =4.8667
N =1,000
0
10
20
30
40
50
Body mass index
Boxplots
The easiest way to produce simple boxplots is to use the Boxplot option with the Explore...
command. See Descriptive Statistics (& Boxplots) By Groups for Numerical Variables.
You can produce only one boxplot at a time using the Boxplot command.
880
684
400
Serum fasting glucose
1. Choose Graphs (& then Legacy
Dialogs, if Version 15) from the
menu bar.
2. Choose Boxplot...
3. Choose Simple or Clustered
4. Choose what the data in the
boxplots represent (e.g.,
summaries for groups of cases).
5. Choose Define
6. Select a variable from the
variable list on the left and then
click on the arrow next to the
Variable box.
7. Select the variable from the
variable list that defines the
groups and then click on the
arrow next to Category Axis.
8. Choose OK
77
673
200
785
0
normal
impaired fasting
glucose
ADA diabetes status
diabetic
30
Normal Probability Plots. To produce Normal probability plots:
1. Choose Graphs (& then Legacy Dialogs, if Version 15) from the menu bar.
2. Choose Q-Q... to get a plot of the quantiles (Q-Q plot) or choose P-P... to get a plot of the
cumulative proportions (P-P plot)
3. Select the variables from the source list on the left and then click on the arrow located in the
middle of the window.
4. Choose Normal as the Test Distribution. The Normal distribution is the default Test
Distribution. Other Test Distributions can be selected by clicking on the down arrow and
clicking on the desired Test distribution.
5. Choose OK
SPSS will produce both a Normal probability plot and a detrended Normal probability plot for
each selected variable. Usually the Q-Q plot is the most useful for assessing if the distribution of
the variable is approximately Normal.
Normal Q-Q Plot of Serum fasting glucose
Normal Q-Q Plot of Body mass index
250
40
Expected Normal Value
Expected Normal Value
200
150
100
50
30
20
0
-50
-200
10
0
200
Observed Value
400
600
10
20
30
Observed Value
40
50
31
Error Bar Plot. To produce an error bar plot of the mean of a numerical variable (or the means
for different groups of subjects):
1.
2.
3.
4.
5.
6.
Choose Graphs (& then Legacy Dialogs, if Version 15) from the menu bar.
Choose Error Bar...
Choose Simple or Clustered
Choose what the data in the error bars represent (e.g., summaries for groups of cases).
Choose Define
Select a variable from the variable list on the left and then click on the arrow next to the
Variable box.
7. Select the variable from the variable list that defines the groups and then click on the arrow
next to Category Axis.
8. Select what the bars represent (e.g., confidence interval, ±standard deviation, ±standard error
of the mean)
9. Choose OK
Error Bar Plot
Mean +- 2 SD Serum fasting glucose
300
250
200
150
100
50
normal
impaired fasting
glucose
diabetic
ADA diabetes status
A bar chart of the mean with error bars can be made
using the commands for making a bar chart
Mean Serum fasting glucose
300
200
100
0
normal
impaired fasting
glucose
ADA diabetes status
Error bars: +/- 2 SD
diabetic
32
Scatter Plot. To produce a scatter plot between two numerical variables:
HDL cholesterol
1. Choose Graphs (& then Legacy
HLD cholesterol vs BMI
Dialogs, if Version 15) on the menu
bar.
140
2. Choose Scatter/Dot...
3. Choose Simple
120
4. Choose Define
100
5. Y Axis: Select the y variable you
80
want from the source list on the left
and then click on the arrow next to
60
the y axis box.
40
6. X Axis: Select the x variable you
20
want from the source list on the left
and then click on the arrow next to
0
the x axis box.
10
20
30
40
50
7. Choose Titles...
Body mass index
8. Enter a title for the plot (e.g., y vs.
x).
9. Choose Continue
10. Choose OK
Adding a linear regression line to a scatter plot. To add a linear regression (least-squares) line
to a scatter plot of two numerical variables:
HLD cholesterol vs BMI
HDL cholesterol
1. While in the Viewer window
double click on the scatter plot. The
scatter plot should now be
140
displayed in a window titled Chart
120
Editor.
100
2. Choose Elements.
3. Choose Fit Line at Total. (A line
80
should be added to the plot, because
60
the next 2 steps are the default
40
options.
R Sq Linear = 0.121
20
4. Choose Linear (in the Properties
window)
0
5. Choose Apply (in the Properties
10
20
30
40
50
window).
Body mass index
Additional options:
o Choose Mean under Confidence Intervals (in the Properties window) to add a prediction
interval for the linear regression line to the scatter plot or
o Choose Individual under Confidence Intervals to add a prediction interval for individual
observations to the scatter plot.
6.
Click on the ``X'' in the upper right hand corner of the Chart Editor window or choose File,
and then Close to return to the Viewer window.
33
Adding a Loess (scatter plot) smooth to a scatter plot. To add a Loess smooth to a scatter plot
of two numerical variables:
HLD cholesterol vs BMI
HDL cholesterol
1. While in the Viewer window
double click on the scatter plot. The
scatter plot should now be
displayed in a window titled Chart
Editor.
140
2. Choose Elements.
120
3. Choose Fit Line at Total.
100
4. Choose Loess (in the Properties
window). Default options for % of
80
points to fit (50%) and kernel
60
(Epanechnikov) are usually the
40
most appropriate options.
5. Choose Apply (in the Properties
20
window). If a line was added to the
0
plot in Step 3, it will be replaced by
10
the loess smooth.
6. Click on the ``X'' in the upper right
hand corner of the Chart Editor
window or choose File, and then
Close to return to the Viewer
window.
Stem-and-leaf Plot. To produce stem-and-leaf plot:
0.
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Descriptive Statistics
Choose Explore...
Dependent List: To select the variables
you want from the source list on the left,
highlight a variable by pointing and
clicking the mouse and then click on the
arrow located next to the dependent list
box. Repeat the process until you have
selected all the variables you want.
5. Choose Plots...
6. Choose Stem-and-leaf from the
Descriptive box. Note the option may
already be selected if the little box is not
empty.
7. Choose None from the Boxplot box
8. Choose Continue
9. Choose Plots for the Display option
10. Choose OK
20
30
40
Body mass index
Severity of Illness Index Stem-andLeaf Plot
Frequency
Stem &
2.00
4
7.00
4
10.00
5
3.00
5
1.00 Extremes
Stem width:
Each leaf:
.
.
.
.
Leaf
34
6688899
0001112344
568
(>=62)
10.00
1 case(s)
50
34
Hypothesis Tests & Confidence Intervals
One-Sample t Test
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Compare Means
Choose One-Sample T Test...
Test Variable(s): Select the variable you want from the source list on the left, highlight
variables by pointing and clicking the mouse and then click on the arrow located in the
middle of the window.
5. Edit the Test Value. The Test Value is the value of the mean under the null hypothesis. The
default value is zero.
6. Choose OK
Confidence Interval for a Mean (from one sample of data)
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Compare Means
Choose One-Sample T Test...
Test Variable(s): Select the variable you want from the source list on the left, highlight
variables by pointing and clicking the mouse and then click on the arrow located in the
middle of the window.
5. The Test Value should be 0, which is the default value.
6. By default a 95% confidence interval will be computed. Choose Options… to change the
confidence level.
7. Choose OK
SIDS Example. There were 48 SIDS cases in King County, Washington, during the years
1974 and 1975. The birth weights (in grams) of these 48 cases were:
2466
3317
2013
2750
2722
3005
2013
2722
3941
3742
3515
2807
2495
2608
2551
2863
2807
3062
3260
2807
3459
2353
2977
2013
3118
3033
2892
3005
3374
4394
3118
3232
2098
2353
1616
3374
1984
3232
2637
2863
3175
3515
4423
3572
2495
3062
1503
2438
The mean (and standard
deviation) of these
measurements is 2891 (623)
grams.
We want to know if the mean birth weight in the population of SIDS infant is different
from that of normal children, 3300 grams. We could construct a 95% confidence interval,
to see if the interval contains the value of 3300 grams or we could perform a one sample t
test to test if the mean in the SIDs population is equal to 3300 (versus not equal to 3300).
35
To construct a 95% confidence interval
When computing the
interval for a mean make
sure the Test Value is 0.
One-Sample Statistics
N
birth weight
48
Mean
2891.1250
Std. Error
Mean
89.97885
Std. Deviation
623.39177
Number of subjects, mean,
standard deviation, and standard
error of the mean.
One-Sample Test
Test Value = 0
95% Confidence Interval
of the Difference
birth weight
t
32.131
df
47
Ignore the t test results
(t, df, sig.) because these
results are for testing if
the mean birth weight is
equal to 0 (versus not
equal to zero).
Sig. (2-tailed)
.000
Mean
Difference
2891.12500
Lower
2710.1109
Upper
3072.1391
95% confidence interval for the
mean birth weight is 2710 to
3072 grams
36
To perform a one sample t test to test if the mean in the SIDs population is equal
to 3300 versus not equal to 3300.
To run the one-sample t
test to test if the mean
birth weight is equal to
3300 you need to change
the Test Value from the
default value of 0 to 3300.
One-Sample Statistics
N
birth weight
Mean
48
Std. Error
Mean
Std. Deviation
2891.1250
623.39177
89.97885
One-Sample Test
Test Value = 3300
95% Confidence
Interval of the
Difference
birth weight
t
-4.544
df
47
Sig. (2-tailed)
.000
Mean
Difference
-408.87500
Sig. (2-tailed) = two tailed p-value = <.001
t = test statistic value = -4.544
df = degrees of freedom = 47
Lower
-589.8891
Upper
-227.8609
Ignore the results for 95%
confidence interval of the
difference, because it is the
confidence interval for the
mean minus 3300.
37
Paired t Test
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Compare Means
Choose Paired-Samples T Test...
Paired Variable(s): Select two paired variables you want from the source list on the left,
highlight both variables by pointing and clicking the mouse and then click on the arrow
located in the middle of the window. Repeat the process until you have selected all the
paired variables you want to test.
5. Choose OK
Confidence Interval for the Difference Between Means from Paired Sample
By default a 95% confidence interval for the difference means of the paired samples will be
computed when performing a paired t test. Choose Options… to change the confidence level.
Prozac Example. To compare the effect of Prozac on anxiety 10 subjects are given one
week of treatment with Prozac and one week of treatment with a placebo. The order of
the treatments was randomized for each subject. An anxiety questionnaire was used to
measure a subject's anxiety on a scale of 0 to 30. Higher scores indicate more anxiety.
Subject
Placebo
Prozac
Difference
1
2
3
4
5
6
7
22
18
17
19
22
12
14
19
11
14
17
23
11
15
3
7
3
2
-1
1
-1
8
9
10
11
19
7
19
11
8
-8
8
-1
Mean difference, d  1.3
Standard deviation, sd  4.5
38
Paired t test and confidence interval for the difference between paired means.
The order of the variables in
calculating the difference is
determined by the order of
the variables in the data set
(and not the order in which
you select the variables).
Paired Samples Statistics
Mean
Pair 1
N
Summaries for each
sample of data (or
variable).
Std. Error
Mean
Std. Deviation
placebo
16.1000
10
4.95424
1.56667
prozac
14.8000
10
4.68568
1.48174
Paired Samples Correlations
N
Pair 1
placebo & prozac
10
Correlation
.556
Sig.
.095
Correlation between the paired
values - usually not useful.
Paired Samples Test
Mean
Std.
Deviation
Paired Differences
Std. Error
95% Confidence Interval of
Mean
the Difference
Lower
Pair 1
placebo
- prozac
1.30000
4.54728
difference = placebo - prozac
1.43798
-1.95293
t
Sig. (2tailed)
df
Upper
4.55293
.904
9
.390
95% confidence interval for the
mean difference is -1.9 to 4.6
mean difference = 1.3
standard deviation of the
differences = 4.5
standard error of the
differences = 1.4
Paired t test
Sig. (2 tailed) = two-sided p-value = 0.39
t = test statistic value = .904
df = degrees of freedom
39
Two-Sample t Test
1.
2.
3.
4.
Choose Analyze on the menu bar.
Choose Compare Means
Choose Independent-Samples T Test...
Test Variable(s): Select the test variable you want from the source list on the left and then
click on the arrow located next to the test variable box. Repeat the process until you have
selected all the variables you want.
5. Grouping Variable: Select the variable which defines the groups and then click on the
arrow located next to the grouping variable box.
6. Choose Define Groups...
7. Click on blank box next to Group 1, then enter the code value (numeric or
character/string) for group 1.
8. Click on blank box next to Group 2, then enter the code value (numeric or
character/string) for group 2.
9. Choose Continue
10. Choose OK
Confidence Interval for the Difference Between Means from Independent
Samples
By default a 95% confidence interval for the difference means from two independent samples
will be computed when performing a two sample t test. Choose Options… to change the
confidence level.
Model Cities Example. Two groups of people were studied - those who had been randomly
allocated to a Fee-For-Service medical insurance group and those who had been randomly
allocated to a Prepaid insurance group.
We would like to compare the two groups on the quality of health care they received in
each group, but first we would like to know how comparable the groups are on other
characteristics that might affect medical outcome. For example, we would like to know if
the mean age in the two groups is similar. Hopefully, the process of random allocation
minimizes this possibility, but there is always a chance that it didn't.
Group
n
Mean
Standard
deviation
Prepaid (GHC)
1167
24.0
15.3
Fee-for-service (KCM)
3207
26.4
17.1
We could compare the average age between the two groups using a two sample t test or a
confidence interval for the difference between the average ages of the two groups.
40
Two sample t test and 95% confidence interval for the difference between means
(from independent samples).
After you select the Grouping Variable,
SPSS will put in question marks to
prompt you to define the code values for
the two groups. Select Define Groups…
to enter the code values.
In this example the group codes
are numeric, 0 (for GHC) and 1 (for
KCM)
T-Test
Group Statistics
age
prov
GHC
KCM
N
Mean
Std. Deviation
Std. Error
Mean
1167
23.9846
15.30787
.44810
3207
26.3676
17.10260
.30200
Summaries for each
sample/group.
Independent Samples Test
Levene's Test for
Equality of Variances
F
age
Equal variances
assumed
Equal variances
not assumed
47.068
Sig.
.000
SPSS by default tests if the
variances are equal using Levene’s
test. A small p-value (sig.)
indicates the variances may be
different.
sig. = p-value = <.001
F = test statistic value = 47.0
41
Independent Samples Test
t-test for Equality of Means
t
age
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
Equal variances
assumed
-4.188
4372
.000
-2.38306
.56896
Equal variances
not assumed
-4.410
2293.698
.000
-2.38306
.54037
Two Sample t test. SPSS by default always performs both versions of the two
sample t test assuming equal variance and unequal variances
Sig. (2 – tailed) = two sided p-value = <.001 (equal var.), <.001 (unequal var.)
t = test statistic value = -4.2 (equal var.), -4.4 (unequal var.)
df = degrees of freedom = 4372 (equal var.), 2294 (unequal var.)
mean difference = difference between means = -2.4 (equal and unequal var.)
std. error difference = standard error of the difference between means = .6 (equal
var.), .5 (unequal var.)
Independent Samples Test
95% Confidence
Interval of the
Difference
age
Lower
Upper
Equal variances
assumed
-3.49851
-1.26760
Equal variances
not assumed
-3.44273
-1.32338
95% confidence interval for
the difference between means
is
-3.4 to -1.3 (assuming equal
variances)
-3.4 to -1.3 (assuming unequal
variances)
42
Sign Test and Wilcoxon Signed-Rank Test
1.
2.
3.
4.
5.
6.
7.
8.
Choose Analyze from the menu bar.
Choose Nonparametric Tests
Choose 2 Related Samples...
Test Pair(s) List: Select two paired variables you want from the source list on the left hand
side, highlight both variables by pointing and clicking the mouse and then click on the arrow
located in the middle of the window. Repeat the process until you have selected all the
paired variables you want to test.
Choose Sign as the Test Type.
or
Choose Wilcoxon as the Test Type.
Choose OK
Aspirin Example. To compare 2 types of Aspirin, A and B, 1 hour urine samples were
collected from 10 people after each had taken either A or B. A week later the same
routine was followed after giving the “other” type to the same 10 people.
Person
1
2
3
4
5
6
7
8
9
10
Type A
15
26
13
28
17
20
7
36
12
18
Mean = 19.2
Standard deviation =
8.63
Type B
13
20
10
21
17
22
5
30
7
11
Difference
2
6
3
7
0
-2
2
6
5
7
15.6
3.6 = d
3.098 = sd
7.78
A Sign test or Wilcoxon Signed Rank test could be used to compare the two types of
Aspirin.
43
The order of the variables in
calculating the difference is
determined by the order of the
variables in the data set (and
not the order in which you
select the variables).
Select Wilcoxon or Sign (or
both)
Under Options you can select summaries
Descriptive (n, mean, etc.) and Quartiles
(median, 25th and 75th percentile)
Descriptive Statistics
Percentiles
N
Mean
Std. Deviation
Minimum
Maximum
25th
50th (Median)
75th
aspirina
10
19.2000
8.62554
7.00
36.00
12.7500
17.5000
26.5000
aspirinb
10
15.6000
7.77746
5.00
30.00
9.2500
15.0000
21.2500
Sign Test
Frequencies
N
aspirinb - aspirina
Negative
Differences(a)
Positive
Differences(b)
Ties(c)
Total
a aspirinb < aspirina
b aspirinb > aspirina
c aspirinb = aspirina
1
1
10
Sign Test
Test Statistics(b)
aspirinb aspirina
Exact Sig. (2-tailed)
8
.039(a)
a Binomial distribution used.
b Sign Test
Exact sig. (2-tailed) = exact, two-sided
p-value = 0.039
The p-value is exact because it is
computed using the Binomial
distribution instead of using an
approximation to the Normal
distribution.
44
Wilcoxon Signed Ranks Test
Ranks
N
aspirinb - aspirina
Negative Ranks
8(a)
Mean Rank
5.38
Sum of Ranks
43.00
Positive Ranks
1(b)
2.00
2.00
Ties
1(c)
Total
10
Information
used in the
test statistic
– not usually
reported; use
the previous
descriptives.
a aspirinb < aspirina
b aspirinb > aspirina
c aspirinb = aspirina
Wilcoxon Signed Rank Test
Test Statistics(b)
Z
aspirinb aspirina
-2.442(a)
Asymp. Sig. (2-tailed)
a Based on positive ranks.
b Wilcoxon Signed Ranks Test
.015
Asymp. Sig. (2-tailed) = two sided p-value = 0.015
Asymp. is an abbreviation for asymptotic, which
means the p-value is computed using a large sample
approximation based on the Normal distribution.
45
Mann-Whitney U Test (or Wilcoxon Rank Sum Test)
1.
2.
3.
4.
Choose Analyze on the menu bar.
Choose Nonparametric Tests
Choose 2 Independent Samples...
Test Variable(s): Select the test variable you want from the source list on the left and then
click on the arrow located next to the test variable box. Repeat the process until you have
selected all the variables you want.
5. Grouping Variable: Select the variable which defines the grouping and then click on the
arrow located next to the grouping variable box. The grouping variable must be numeric for
the variable to appear on the left hand side.
6. Choose Define Groups...
7. Click on the blank box next to group 1, then enter the code value (it must be numeric) for
group 1.
8. Click on the blank box next to group 2, then enter the code value (it must be numeric) for
group 2.
9. Choose Continue to return to Two Independent Samples dialog box.
10. Choose Mann-Whitney U as the Test Type. Note that the option may already be selected if
the little box is not empty.
11. Choose OK
Legionnaires Example. During July and August, 1976, a large number of Legionnaires
attending a convention died of mysterious and unknown cause. Chen et al. (1977) examined
the hypothesis of nickel contamination as a toxin. They examined the nickel levels in the
lungs of nine cases and nine controls. There was no attempt to match cases and controls.
The data are as follows (μg/100g dry weight):
Legionnaire cases 65 24 52 86 120 82 399 87 139
Controls
12 10 31 6 5 5 29 9 12
The Mann Whitney U test could be used to compare the two groups.
After you select the Grouping
Variable, SPSS will put in question
marks to prompt you to define the
code values for the two groups.
Select Define Groups… to enter the
code values.
Note: The codes must be numeric,
otherwise the grouping variable will
not appear on the left hand side.
46
In this example the group codes are
1 for legionnaires and 2 for controls.
Mann-Whitney Test
Ranks
nickel
group
1
N
2
Total
Mean Rank
13.78
124.00
9
5.22
47.00
18
Test Statistics(b)
Mann-Whitney U
nickel
2.000
Wilcoxon W
47.000
Z
Asymp. Sig. (2-tailed)
-3.403
.001
Exact Sig. [2*(1-tailed
Sig.)]
.000(a)
a Not corrected for ties.
b Grouping Variable: group
Sum of Ranks
9
Information used in the test
statistic – not usually reported.
The descriptives under Options
are not useful; you can produce
relevant descriptives (e.g.
median and interquartile range
for each group) using the
Explore command.
Mann Whitney test
Asymp. Sig. (2-tailed) = two-sided p-value =
0.001
This p-value is computed based a large
sample approximation to the Normal
distribution and it corrects for ties in the
data, if present.
Exact Sig. [2*(1-tailed Sig.)] = two-sided pvalue = <.001
This p-value is an exact p-value, but it does
not correct for ties in the data, if present.
In this example, given the small sample sizes
and few ties in the data, the exact p-value
would be appropriate to report.
47
One-way ANOVA (Analysis of Variance) (E.g., to compare two or more means
from two or more independent samples)
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Compare Means
Choose One-Way ANOVA...
Dependent: Select the variable from the source list on the left for which you want to use to
compare the groups and then click on the arrow next to the dependent variable box. You run
multiple one-way ANOVAs by selecting more than one dependent variable.
5. Factor: Select the variable from the source list on the left which defines the groups.
6. Choose OK
To perform pairwise comparisons to determine which groups are different while controlling for
multiple testing use the Post Hoc... option. There are many methods to choose from (e.g.,
Bonferroni and R-E-G-W-Q).
Other useful options can be found under Options... For example, choose Descriptive to get
descriptive statistics for each group (e.g., mean, standard deviation, minimum value, and
maximum value). Choose Homogeneity-of-variance to perform the Levene Test to test if the
group variances are all equal versus not all equal. A small p-value for the Levene's Test may
indicate that the variances are not all equal.
CHD Example. We can use one-way ANOVA to compare HDL levels between subjects with
different hypertensive status (0=normotensive, 1=borderline, 2=definite)
Hypertensive
Group
Normotensive
Borderline
Definite
n
1568
547
1310
Mean
55.8
55.7
53.5
Standard
Deviation
15.5
16.2
15.2
You can select 1 or more variables to
compare between groups.
The variable selected as the Factor
defines the groups. The variable can
be numeric or character/string.
48
Oneway
ANOVA
HDL cholesterol
Sum of
Squares
Between Groups
df
Mean Square
4344.834
2
2172.417
Within Groups
821904.577
3422
240.183
Total
826249.411
3424
F
Sig.
9.045
.000
One-way analysis of variance
Sig. = p-value = <.001
F = test statistic = 9.0; df = degrees of freedom
Sometimes the test statistic and degrees of freedom of the test statistics are
reported along with the p-value; in this example, F=9.0 with degrees of freedom 2
and 3422. Sum of squares and mean square are used to compute the test statistic;
they are usually not reported.
Descriptives
Under Options you can request Descriptives for each group to be
computed. This information can be used to describe the differences
between the groups.
HDL cholesterol
Std.
Deviation
Std.
Error
95% Confidence Interval for
Mean
N
Mean
1568
55.82
15.500
.391
Lower Bound
55.05
Upper Bound
56.59
21
138
547
55.67
16.202
.693
54.30
57.03
24
149
definite
1310
53.47
15.192
.420
52.64
54.29
15
129
Total
3425
54.90
15.534
.265
54.38
55.42
15
149
normotensive
borderline
Minimum
Maximum
49
Post Hoc Tests
Under Post Hoc… you can request further comparisons be done between each of the
possible pair of groups to determine which groups are different from each other. These
are multiple comparison procedures, which control for the number of tests/comparison
being performed. There are many methods to choose from; below is an example of the
Bonferroni method and Ryan-Einot-Gabriel-Welsch method.
Multiple Comparisons
Dependent Variable: HDL cholesterol
(I)
(J)
Hypertension
Hypertension
status
status
Bonferroni
normotensive
borderline
definite
borderline
normotensive
Mean
Difference
(I-J)
definite
definite
normotensive
borderline
Std.
Error
Sig.
95% Confidence Interval
.157
2.356(*)
.770
.580
1.000
.000
Lower Bound
-1.69
.97
Upper Bound
2.00
3.74
-.157
.770
1.000
-2.00
1.69
2.198(*)
-2.356(*)
-2.198(*)
.789
.580
.789
.016
.000
.016
.31
-3.74
-4.09
4.09
-.97
-.31
* The mean difference is significant at the .05 level.
The Bonferroni method is a method that shows all pairwise comparisons/differences along
with a p-value (sig.) adjusted for the number of comparisons. In this example, subjects
with normal blood pressure and borderline hypertension have similar HDL cholesterol
levels, but subjects with definite hypertension have different HDL cholesterol levels than
both subjects with normal blood pressure and borderline hypertension.
Homogeneous Subsets
HDL cholesterol
Subset for alpha = .05
Ryan-Einot-GabrielWelsch Range
Hypertension status
definite
N
borderline
normotensive
1
1310
547
55.67
1568
Sig.
2
53.47
55.82
1.000
.867
Means for groups in homogeneous subsets are displayed.
The Ryan-Einot-Gabriel-Welsch (R-E-G-W-Q) method is a method that groups together
groups that are similar in the same subset and groups that are different are in different
subsets. In this example, subjects with normal blood pressure and borderline
hypertension are in one subset and subjects with definite hypertension are in a different
subset. Hence, subjects with definite hypertension have different HDL cholesterol levels
than subjects with normal blood pressure and borderline hypertension, but subjects with
normal blood pressure and borderline hypertension have similar HDL cholesterol levels.
50
Kruskal-Wallis Test
1.
2.
3.
4.
Choose Analyze on the menu bar.
Choose Nonparametric Tests
Choose K Independent Samples...
Test Variable(s): Select the test variable you want from the source list on the left and then
click on the arrow located next to the test variable box. Repeat the process until you have
selected all the variables you want to test.
5. Grouping Variable: Select the variable which defines the grouping and then click on the
arrow located next to the grouping variable box.
6. Choose Define Range...
7. Click on the blank box next to Minimum, then enter the smallest numeric code value for
the groups.
8. Click on the blank box next to Maximum, then enter the largest numeric code value for the
groups.
9. Choose Continue
10. Choose Kruskal-Wallis H as the Test Type. Note that the option may already be selected if
the little box is not empty.
11. Choose OK
CAUTION: The group variable must be numeric and you must correctly enter the smallest
numeric code value and the largest numeric code value. SPSS will allow you to select a
character/string variable as the grouping variable, as well as allow you to incorrectly enter the
numeric code values. The results displayed for the Kruskal Wallis test in these cases will be
incorrect, but no error or warning message will be displayed.
CHD Example. We can use one-way ANOVA to compare serum insulin levels between
subjects with different hypertensive status (0=normotensive, 1=borderline, 2=definite)
Hypertensive
Group
Normotensive
Borderline
Definite
n
1568
547
1310
Median
12
12
14
IQR*
9, 15
9, 17
11, 20
*IQR, interquartile range = 25th percentile, 75th percentile
51
Kruskal Wallis test
You can select 1 or more
variables to compare between
groups.
The variable selected as the
Grouping Variable defines the
groups. THE VARIABLE
SHOULD BE NUMERIC.
In this example the smallest numeric
code is 0 (for normal) and the largest
numeric code is 2 (for definite).
Kruskal-Wallis Test
Ranks
Serum insulin
Hypertension status
normotensive
borderline
N
Mean Rank
1568
1526.31
547
1685.28
definite
1310
1948.03
Total
3425
Information used in the test
statistic – not usually reported.
The descriptives under Options
are not useful; you can produce
relevant descriptives (e.g.
median and interquartile range
for each group) using the
Explore command.
Test Statistics(a,b)
Chi-Square
df
Asymp. Sig.
Serum insulin
130.816
2
Kruskal Wallis test
Asymp. Sig. = p-value = <.001
.000
a Kruskal Wallis Test
b Grouping Variable: Hypertension status
Asymp. is an abbreviation for asymptotic,
which means the p-value is computed
using a large sample approximation based
on the Normal distribution.
Chi-Square = test statistic value = 130.8
Df = degrees of freedom = 2
52
One-Sample Binomial Test
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Nonparametric Tests
Choose Binomial...
Test Variable List: Select the test variable you want from the source list on the left and then
click on the arrow located next to the test variable box. Repeat the process until you have
selected all the variables you want.
5. Test Proportion: Click on the box next to Test Proportion and enter/edit the proportion
value specified by your null hypothesis.
6. Choose OK
Example. In the TRAP study, 125 patients of the 527 patients who were negative for
lymphocytotoxic antibodies at baseline became antibody positive. The expected rate for
being antibody positive is 30%. We could use the one-sample binomial test to test if the
rate is different in the TRAP study population.
Positive is a variable
coded 1 if positive and 0
if negative.
Make sure to edit the
test proportion value.
This case .30 or 30%.
The default is .50.
NPar Tests
Binomial Test
positive
Group 1
Category
yes
Group 2
no
125
Observed
Prop.
.24
402
.76
N
Test Prop.
.3
Asymp. Sig.
(1-tailed)
.001(a,b)
Total
527
1.0
a Alternative hypothesis states that the proportion of cases in the first group < .3.
b Based on Z Approximation.
One-sample binomial test, two-sided p-value given by 2 x .001 = .002
(Note: SPSS reports the one-sided p-value).
53
McNemar's Test
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Descriptive Statistics
Choose Crosstabs...
Row(s): Select the row variable you want from the source list on the left and then click on
the arrow located next to the Row(s) box. Repeat the process until you have selected all the
row variables you want.
5. Column(s): Select the column variable you want from the source list on the left and then
click on the arrow located next to the Column(s) box. Repeat the process until you have
selected all the column variables you want.
6. Choose Cells...
7. For cell values choose total under percentages.
8. Choose Continue
9. Choose Statistics...
10. Choose McNemar
11. Choose Continue
12. Choose OK
There is also another way to run McNemar’s test (but the test pair variables must be numeric and
an asymptotic (Asymp.) p-value, based a large sample approximation based on the Normal
distribution, is reported instead of a p-value based on exact methods).
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Nonparametric Tests
Choose 2 Related Samples...
Test Pair(s) List: Select two paired variables you want from the source list on the left,
highlight both variables by pointing and clicking the mouse and then click on the arrow
located in the middle of the window. Repeat the process until you have selected all the
paired variables you want.
5. Choose McNemar as the Test Type.
6. Choose Wilcoxon to turn off the option. Note that the option is turned off when the little box
is empty.
7. Choose OK
Example. Suppose we want to compare two different treatments for a rare form of
cancer. Since relatively few cases of this disease are seen, we want the two treatment
groups to be as comparable as possible. To accomplish this goal, we set up a matched study
such that a random member of each matched pair gets treatment A (chemotherapy),
whereas the other member gets treatment B (surgery). The patients are assigned to pairs
(621 pairs) matched on age (within 5 years), sex, and clinical condition. The patients are
followed for 5 years, with survival as the outcome variable.
The 5-year survival rate for treatment A is 17.1% (106/621) and for treatment B is 15.3%
(95/621). We could use McNemar’s test to compare the survival rate of the two
treatments.
54
McNemar’s test
It doesn’t matter for McNemar’s
test which variable is selected for
the Row(s): or Columns(s). You can
run more than one test at a time.
Under
Statistics…
select
McNemar.
Under Cells…,
in this
example,
select Total
percentages.
Crosstabs
TreatmentA * TreatmentB Crosstabulation
Total
TreatmentB
TreatmentA
died
died
510
Count
% of Total
survived
5
515
82.1%
.8%
82.9%
16
106
2.6%
90
14.5%
526
95
621
84.7%
15.3%
100.0%
Count
% of Total
Total
Count
% of Total
survived
17.1%
Survival rate for
Treatment A is
17.1%
Survival rate for
Treatment B is
15.3%
Chi-Square Tests
Value
McNemar Test
N of Valid Cases
a Binomial distribution used.
Exact Sig.
(2-sided)
.027(a)
621
McNemar’s test
Exact Sig. (2-sided) = exact two-sided p-value
= 0.027
The p-value is exact because it is computed
using the Binomial distribution instead of using
an approximation to the Normal distribution.
55
Chi-square Test, Fisher’s Exact test and Trend test for Contingency Tables
If the Chi-square test is requested for a 2 x 2 table, SPSS will also compute the Fisher's Exact
test. If the Chi-square test is requested for a table larger than 2 x 2, SPSS will also compute the
Mantel-Haenszel test for linear or linear by linear association between the row and column
variables.
1.
2.
3.
4.
Choose Analyze from the menu bar.
Choose Descriptive Statistics
Choose Crosstabs...
Row(s): Select the row variable you want from the source list on the left and then click on
the arrow located next to the Row(s) box. Repeat the process until you have selected all the
row variables you want.
5. Column(s): Select the column variable you want from the source list on the left and then
click on the arrow located next to the Column(s) box. Repeat the process until you have
selected all the column variables you want.
6. Choose Cells...
7. Choose the cell values (e.g., observed and expected counts; row, column, and margin (total)
percentages). Note the option is selected when the little box is not empty.
8. Choose Continue
9. Choose Statistics...
10. Choose Chi-square
11. Choose Continue
12. Choose OK
Asthma Example. An investigator studied the relationship of parental smoking habits and
the presence of asthma in the oldest child. Type A families are defined as those in which
both parents smoke and Type B families are those in which neither parent smokes. Of 100
type A families, 15 eldest children have asthma, and of 200 type B families, 6 children
have asthma. We could use a chi-square test or Fisher’s exact test to test if the
proportion of first born children with asthma different in these two types of families?
It doesn’t matter for the chi-square,
Fisher’s Exact or trend test which
variable is selected for the Row(s): or
Columns(s). You can run more than one
test at a time.
56
Under
Statistics…
select Chisquare.
Under Cells…,
in this
example,
select Row
percentages.
Crosstabs
familytype * asthma Crosstabulation
asthma
No
familytype
A
Count
% within familytype
B
Count
% within familytype
Total
Count
% within familytype
15% of first born in family
type A have asthma
Total
Yes
85
15
85.0%
15.0%
100
100.0%
194
6
200
97.0%
3.0%
100.0%
279
21
300
93.0%
7.0%
100.0%
3% of first borin in family
type B have asthma
Chi-Square Tests
Value
Pearson Chi-Square
Continuity
Correction(a)
Likelihood Ratio
Asymp.
Sig. (2sided)
df
14.747(b)
1
.000
12.961
1
.000
13.745
1
.000
Fisher's Exact Test
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
.000
.000
N of Valid Cases
300
a Computed only for a 2x2 table
b 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.00.
Fisher’s Exact test
Exact Sig. (2-sided)
= exact two-side pvalue = <.001
Chi-square test
Pearson Chi-square (without continuity correction), p-value = <.001
Pearson Chi-square with continuity correction, p-value = <.001
Asymp. Sig. (2-sided) = two-sided p-value. Asymp. is an abbreviation for asymptotic, which
means the p-value is computed using a large sample approximation based on the Normal
distribution. Check that all cells have expected cell counts 5 or greater.
Value = test statistic value
df = degrees of freedom
57
Trend Test Example. A clinical trial of a drug therapy to control pain was
performed. The investigators wanted to investigate whether adverse responses to
the drug increased with larger drug doses. Subjects received either a placebo or
one of four drug doses. In this example dose is an ordinal variable, and it
reasonable to expect that as the dose increases and rate of adverse events will
increase.
Dose
Placebo
500 mg
1000 mg
2000 mg
4000 mg
Adverse event
% (n)
18.8% (6)
21.9% (7)
28.1% (9)
31.3% (10)
50.0% (16)
n
32
32
32
32
32
There are several different methods for performing a trend test with ordinal
variables. One test, which is available in SPSS is the Mantel-Haenszel chi-square,
also called the Mantel-Haenszel test for linear association or linear by linear
association chi-square test.
Adverse events
No
dose
0
% within dose
500
2000
81.3%
18.8%
100.0%
25
7
32
78.1%
21.9%
100.0%
23
9
32
71.9%
28.1%
100.0%
22
10
32
68.8%
31.3%
100.0%
Count
% within dose
Total
32
Count
% within dose
4000
6
Count
% within dose
Count
% within dose
Total
26
Count
% within dose
1000
Yes
Count
16
16
32
50.0%
50.0%
100.0%
112
48
160
70.0%
30.0%
100.0%
Chi-Square Tests
Value
Pearson Chi-Square
Likelihood Ratio
Linear-by-Linear
Association
N of Valid Cases
Asymp. Sig.
(2-sided)
df
9.107(a)
8.836
4
4
.058
.065
8.876
1
.003
160
In this example, there is a
significant trend (p-value =
0.003, chi-square trend test),
and we would conclude that
the rate of adverse responses
increases with drug dose.
a 0 cells (.0%) have expected count less than 5. The minimum expected count is 9.60.
58
Using Standardized Residuals in R x C tables. When the contingency table has
more then 2 rows and 2 columns it can be hard to determine the association or the
largest differences. Standard residuals are often helpful in describing the
association, if the chi-square test indicates there is a statistically significant
association. The (adjusted) standardized residual re-expresses the difference
between the observed cell count and expected cell count in terms of standard
deviation units below or above the value 0 (the expected differences if there is no
association), and the distribution of the standardized residuals has a standard
Normal distribution. Hence, values less than -2 or greater than 2 indicate large
differences and values less than -3 or greater than 3 indicate very large
differences.
Under Cells…, select Adjusted
standardized for Residuals
Education vs Stage of Disease at Diagnosis Example. The chi-square indicated a
significant association between education level and stage of disease at diagnosis (
Chi-square test, p-value = 0.016).
Stage of Disease
Education
≤12 years
I
Count
% within education
Adjusted Residual
College
Count
% within education
Adjusted Residual
College graduate
Count
% within education
Adjusted Residual
II
III
20
24
35
25.3%
30.4%
44.3%
-2.6
-.5
3.3
37
32
23
40.2%
34.8%
25.0%
.8
.6
-1.4
40
29
21
44.4%
32.2%
23.3%
1.8
-.1
-1.8
The adjusted standardized
residuals indicate the biggest
difference between the
observed and expected cell
counts (i.e., the most unusual
differences under the
assumption of no association
between education and stage
of disease) are for subjects
with ≤12 years of education,
where there are fewer subjects with Stage I and more subjects with Stage III or
IV than expected if there was no association between education and stage of
disease. Also, to a lesser extent, among the subjects with a college graduate
degree there a more subjects with Stage I and fewer subject with Stage III or
IV than expected if there was no association between education and stage of
disease.
59
One sample binomial test, McNemar's test, Fisher's Exact test and Chi-square
test for 2 x 2 and R x C Contingency Tables Using Summary Data
There is an easy way in SPSS to perform a one sample binomial test, a McNemar's test, a
Fisher's Exact test or a Chi-square test for a 2 x 2 or R x C table when you only have summary
data (i.e., the number of observations in each cell).
One sample binomial test. Suppose you observe 15 cases of myocardial infarction (MI) in 5000
men over a 1 year period and you want to test if the rate of MI is equal to a previously reported
incidence rate of 5 per 1000 (or 0.005).
1. In a new (empty) SPSS Data Editor window enter the following 2
rows of data:
MI
0
1
Observed
4985
15
The values of 0 and 1 used to indicate MI (no/yes) are arbitrary. The variable names are also
arbitrary (e.g., you can leave them as var0001 and var0002).
2. Next, you want to weight cases by Observed:
Choose Data
Choose Weight Cases...
Choose Weight cases by
Choose Observed and then the arrow button so the variable appears in the Frequency variable
box.
Choose OK
3. Now, run the one sample binomial test:
Choose Analyze
Choose Nonparametric Tests
Choose Binomial...
Choose MI so that in appears in the Test Variable List
Change (edit) Test Proportion to .005.
Choose OK
60
McNemar's test. Suppose you have the following summary table of presence and absence of
DKA before and after therapy for paired data,
Before
therapy
No DKA
DKA
After therapy
No DKA
DKA
128
7
19
7
1. In a new (empty) SPSS Data Editor window enter the following 4
rows of data:
Before After Observed
1
1
128
1
0
19
0
1
7
0
0
7
The values of 0 and 1 used to indicate DKA and no DKA are arbitrary. The variable names
are also arbitrary (e.g., you can leave them as var0001, var0002, and var0003).
2. Next, you want to weight cases by Observed:
Choose Data
Choose Weight Cases...
Choose Weight cases by
Choose Observed and then the arrow button so the variable appears in the Frequency variable
box.
Choose OK
3. Now, run McNemar's test:
Choose Analyze
Choose Nonparametric Tests
Choose 2 Related Samples...
Choose Before and After so that they appear in the Test Pair(s) List.
Choose McNemar as the Test Type
Choose Wilcoxon to turn off the option
Choose OK
61
Chi-square test and Fisher's Exact test for a 2 x 2 table. Suppose you have the following
summary table for oral contraceptive (OC) use by presence or absence of cancer (case or
control),
OC Use
No
Yes
Cases (cancer)
111
6
Controls
387
8
1. In a new (empty) SPSS Data Editor window enter the following 4
rows of data:
Case OCuse Observed
1 0 111
1 1
6
0 0 387
0 1
8
The values of 0 and 1 used to indicate case/control and OC use (no/yes)
are arbitrary. The variable names are also arbitrary (e.g., you can
leave them as var0001, var0002, and var0003).
2. Next, you want to weight cases by Observed:
Choose Data
Choose Weight Cases...
Choose Weight cases by
Choose Observed and then the arrow button so the variable appears in the Frequency variable
box.
Choose OK
3. Now, run the Chi-square (\& Fisher's Exact) test
Choose Analyze
Choose Crosstabs
Choose Case and OCuse as the row the column variables
Choose Statistics...
Choose Chi-square
Choose Continue
Choose OK
62
The commands are similar for running the Chi-square test for tables larger than 2x 2. Suppose
you have the following summary table for education level by stage of disease at diagnosis
Education level
High school or less
College
College graduate
I
20
37
40
Stage of Disease
II
III or IV
24
35
32
23
29
21
1. In a new (empty) SPSS Data Editor window enter the following 9
rows of data:
Educ Stage Observed
1 1 20
1 2 24
1 3 35
2 1 37
2 2 32
2 3 23
3 1 40
3 2 29
3 3 21
The values used to indicate education level and stage are arbitrary, and the variable names are
also arbitrary.
Follow steps 2. and 3. on the previous page (except use variables Educ and Stage, instead of
Case and OCuse).
63
Confidence Interval for a Proportion
To construct a confidence interval for a proportion or rate is rather awkward in SPSS, but you
can do it with the raw data or with summary data (as long as the sample size is large enough to
use the Normal approximation methods for binomial data).
To construct a confidence interval using the raw data you need 1) a binary indicator variable
equal to 1 if the variable is present for a subject and equal to 0 if the variable is absent for a
subject, and 2) a variable that is equal to 1 for all subjects. For example, suppose you want to
construct a confidence interval for the proportion of males in your data set. First you need a
binary indicator variable for males, e.g. you could have a variable named Gender which is equal
to 1 if the subject is a male and equal to 0 if the subject is a female. Second you need to create a
variable that is equal to 1 for all subjects (e.g., use the Compute statement and create a variable
Allones = 1). Now,
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Descriptive Statistics
Choose Ratio...
Numerator: Select the binary indicator variable from the source list on the left and then
click on the arrow located in the middle of the window (e.g. select Gender)
5. Denominator: Select the variable equal to 1 for all subjects from the source list on the left
and then click on the arrow located in the middle of the window (e.g. select Ones)
6. Choose Statistics...
7. Choose Mean under Central Tendency
8. Choose Confidence intervals (default is a 95% confidence interval)
9. Choose Continue
10. Choose OK
To illustrate how you would construct a confidence interval with summary data, suppose in a
data set of 3425 subjects, 1341 are males and 2084 are females:
1. In a new (empty) SPSS Data Editor window enter the following 2
rows of data:
Gender Observed Allones
0
2084
1
1
1341
1
2. Next, you want to weight cases by Observed:
Choose Data
Choose Weight Cases...
Choose Weight cases by
Choose Observed and then the arrow button so the variable appears in the Frequency variable
box.
Choose OK
64
3. Now,
Choose Analyze on the menu bar
Choose Descriptive Statistics
Choose Ratio...
Numerator: Select Gender
Denominator: Select Allones
Choose Statistics...
Choose both Mean and Confidence intervals under Central Tendency
Choose Continue
Choose OK
Example of the SPSS output using the previous summary data.
Ratio Statistics
Ratio Statistics for Gender / Allones
Mean
95% Confidence Interval
for Mean
.392
Lower Bound
Upper Bound
.375
.408
Price Related Differential
1.000
Coefficient of Dispersion
.
Coefficient of Variation
Median Centered
.
The confidence intervals are constructed by assuming a Normal distribution
for the ratios.
The observed
proportion was .392 or
39.2%.
A 95% confidence
interval is 37.5% to
40.8%.
65
Correlation & Regression
Pearson and Spearman Rank Correlation Coefficient
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Correlate
Choose Bivariate...
Variable(s): Select the variables from the source list on the left and then click on the arrow
located in the middle of the window.
5. Choose Pearson or/and Spearman as the Correlation Coefficients. Note that the option is
selected if the box has a check mark in it.
6. Choose Two-tailed as the Test of Significance. SPSS will perform the test testing if the
correlation is equal to zero versus it is not equal to zero.
7. Choose OK
Note that you can use the Crosstabs command to calculate confidence intervals for the
correlation.
Example. Pain-related beliefs, catastrophizing, and coping have been shown to be
associated with measures of physical and psychosocial functioning among patients with
chronic musculoskeletal and rheumatologic pain. However, little is known about the
relative importance of these process variables in the functioning of patients with
temporomandibular disorders (TMD).
Correlation coefficients could be calculated to examine the association between
catastrophizing, depression (Beck Depression Inventory), pain-related activity
interference and jaw opening (maximum assisted opening).
(Reference: JA Turner, SF Dworkin, L Mancl, KH Huggins, EL Truelove. “The roles of
beliefs, catastrophizing, and coping in the functioning of patients with temporomandibular
disorders.” Pain, 92, 41-51, 2001.
Typically, you would only
report either the Pearson or
Spearman (rank) correlation
coefficients, but you might
calculate both to see if you
get different results or
conclusions.
The correlations are shown on the next page. Note that SPSS will display the correlation between
variable 1 and variable 2 and between variable 2 and variable 1, which are equivalent, and similarly
the correlations between all possible pairs of variables. So, all results displayed below the diagonal
of the matrix of results are redundant.
66
Correlations
1st entry = Pearson correlation coefficient
2nd entry = Sig. (2-tailed) = p-value
3rd entry = N = the number observations or subjects with non-missing data for both variables
Correlations
Catastroph
Pearson Correlation
-izing
Sig. (2-tailed)
.000
.000
Maximum
assisted
opening
-.029
.758
118
118
118
116
.602(**)
1
.445(**)
-.079
.000
.397
Catastroph
izing
1
N
Beck inventory
Pearson Correlation
score
Sig. (2-tailed)
Beck
inventory
score
.602(**)
.451(**)
.000
N
Interference
Interference
118
118
118
116
.451(**)
.445(**)
1
-.068
Sig. (2-tailed)
.000
.000
N
118
118
118
116
1
Pearson Correlation
.468
Maximum
Pearson Correlation
-.029
-.079
-.068
assisted
Sig. (2-tailed)
.758
.397
.468
opening
N
116
116
116
Correlation
between
Catastrophizing and
Interference
= .45
P-value =
<.001
N = 118
subjects
116
** Correlation is significant at the 0.01 level (2-tailed).
Nonparametric Correlations
1st entry = Spearman rank correlation coefficient
2nd entry = Sig. (2-tailed) = p-value
3rd entry = N = the number observations or subjects with non-missing data for both variables
Correlations
Interference
Beck
inventory
score
Catastrophizing
Spearman's
rho
Catastrophizing
Correlation
Coefficient
Sig. (2-tailed)
1.000
.625(**)
.451(**)
-.013
.
.000
.000
.892
118
118
118
.625(**)
1.000
.455(**)
116
-.110
.000
.
.000
.241
118
118
118
116
.451(**)
.455(**)
1.000
-.046
.000
.000
.
.621
118
118
118
116
-.013
-.110
-.046
1.000
Sig. (2-tailed)
.892
.241
.621
.
N
116
116
116
116
N
Beck inventory
score
Correlation
Coefficient
Sig. (2-tailed)
N
Interference
Correlation
Coefficient
Sig. (2-tailed)
N
Maximum
assisted
opening
Maximum
assisted
opening
Correlation
Coefficient
** Correlation is significant at the 0.01 level (2-tailed).
Rank
correlation
between
Catastrophiz
-ing and
Interference
= .45
P-value =
<.001
N = 118
subjects
67
Confidence Interval for a Correlation Coefficient
Typically the Crosstabs command is used to produce contingency tables for categorical
variables. One of the options under Statistics… is used to compute the correlation coefficient,
which would you might want to calculate for ordinal variables. However, you can also use this
option for quantitative variables.
The Crosstabs command is found by selecting
Analyze and then Descriptive Statistics.
In this example the correlation between the
quantitative variables catastrophizing and
interference will be calculated.
Select Statistics… and then select Correlations.
SPSS will produce a contingency table of the
cross-tabulation of the two variables which you
can ignore.
SPSS will display the correlation coefficient and
standard error estimate for the correlation
coefficient, which can be used to calculate
confidence intervals.
Symmetric Measures
Value
Asymp. Std.
Error(a)
Approx. T(b)
Approx. Sig.
Interval by Interval
Pearson's R
.451
.068
5.445
.000(c)
Ordinal by Ordinal
Spearman Correlation
.451
.076
5.449
.000(c)
N of Valid Cases
118
a Not assuming the null hypothesis.
b Using the asymptotic standard error assuming the null hypothesis.
c Based on normal approximation.
An approximate 95% confidence interval for the correlation coefficient is given by
Correlation coefficient ± 1.96 x Asymp. Std Error
In this example, 95% confidence interval for the Pearson correlation coefficient is given
by .451 ± 1.96 x .068 or .31, .58
95% confidence interval for the Spearman rank correlation coefficient is given by .451 ±
1.96 x .076 or .30, .60
68
Linear Regression
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Regression
Choose Linear...
Dependent: Select the dependent variable from the source list on the left and then click on
the arrow next to the dependent variable box.
5. Independent(s): Select the independent variable and then click on the arrow next to the
independent variable(s) box. Repeat the process until you have selected all the independent
variables you want.
6. Choose Statistics...
7. Choose Estimates. SPSS will print the regression coefficient estimate, standard error, t
statistic and p-value for each independent variable (as well as the intercept/constant). By
default the option should be selected (i.e., the box has a check mark in it).
8. Choose Model fit. SPSS will print the multiple R, R squared, Adjusted R-squared, standard
error of the regression line, and the ANOVA table. By default the option should be selected.
9. Choose Continue
10. Choose Enter as the Method. Enter is the default method for independent variable entry.
Other methods of variable entry can be selected by clicking on the down arrow and clicking
on the desired method of entry.
11. Choose OK
Additional options are available under Statistics..., Plots..., Save..., Method, and Options... For
example:
Statistics...
 Estimates. Default option, which prints the usual linear regression results.
 Model fit. Default option, which prints the usual linear regression results.
 Confidence intervals (for the regression coefficient estimates)
 Covariance matrix (and correlation matrix for the regression coefficient estimates).
 R squared change. If independent variables are entered in Blocks (using the Block option;
see below), this option computes the change in the R squared between models with different
blocks of independent variables. It is also useful for computing a partial F test for a
categorical variable with more than two categories by entering the indicator variables for the
categorical variable in the second block (Block 2 of 2) and all other independent variables in
the first block (Block 1 of 2) and using the R squared change option.
 Part and Partial Correlations. This option computes the Pearson correlation coefficient
between the dependent variable and each independent variable (Zero-order correlation) and
the correlation coefficient between the dependent variable and an independent variables after
controlling for all the other independent variables in the regression model (Partial correlation).
Squaring the partial correlation gives you the partial R-squared for an independent variable.
This option also computes a Part correlation, which is the correlation between the dependent
variable and an independent after (only) the independent variable has been adjusted for all the
other independent variables in the regression model. The square of the Part correlation is
equal to the change in the R-squared when an independent is added to the regression model
with all the other independent variables.
69
 (Multi-)Collinearity diagnostics. This option computes various statistics for detecting
collinearity between the independent variables. For example, Tolerance is the proportion of a
variable's variance not accounted for by other independent variables in the equation. A
variable with a very low tolerance contributes little information to a model, and can cause
computational problems. Another statistic is the VIF (variance inflation factor). Large values
are an indicator of multicollinearity between independent variables.
Plots... which are useful for doing regression diagnostics:
 Histogram or Normal Probability Plot (P-P plot) (of the standardized residuals).
 Produce all partial (residual) plots
 Other scatter plots
Save... which produced variables which are useful for doing regression diagnostics:
 Predicted Values (unstandardized, standardized, adjusted)
 Residuals (unstandardized, standardized, studentized, delete)
 Distances (Mahalanobis, Cook's, Leverage)
 Influence Statistics (dfBeta, dfFit)
Note that SPSS creates a new variable for each selected Save... option and adds the new
variables to the data file. The variable names are defined in the Variable View of the Data
Editor. Once you are done using these variables you may want to delete them from the data file
or save them (by re-saving the data file).
Method. Click on the down arrow to the right of Method to display the methods available for
independent variable entry (enter, stepwise, remove, backward, forward). Enter is the default
option. The other options you enter independent variables into the model using various stepwise
methods.
Options...
 You can modify the entry and removal criteria used by stepwise, remove, backward, and
forward independent variable entry methods.
 You can define how observations with missing data are handled.
Previous, Block \# of \#, Next
 You can use these options to enter independent variables in blocks into the regression model.
 You can select different methods of variable entry for each block. This option is also useful
for computing partial F tests with the R squared change option.
70
Example. Simple linear regression of forced expiratory volume (volume, 1 second) on
height (cm).
The dependent variable
in this example is
forced expiratory
volumne (fev1).
There is only 1
independent variable in
this example, height.
Additional options can
be found under
Statistics, Plots, Save,
& Options.
Here are the Statistics… options
Usually you want the default options
Estimates and Model fit selected.
In this example, (95%) confidence interval
for the regression coefficients is also
selected.
Here are the Plots… options
By default no options are selected.
In this example, the normal probability
plot of the residuals is requested.
71
Regression
Information on the independent
variables and dependent variable in the
regression model, and the method of
entering the independent variables into
the regression model.
Variables Entered/Removed(b)
Model
1
Variables
Entered
Variables
Removed
height(a)
a All requested variables entered.
b Dependent Variable: fev1
Method
.
Enter
R-Square = proportion of the total
variation in the dependent variable
explained by the independent
variable(s) = .315 or 31.5%
R is square root of R Square
Model Summary(b)
Model
1
R
R Square
.315
.562(a)
a Predictors: (Constant), height
b Dependent Variable: fev1
Adjusted R
Square
Std. Error of
the Estimate
.314
.55337
Adjusted R Square – “adjusts” the
R square for the number of
variables in the model
Std. error of the estimate =
standard deviation of the error or
residuals. Not usually reported, but
used in estimating the standard
error of the regression
coefficients.
ANOVA(b)
df
Regression
Sum of
Squares
112.380
1
Mean
Square
112.380
Residual
244.054
797
.306
356.434
a Predictors: (Constant), height
b Dependent Variable: fev1
798
Model
1
Total
F
366.997
Sig.
.000(a)
ANOVA = analysis of
variance table. Not
needed when there is
only 1 independent
variable in the model.
The F test is
equivalent to the t test
for testing if the slope
is equal to zero in the
output that follows. (F
= t2)
72
Coefficients(a)
Unstandardized
Coefficients
Std.
B
Error
Model
1
(Constant)
height
-4.330
.039
Standardized
Coefficients
t
Sig.
Beta
.335
.002
.562
95% Confidence Interval for B
Lower Bound
-12.943
19.157
.000
.000
Upper Bound
-4.987
.035
-3.673
.043
a Dependent Variable: fev1
Unstandardized coefficients B = regression coefficient
In this example B = 0.039 is the slope and B = -4.330 the intercept
Std. Error = standard error of the regression coefficient.
Standardized coefficients Beta = standardized regression coefficient
t = t statistic for testing if the regression coefficient is equal to zero (versus not equal
to zero)
Sig. = p – value for testing if the regression coefficient is equal to zero (versus not
equal to zero).
95% confidence interval for B = 95% confidence interval for the regression coefficient
In this example, you would report the slope (.039), standard error of the slope (.002)
and the p-value (<.001), or the slope (.039) and 95% confidence interval (.035 to 0.043).
Charts
Normal P-P Plot of Regression Standardized Residual
Dependent Variable: fev1
Normal probability plot of
the residuals. The points
fall along a straight line,
indicating the residuals
have, at least
approximately, a Normal
distribution.
1.0
Expected Cum Prob
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
Observed Cum Prob
1.0
73
Linear Regression Example with three independent variables
The dependent variable is
forced expiratory volume
(fev1).
The independent variables are
height, age and enter.
The Enter method means all 3
independent variables will be
included in the regression
model.
Statistics… options
By default, Estimates and Model fit are
selected.
In this example, part and partial
correlations and collinearity diagnostics
are also selected.
Plots… options
Normal probability plot (of the
standardized residuals) and partial
(residual) plots are selected.
74
Regression
Variables Entered/Removed(b)
Model
1
Variables
Entered
Variables
Removed
gender,
age,
height(a)
Information on the independent
variables, method of variable entry, and
dependent variable.
Method
Enter
.
a All requested variables entered.
b Dependent Variable: fev1
R-square is .361 or 36.1%
(adjusted R-square is 35.8%).
About 36% of the variation in
the dependent variables can be
explained by the 3 independent
variables.
Model Summary(b)
Model
1
R
Adjusted R
Square
R Square
Std. Error of
the Estimate
.361
.358
.601(a)
a Predictors: (Constant), gender, age, height
b Dependent Variable: fev1
.53531
ANOVA(b)
Model
1
Regression
Sum of
Squares
128.623
Residual
227.811
3
Mean
Square
42.874
795
.287
df
F
149.621
The overall F test,
indicates 1 or more the
independent variables is
significant (P < .001).
Degrees of freedom of
the F test are 3 and 795.
Sig.
.000(a)
Total
356.434
798
a Predictors: (Constant), gender, age, height
b Dependent Variable: fev1
Coefficients(a)
Unstandardized
Coefficients
Std.
B
Error
Standardized
Coefficients
t
Sig.
Beta
Collinearity
Statistics
Correlations
Zeroorder
Partial
Part
Tolerance
VIF
(Constant)
height
-.780
.028
.593
.003
.399
9.143
.189
.000
.562
.308
.259
.423
2.364
age
-.025
.004
-.200
-6.857
.000
-.206
-.236
-.194
.944
1.059
.273
.059
.201
4.591
.000
.478
.161
.130
.420
2.379
gender
-1.315
a Dependent Variable: fev1
Height, age, and gender are all statistically significant (P < .001), i.e., the regression
coefficients are different from zero.
The partial correlations (and partial R-squares, .3082=.095, -.2362 =.056, and .1612=.026)
indicate the correlation with the dependent variable adjusted for the other variables in
the regression model.
A low tolerance value (say, <.20) or a high variance inflation factor (VIF) (say, > 5 or 10)
may indicate a multicollinearity problem.
75
Normal P-P Plot of Regression Standardized Residual
Dependent Variable: fev1
Normal probability plot of the
residuals. The points fall
approximately along a straight
line, indicating the residuals have
(approximately) a Normal
distribution.
1.0
Expected Cum Prob
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Observed Cum Prob
Partial Regression Plot
Partial regression plots for
height and age with lowess
smooths.
Similarly, the plot for age is
assessing the relationship
between age and fev1
adjusting for height and
gender.
2.00
fev1
0.00
-2.00
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
height
Partial Regression Plot
Dependent Variable: fev1
2.00
0.00
fev1
The plot for height is
assessing the relationship
between height and fev1 after
adjusting for age and gender
(e.g., is the relationship
linear).
Dependent Variable: fev1
-2.00
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
age
Note that SPSS will also produce a partial residual plot for gender. In general, the partial
residuals plots for categorical/nominal variables are not very useful. Boxplots of the
residuals for each category of a categorical/nominal variable are useful for regression
diagnostics. To produce the boxplots you could use the Save… options to save the
residuals from a regression and then the Boxplot commands to plot the residuals.
76
Linear Regression via ANOVA Commands
It is possible to use the analysis variance commands of SPSS to perform a linear regression
analysis, because the methods are mathematically equivalent. Performing a linear regression
analysis via analysis of variance in SPSS is more complicated than using the linear regression
commands. However, the advantage of using the analysis of variance commands to perform a
linear regression is that you do not have to create indicator variables for categorical variables or
create interaction terms. To perform a linear regression via analysis of variance commands
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose General Linear Model
Choose Univariate...
Dependent: Select the dependent variable from the source list on the left and then click on
the arrow next to the dependent variable box.
5. Fixed Factor(s): Select the independent variables that are categorical/qualitative and then
click on the arrow next to the fixed factor(s) box. Repeat the process until you have selected
all the categorical variables you want.
6. Covariate(s): Select the independent variables that are continuous/quantitative and then click
on the arrow next to the covariate(s) box. Repeat the process until you have selected all the
continuous variables you want.
7. Choose Model...
8. Choose Custom
9. Factors & Covariates: Select/highlight all the variables, then under Build Terms select
Main Effects. You may need to click on the down arrow to display the Main Effects option.
After you have selected Main Effects, select the arrow under the Build Terms. All the
variables should now appear in the Model box on the right hand side.
10. Choose Continue
11. Choose Options...
12. Choose Parameter Estimates under Display
13. Choose Continue
14. Choose OK
For categorical variables the last category (i.e., the category with the largest numeric coding
value) will be the referent group/category. SPSS will compute the F test for each continuous
independent variable and for categorical independent variable. By selecting to have the
parameter estimates displayed, SPSS will also compute the regression coefficient estimates,
standard errors, t (statistic) values, p-values, and 95% confidence intervals that you get from the
linear regression commands.
To include interaction terms in the regression model, in Step 9 highlight two variables you want
to create an (two-way) interaction term. Under Build Terms select Interaction, and then select the
arrow under the Build Terms. A two-way interaction between two variables (variable 1 *
variable 2) should now appear in the Model box on the right hand side.
77
Example. Linear regression of forced expiratory volume on height (continuous variable)
and diabetes status (categorical variables; normal, impaired fasting glucose, diabetic).
Forced expiratory volume
(fev1) is the dependent
variable.
Diabetes is a categorical
variables with the 3
categories
Height is a continuous
variable
Under Model…, select
Custom, then select each
of the variables separately
until they all appear under
Model: or select Main
Effects under Build
Terms(s), select all
Factors & Covariates, and
then select the arrow
under Build Term(s).
Under Options…, select
Parameter estimates to
have usual linear
regression results
displayed in the output.
78
Univariate Analysis of Variance
Between-Subjects Factors
Tests of Between-Subjects Effects
Dependent Variable: fev1
Source
Corrected Model
Type III Sum
of Squares
114.617(a)
Intercept
diabetes
height
3
Mean
Square
38.206
F
125.606
Sig.
.000
51.195
2.237
1
2
51.195
1.118
168.308
3.677
.000
.026
366.168
.000
df
111.378
1
111.378
Error
241.817
795
.304
Total
3773.779
799
The overall test for
the significant of
diabetes is
displayed (p-value =
0.026)
Corrected Total
356.434
798
a R Squared = .322 (Adjusted R Squared = .319)
Parameter Estimates
Dependent Variable: fev1
Parameter
Intercept
B
Std.
Error
t
Sig.
95% Confidence Interval
Lower
Upper
Bound
Bound
-4.392
.337
-13.025
.000
-5.054
-3.730
[diabetes=1.00]
.126
.049
2.549
.011
.029
.223
[diabetes=2.00]
.046
.056
.830
.407
-.063
.156
[diabetes=3.00]
0(a)
.
.
.
.
.
.039
.002
19.136
.000
a This parameter is set to zero because it is redundant.
.035
.043
height
This table displays
the usual linear
regression results.
In this example
diabetes = 3
(diabetic) is the
reference group.
79
Example. Adding an interaction between diabetes status and height in the regression
model
To add an interaction
between two variables,
select the Build Term(s)
to show Interaction,
select two variables
under Factors &
Covariates and then
select the arrow under
Build Term(s)
Univariate Analysis of Variance
Tests of Between-Subjects Effects
Dependent Variable: fev1
Source
Corrected Model
Type III Sum
of Squares
Mean
Square
df
F
Sig.
114.946(a)
5
22.989
75.492
.000
Intercept
42.741
1
42.741
140.354
.000
diabetes
.272
2
.136
.447
.639
94.349
.328
1
2
94.349
.164
309.823
.539
.000
.583
Error
241.488
793
.305
Total
3773.779
799
height
diabetes * height
This table displays the
significant of the
diabetes status by
height interaction (pvalue = 0.58).
Corrected Total
356.434
798
a R Squared = .322 (Adjusted R Squared = .318)
Parameter Estimates
Dependent Variable: fev1
Parameter
B
Intercept
Std. Error
t
Sig.
-4.373
.673
-6.498
.000
[diabetes=1.00]
-.168
.818
-.206
.837
[diabetes=2.00]
.614
.963
.637
.524
[diabetes=3.00]
0(a)
.
.
.
height
.039
.004
9.506
.000
[diabetes=1.00] * height
.002
.005
.361
.719
[diabetes=2.00] * height
-.003
.006
-.593
.553
[diabetes=3.00] * height
0(a)
.
.
.
a This parameter is set to zero because it is redundant.
This table displays the
usual linear regression
results which includes
the results for diabetes
status, height and the
interaction between
diabetes status and
height.
80
Logistic Regression
1.
2.
3.
4.
Choose Analyze on the menu bar
Choose Regression
Choose Binary Logistic...
Dependent: Select the dependent variable from the source list on the left and then click on
the arrow next to the dependent variable box.
5. Covariate(s): Select the independent variable and then click on the arrow next to the
Covariate(s) box. Repeat the process until you have selected all the independent variables
you want.
6. Choose Enter as the Method. Enter is the default method for independent variable entry.
Other methods of variable entry can be selected by clicking on the down arrow and clicking
on the desired method of entry.
7. Choose OK
Additional options are available under >a*>b, Categorical..., Save..., Method, or Options... .
For example:
>a*>b (for adding two-way interactions) You can add an interaction between two independent
variables to the regression model by selecting two variables from the source list on the left (hold
down the Ctrl key while selecting the two variables) and then clicking on >a*>b (after you
highlight two variables from the source list on the left the >a*>b should be available to select).
Categorical... You can use the categorical option to have SPSS create indicator or dummy
variables for categorical variables.
1. Choose Categorical
2. Categorical Covariates: Select a covariate that is categorical and then click on the arrow next
to the Covariates box.
3. Choose Indicator as the Contrast: Indicator is the default method for creating indicator
variables. Other methods can be selected by clicking on the down arrow and clicking on the
desired method.
4. Choose the reference category as the last category (i.e., the category with the largest numeric
coding value) or the first the category (i.e., category with the smallest numeric coding value).
5. Choose Change.
6. Repeat steps 2 through 5 until you have defined all categorical variables.
7. Choose Continue.
Save...
 Predicted Values (Probabilities and Group Membership). This options creates new variables
that are the predicted probabilities and the predicted group membership. The predicted group
membership (0 or 1) is based on the whether the predicted probability is less than (group
membership=0) or greater than or equal to (group membership=1) the classification cutoff. By
default the classification cutoff value is 0.5. You can change the cutoff value using Options...
 Residuals (Unstandardized, Logit, Studentized, Standardized, Deviance)
 Influence (Cook's, leverage, dfBeta)
81
Note that SPSS creates a new variable for each selected Save... option and adds the new
variables to the data file. The variable names are defined in the Viewer window. Once you are
done using these variables you may want to delete them from the data file or save them (be resaving the data file).
Method… Click on the down arrow to the right of Method to display the methods available for
independent variable entry (enter, forward:conditional, forward:LR, forward:Wald,
backward:conditional, backward:LR, backward:Wald).
Options...
 Confidence interval for odds ratio (CI for exp(B))
 Hosmer-Lemeshow goodness-of-fit
 You can modify the entry and removal criteria used by the backward and forward variable
entry methods.
Previous, Block # of #, Next You can use these options to enter independent variables in blocks
into the regression model. You can select different methods of variable entry for each block.
Example. Logistic regression will be used to determine the relationship between any use
of health services (coded 0 = no use, 1 = any use) and age, health index, gender and race.
Subjects in the study (Model Cities Data Set) were followed for a varying amount of time,
so the number of months followed (expos) will also be included as an independent variable
in the logistic regression model.
The dependent variable,
anyuse, is binary.
There are 5 independent
variables. Female and Race
are categorical/nominal
variables.
82
You can use the Categorical option to
define which variables are categorical
and SPSS will create the indicator
variables.
By default the category with the
largest numerical value (last) will be
the reference group. Here, the
category with the smallest numerical
value was selected as the reference
group.
Under Options you can select to have
the 95% confidence intervals for the
odds ratios displayed in the output.
Also, you can run the HosmerLemeshow goodness-of-fit test.
Logistic Regression
Case Processing Summary
Unweighted Cases(a)
Selected Cases
Included in Analysis
N
3199
Percent
73.1
Missing Cases
1175
26.9
Total
4374
100.0
0
.0
4374
100.0
Unselected Cases
Total
Information on the
number of observations
used in the logistic
regression. Subjects with
missing data are excluded.
a If weight is in effect, see classification table for the total number of cases.
Dependent Variable Encoding
Original Value
.00
1.00
Internal Value
0
1
SPSS will always recode the dependent variable to a 0
or 1 binary variable (internal value), and will estimate
the odds ratio for the event coded as 1 (vs the event
coded as 0). If your dependent variable is not coded 0
or 1, check this table to determine the interpretation of
the odds ratios.
83
Categorical Variables Codings
This table gives the definition of the
indicator variables. E.g.,
race(1) = other
race(2) = black
(race = white, is the reference group)
Parameter coding
race
female
Frequency
497
(1)
.000
other
455
1.000
.000
black
2247
.000
1.000
male
1450
.000
female
1749
1.000
white
(2)
.000
female(1) = female
(male is the reference group)
Caution! – Make sure you understand the interpretation of the indicator variables that
SPSS creates. It is very easy to get confused. For example, in this example the variable
race is coded 1=white, 2=other, 3=black. A common mistake would be to interpret race(1) =
white and race(2) = other.
Ignore all the output under Block 0. The output
displays information for the logistic regression
model with no independent variables in the model.
Block 0: Beginning Block
Block 1: Method = Enter
Omnibus Tests of Model Coefficients
Chi-square
Step 1
df
Sig.
Step
301.534
6
.000
Block
301.534
6
.000
Model
301.534
6
.000
Model Summary
Step
1
-2 Log
likelihood
2609.415(a)
Cox & Snell
R Square
.090
Nagelkerke R
Square
.151
Unless you are using stepwise
methods to enter variables or
entering variables in different
blocks you can ignore this output.
“R-square” measures for logistic
regression – usually not very
useful.
a Estimation terminated at iteration number 5 because parameter estimates changed by less than .001.
Classification Table(a)
Observed
Step 1
anyuse
Overall
percentage
a The cut value is .500
.00
.00
1.00
Predicted
anyuse
percent
1.00
correct
0
542
.0
0
2657
100.0
83.1
Ignore this table also. It is
describing how the logistic
regression predicts any use
if a predicted probability >
0.5 is to used to indicate
any use. All subjects are
predicted to have use.
84
Hosmer and Lemeshow Test
Step
1
Chi-square
df
Hosmer-Lemeshow goodness-of-fit
statistic is formed by grouping the
data into g groups (usually
Sig.
8.368
8
.398
Contingency Table for Hosmer and Lemeshow Test
anyuse = .00
Step 1
anyuse = 1.00
g=10) based on the
percentiles of the
estimated probabilities
and calculating the
Pearson chi-square
statistic from the 2 x g
table of observed and
estimated expected
frequencies. A small pvalue indicates a lack of
fit. Large differences
between the observed
Total
Observed
Expected
Observed
1
124
123.653
197
Expected
197.347
Observed
321
2
101
97.310
218
221.690
319
3
79
81.589
241
238.411
320
4
73
67.769
248
253.231
321
5
57
54.600
263
265.400
320
6
33
41.820
287
278.180
320
7
32
29.724
288
290.276
320
8
16
21.258
304
298.742
320
9
13
15.538
307
304.462
320
10
14
8.740
304
309.260
318
and expected values can be used to help identify where there is lack-of-fit when present.
The last table of the output usually has the results we are most interested in. It lists the
odds ratios, p-values and 95% confidence intervals for the odds ratios.
Variables in the Equation
B
S.E.
Wald
df
Sig.
Exp(B)
95.0% C.I.for EXP(B)
Lower
Step
1(a)
expos
.077
.006
age
.009
female(1)
.501
race(1)
-.424
.190
race(2)
-.530
health
.048
167.398
1
.000
1.080
1.068
1.093
.003
8.118
1
.004
1.009
1.003
1.016
.099
25.363
1
.000
1.650
1.358
2.005
12.715
2
.002
4.964
1
.026
.655
.451
.950
.149
12.689
1
.000
.588
.440
.788
.010
23.603
1
.000
1.049
1.029
1.070
-.337
.196
2.958
1
.085
.714
race
Constant
Upper
a Variable(s) entered on step 1: expos, age, female, race, health.
Exp(B) = Odds Ratio
95.0% C.I. for EXP(B) = 95% confidence interval for the odds ratio
Sig. = P-value for the individual odds ratio or the overall significant of a
categorical/nominal variable if there is no Exp(B) listed.
85
B = the logistic regression coefficient, the log odds ratio
S.E. = the standard error the of the logistic regression coefficient
Wald = the Wald test statistic for testing if B=0 (or equivalently odds ratio = 1)
or if all B’s = 0 for a categorical variable with >2 indicator variables.
d.f. = degrees of freedom of the test statistic.
It is often helpful to write on your output the definition of the indicator variables, so you
don’t get confused about the interpretation of the results. Also, helpful to change Exp(B)
to odds ratio, and sig. to P-value.
Odds
Ratio
Step
1(a)
expos
95.0% C.I.for
odds ratio
Lower
Upper
P-value
1.080
1.068
1.093
.000
age
1.009
1.003
1.016
.004
female (vs male)
1.650
1.358
2.005
.000
other vs white
.655
.451
.950
.026
black vs white
.588
.440
.788
.000
1.049
1.029
1.070
.000
race
health
.002