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```LSP 121
Intro to Statistics and SPSS
Statistics
• One of many definitions:
The mathematics of collecting and analyzing
data to draw conclusions and make
predictions.
• It involves looking at quantified data and
determining if there are any patterns.
Descriptive Statistics
(some of these are used as predictors)
• Mean - average
• Median – the middle score
• Percent Rank – calculates the position of a
datapoint in a data set. More precisely, tells
you approximately what percent of the data is
less than the datapoint.
• Range – difference between the maximum
and minimum values in the data set
The mean or the median?
• Advantages of the median are:
· If one of the extreme values changes, then the
median remains unaltered. Whereas the mean
would be affected hugely.
· If a set of numbers has a lop-sided pattern – if for
example, most of the scores are small, several
medium sized, but only one or two high – then the
median may again be more appropriate than the
mean, as its value will be close to the majority of
numbers
Descriptive Statistics
• Lower quartile – or first quartile, it is the
median of the data values in the lower half of
a data set
• Middle quartile – or second quartile, this is
the overall median
• Upper quartile – or third quartile, it is the
median of the data values in the upper half of
a data set
• Quartiles may help in seeing the variation in a
data set
Quartiles
• For example (bank waiting times):
lower quartile
Big Bank:
median
upper quartile
4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0
Best Bank: 6.6 6.7 6.7 6.9 7.1 7.2 7.3 7.4 7.7 7.8 7.8
Big Bank range: 11.0 – 4.1 = 6.9
Best Bank range: 7.8 – 6.6 = 1.2
Descriptive Statistics
• The Five Number Summary consists of:
– The minimum value
– The lower quartile (first quartile)
– The median (second quartile)
– The upper quartile (third quartile)
– The maximum value
• In SPSS, first quartile is 25th percentile, second
quartile is 50th percentile, and third quartile is 75th
percentile
Standard Deviation
• Quartiles are OK for characterizing data, but
standard deviation is preferred by statisticians
• It is a measure of how far data values are
spread around the mean of a data set
• Don’t calculate by hand, use SPSS
Standard Deviation
• A simple way to estimate standard deviation is
the range estimate rule
• Divide range by 4
• Watch for outliers. These are too high or too
low values.
• If a value is more than 2*std above or below
the mean, it could possibly be an outlier.
Calculate: mean + 2*STD and mean – 2*STD
Look for outliers, how?
•
•
•
•
•
•
•
•
Find the mean
Find the standard deviation
high = mean + 2 * STD
low = mean – 2 * STD
e.g., mean = 124, STD = 32, then
high = mean + 2*32 = 124 + 64 = 188
low = mean – 2*32 = 124 – 64 = 60
look for values >188 and values <60
Estimate Standard Deviation
• Go back to Big Bank / Best Bank example
– Big Bank: range = 6.9
– 6.9 / 4 = 1.7
– Actual standard deviation is 1.96
• Best Bank: range = 1.2
– 1.2 / 4 = 0.3
– Actual standard deviation is 0.44
Normal ‘bell curve’
numbers, from -4 to 4, represent the standard deviations units
normal curve with std
region of bell curve: +/- 1 std
(2 * 34.13 % = 68.3%)
region of bell curve: +/- 2 std
(2*13.59%+2*34.13% = 95.4%)
red: < 2 std or > 2 std from the mean
Histograms
• Nice way to view a data set
• A histogram is a chart similar to a dotplot
created by defining a set of bins and counting
how many data points lie in each bin. Bars are
drawn with height proportional to the number
of data points in each bin.
Example Histogram
Statistics and SPSS
• While Excel can do some basic statistics, it is
not considered a serious statistics tool
• You really should use something like SPSS
(statistical package for social sciences)
• We will be using SPSS since DePaul has a site
Try this example
QRC website (under older data) and start SPSS
• Import the Excel data into SPSS
• Change the variable names and set data to
numeric (not text)
• Click on Analyze -> Descriptive Statistics ->
Frequencies
Example continued
• When importing data, if the numeric fields
show as ‘\$’, ‘%’, or ‘#’, then PASW will have
difficulty converting to numeric
• In most cases, SPSS will briefly display dollar
signs indicating that conversion is taking place.
Example continued
• Using the grades for Exam 2, find the
– 5 number summary (minimum, 1st quartile,
median, 3rd quartile, maximum)
– mean
– range, and
– standard deviation
SPSS results
Some interesting tools
• Random coin flipper
http://www.random.org/coins/
• simulation of rolling pairs of dice
• http://www2.whidbey.net/ohmsmath/webwo
rk/javascript/dice2rol.htm
• check for bell curve with dice
ngscience/flash/sumdice.html
Pivot Tables/Crosstabs
• Next topic pivot tables and crosstabs
Pivot Tables
• Suppose you have just performed a survey.
• One of the questions you ask is, what type of
home computer connection do you have?
• Answers can be: none, dial-up, dsl, cable,
other, not sure.
Pivot Tables
• Here are some of your results
Respondent ID
11111
11112
11113
11114
11115
11116
Cable Type
no
ds
cm
dk
du
du
Where no = none; ds = dsl; cm = cable modem;
du = dial up; dk = don’t know; ot = other
Frequency Tables
• SPSS can be used to count the occurences of
data, similar to pivot table in Excel
• Enter or import data into SPSS
• Use Analyze -> Descriptive Statistics ->
Frequencies
• Select variables, move from left box to the
right . Uncheck Display Frequencies Table
• Run it
Crosstabulations
(Crosstabs)
• Crosstabs are an extension of pivot tables
• Suppose you have asked a number of
students: How many schools did you apply to?
• You get results something like the following (in
Crosstabs
Respondent ID
1
2
3
4
5
6
7
8
9
10
11
Sex
F
M
F
F
M
M
F
F
F
M
M
Number of Schools
3
3
4
1
2
5
4
2
3
5
6
Crosstabs
• Now open the data in SPSS (import survey1.xls
from class D2L)
• Then pull down the menu Analyze and click on
Descriptive Statistics, then Crosstabs
• What variable do you want in the row? The
column?
• When ready, click OK to perform the crosstab
Crosstabs in Access
• You can also perform cross-tabulations using
an Access (Microsoft database app)
• You need to create a crosstab query*
• In the Show Table dialog box, click the tab that
lists the table whose data you want to work
with.
*query is a tool for extracting information from your database
Crosstabs in Access
• Add the fields to the Field row in the design
grid. Note: Since we want to perform a
crosstab query on ‘Sex’ and ‘Number of
Schools’, bring the field ‘Sex’ down once and
‘Number of Schools’ down twice.
Crosstabs
• Click on the Query drop down menu and select
Crosstab Query.
• Now, under Crosstab under the Sex column, click on
Column Heading. Under the first Number Schools
Crosstab, click on Row Heading. Under the second
Number Schools Crosstab, click on Value. On this
second Number Schools column, click on Group By
and select Count.
• Run the Query
```
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