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STATISTICS
David Pieper, Ph.D.
[email protected]
Types of Variables
Categorical Variables

Organized into category

No necessary order

No quantitative measure

Examples
 male,
female
 race
 marital
status
 treatment
A and treatment B
Types of Variables
Continuous Variables

Have specific order

Examples:
 weight
 temperature
 blood
pressure
 Age
 Test

score
May be converted to categorical or ordinal
Descriptive Statistics

Measures of central tendency
 mean

(average)
Measures of variability
 range
 standard
deviation
Results of Memory Test
Age
Gender
Age
Group
Student
or Parent
Total
Score
17
M
HS
S
52
16
M
HS
S
49
30
F
Adult
P
50
16
M
HS
S
47
43
F
Adult
P
41
36
M
Adult
P
51
16
F
HS
S
43
43
F
Adult
P
41
36
F
Adult
P
33
Descriptive Statistics for
Memory Test
Age
Total Score
196
196
Minimum
7
12
Maximum
72
54
24.9
37.4
16
8
Number of Cases
Mean
SD
Research Hypothesis

Null hypothesis: relationship among
phenomena does not exist

Example: Age does not have an
influence on memory
Probability and p Values

p < 0.05
1
in 20 or 5% chance groups are not
different when we say groups are
significantly different

p < 0.01
1

in 100 or 1% chance of error
p < 0.001
1
in 1000 or .1% chance of error
Type of Statistical
Test to Use


Continuous variable as end point
2
groups: t-test
3
or more groups: ANOVA
Relation between 2 categorical variables:
 Chi-square
 Fisher’s

test
Exact test (2 x 2)
Relation between 2 continuous variables:
 Regression
analysis or correlation
T-test

When comparing 2 groups and endpoint variable is continuous

Purpose is determine if the difference
between the 2 groups is unlikely due to
chance
T-test

Examples:

Blood pressure before and after exercise
program

Would parents do better on a memory test
than students
Results of Memory Test
Age
Gender
Age
Group
Student
or Parent
Total
Score
17
M
HS
S
52
16
M
HS
S
49
30
F
Adult
P
50
16
M
HS
S
47
43
F
Adult
P
41
36
M
Adult
P
51
16
F
HS
S
43
43
F
Adult
P
41
36
F
Adult
P
33
T-test results comparing Parents
and Students Total Score
Number
Mean
SD
Students
117
36.3
7.5
Parents
79
39.1
8.1
p < 0.02
Parents had higher scores than students
Analysis of Variance
(ANOVA)

When comparing 3 or more groups and
end-point is continuous

Example: Compare score on memory
test among:
 Grade
school students
 Middle school students
 High school students
 Parents
Total Score
Analysis of Variance p < 0.03
High School Students and Adults scored better
than Grade School or Middle School Students
Chi-square Test

When comparing 2 or more groups and
the end point is categorical
Chi-square Gender
and Parent vs Student
Student Parent
Total
Female
65
48
113
Male
52
31
83
Total
117
79
139
p = 0.5
There was no significant gender
difference between students and
parents
Correlation or Regression

When determining if there is a linear
relationship between 2 continuous variables

Ranges from -1 to 1
Pearson’s Correlation Coefficient
Diastolic BP (mm)
Weight (kg)
90
82
140
114
68
56
110
62
100
83
95
110
Is Diastolic BP related to Weight?
r = 0.805 p < 0.01
Correlation of Age and Score on Memory Test
r = 0.6
No correlation of age and score on memory test
Illustrations: Use Graphs
p < 0.01
Figure 1: Patients that failed the
exercise test had a higher mortality
than patients that passed
• Label axes
• Include brief
description
Free Statistics Software
Mystat: http://www.systat.com/MystatProducts.aspx
List of Free Statistics Software:
http://statpages.org/javasta2.html