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STATISTICS
David Pieper, Ph.D.
[email protected]
Types of Variables
Categorical Variables
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Organized into category
No necessary order
No quantitative measure
Examples
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male, female
race
marital status
treatment A and treatment B
Types of Variables
Ordinal Data
• Ranked or ordered
• Examples:
– strongly agree, agree, disagree
– worse, no change, better
– 1st place, 2nd place, 3rd place
Types of Variables
Continuous Variables
• Have specific order
• Examples:
–
–
–
–
weight
temperature
blood pressure
time
• May be converted to categorical or ordinal
Types of Statistics
• Descriptive
– summarize data for clearer understanding
• Inferential
– generalize results from sample to
population
– make probability decisions
Descriptive Statistics
• Measures of central tendency
– mean
– mode
– median
• Measures of variability
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range
variance
standard deviation
standard error
Research Hypothesis
• Null hypothesis: relationship among
phenomena does not exist
• Example: kids who attend daycare have
no greater incidence of colds than kids
who do not attend daycare
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 test
– Fisher’s Exact test (2 x 2)
• Relation between 2 continuous variables:
– Regression analysis or correlation
T-test
• When comparing 2 independent
groups and end-point variable
(dependent variable) is continuous
• Purpose is determine if the
difference between the 2 groups is
unlikely due to chance
• May be paired or unpaired
T-test
• Example:
• Blood pressure before and after
exercise program (paired t-test)
• Compare blood pressure in a group
undergoing cardiac rehab to a
control group not undergoing rehab
(unpaired t-test)
Analysis of Variance
(ANOVA)
When comparing 3 or more groups
(independent variables) and end-point
(dependent variable) is continuous.
Analysis of Variance (ANOVA)
Treatment A Treatment B Treatmnet C
Patient 1
25
10
23
Patient 2
30
13
28
Patient 3
32
15
30
Patient 4
26
14
32
Patient 5
24
15
25
Analysis of Variance
(ANOVA)
mean 
SE
Treatment A
Treatment B
Treatmnet C
27.4  1.5
13.4  0.9
27.6  1.6
p < 0.001 overall there is a difference between
groups - does not tell us which groups are
different from one another
Post-hoc analysis with Tukey’s multiple comparison
test
A vs B p < 0.001
A vs C p > 0.05 (not significantly different)
B vs C p < 0.001
Chi-square Test
• When comparing 2 or more groups and
the dependent variable is categorical
• Minimum frequency in any cell must be
at least 5
• If less than 5 and a 2 x 2 analysis - use
Fisher’s Exact Test
Male Female
Hypertensive
35
17
Not Hypertensive
22
68
Is there a relationship between hypertension and gender?
Chi square analysis - p < 0.001
Correlation or Regression
• When determining if there is a linear
relationship between 2 continuous variables
• Ranges from -1 to 1
• Assumptions:
– Relationship is linear
– Random variables
Pearson’s Correlation Coefficien
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
Pearson’s Correlation
Coefficient
• r = 0.805 does not mean weight gain
causes increase in BP or vice versa
• Correlation does not prove cause and
effect
Type of Variable
Descriptive Statistics
Central
Tendency
Nominal
(Categorical)
(Non-parametric)
Variability
Compare Groups
 3 groups
1 or 2 groups
2
2
Mode
Relationship of
Groups
Fisher’s Exact Test
Mode
Ordinal
(Ranks)
Standard
deviation
Kruskal-Wallis
Spearman’s Rank Order
Confidence
Interval
t-test
ANOVA
Pearson’s r
Median
Mean
(Continuous)
(Parametric)
Mann-Whitney
Wilcoxon
Median
Mode
Interval
or
Ratio
Range
Standard
error
Variance
Range
Regression
Name the Statistical Test
Do students improve their knowledge after a lecture,
as measured by the number of correct answers on a
quiz before and after the lecture?
a.
b.
c.
d.
ANOVA
Chi-Square
Paired t-test *
Unpaired t-test
Name the Statistical Test
Is there an association between smoking status and
3 levels of socioeconomic status?
a.
b.
c.
d.
Mann-Whitney U-test
Pearson’s correlation
Turkey’s test
Chi-Square *
Name the Statistical Test
Is there a relationship between length of
hospitalization and number of medications
prescribed when patient is discharged?
a. Logistic regression
b. Pearson’s correlation *
c. Repeated measures
ANOVA
d. Chi-Square
Free Statistics Software
http://freestatistics.altervista.org/click/fclick.php?fid=4
Illustrations
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Graphs - not tables
Replace keys with direct labels
Use color
Each axis must have a label
with units
• Each graph must have a legend
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CFR
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Exam Score (%)
100
Girls
80
60
Boys
40
20
0
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Feb
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Month
April