STATISTICS

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STATISTICS

• David Pieper, Ph.D.
• dpieper_at_med.wayne.edu

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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

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Types of Variables Ordinal Data

• Ranked or ordered
• Examples
• strongly agree, agree, disagree
• worse, no change, better
• 1st place, 2nd place, 3rd place

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Types of Variables Continuous Variables

• Have specific order
• Examples
• weight
• temperature
• blood pressure
• time
• May be converted to categorical or ordinal

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Types of Statistics

• Descriptive
• summarize data for clearer understanding
• Inferential
• generalize results from sample to population
• make probability decisions

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Descriptive Statistics

• Measures of central tendency
• mean
• mode
• median
• Measures of variability
• range
• variance
• standard deviation
• standard error

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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

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Probability and p Values

• p lt 0.05
• 1 in 20 or 5 chance groups are not different
  when we say groups are significantly different
• p lt 0.01
• 1 in 100 or 1 chance of error
• p lt 0.001
• 1 in 1000 or .1 chance of error

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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
• Fishers Exact test (2 x 2)
• Relation between 2 continuous variables
• Regression analysis or correlation

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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

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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)

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Analysis of Variance (ANOVA)

• When comparing 3 or more groups (independent
  variables) and end-point (dependent variable) is
  continuous.

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Analysis of Variance (ANOVA)
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Analysis of Variance (ANOVA)
p lt 0.001 overall there is a difference between
groups - does not tell us which groups are
different from one another
Post-hoc analysis with Tukeys multiple
comparison test A vs B p lt 0.001 A vs C p gt
0.05 (not significantly different) B
vs C p lt 0.001
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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
  Fishers Exact Test

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Is there a relationship between hypertension and
gender? Chi square analysis - p lt 0.001
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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

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Pearsons Correlation Coefficient
Is Diastolic BP related to Weight?
r 0.805 p lt 0.01
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Pearsons Correlation Coefficient

• r 0.805 does not mean weight gain causes
  increase in BP or vice versa
• Correlation does not prove cause and effect

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Name the Statistical TestDo students improve
their knowledge after a lecture, as measured by
the number of correct answers on a quiz before
and after the lecture?

1. ANOVA
2. Chi-Square
3. Paired t-test
4. Unpaired t-test

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Name the Statistical TestIs there an
association between smoking status and 3 levels
of socioeconomic status?

1. Mann-Whitney U-test
2. Pearsons correlation
3. Turkeys test
4. Chi-Square

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Name the Statistical TestIs there a
relationship between length of hospitalization
and number of medications prescribed when patient
is discharged?

1. Logistic regression
2. Pearsons correlation
3. Repeated measures ANOVA
4. Chi-Square

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Free Statistics Software

• http//freestatistics.altervista.org/click/fclick.
  php?fid4

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Illustrations

• 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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Girls
Boys