 # David Pieper, Ph.D. dpieper@med.wayne.edu STATISTICS David Pieper, Ph.D. dpieper@med.wayne.edu.

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David Pieper, Ph.D. dpieper@med.wayne.edu
STATISTICS David Pieper, Ph.D.

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 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 Inferential
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 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
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)

Analysis of Variance (ANOVA)
p < 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

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 Coefficient
Is Diastolic BP related to Weight? r = p < 0.01

Pearson’s Correlation Coefficient
r = does not mean weight gain causes increase in BP or vice versa Correlation does not prove cause and effect

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? 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? Mann-Whitney U-test Pearson’s correlation Turkey’s test Chi-Square *

Pearson’s correlation * Repeated measures ANOVA Chi-Square
Name the Statistical Test Is there a relationship between length of hospitalization and number of medications prescribed when patient is discharged? Logistic regression Pearson’s correlation * Repeated measures ANOVA Chi-Square

Free Statistics Software

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

Girls Boys