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

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

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 49 30 F Adult P 50 47 43 41 36 51 33

Descriptive Statistics for Memory Test Age Total Score Number of Cases 309 Minimum 7 12 Maximum 72 54 Mean 24.9 38.0 SD 16 8

Research Hypothesis Null hypothesis: relationship among phenomena does not exist Example: Age does not have an influence on memory

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 Relation between 2 continuous variables: Regression analysis or correlation

T-test When comparing 2 groups and end-point variable is continuous Purpose is to 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

T-test results comparing Parents and Students Total Score Number Mean SD Students 180 37.0 8.0 Parents 129 39.5 7.9 p < 0.05 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 < 0.001 High School Students and Adults scored better than Grade School or Middle School Students Middle School Students scored better than Grade School Students

Chi-square Test When comparing 2 or more groups and the end point is categorical

Chi-square Gender and Parent vs Student Total Female 101 (56%) 77 (60%) 142 Male 79 (44%) 52 (40%) 103 140 105 245 Percent P = 0.6 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 Is Diastolic BP related to Weight? r = 0.805 p < 0.01

(mm Hg) (kg) (

Correlation of Age and Score on Memory Test No correlation of age and score on memory test

Illustrations: Use Graphs Label axes Include brief description p < 0.01 Patients that failed the exercise test had a higher mortality than patients that passed

Free Statistics Software Systat: https://systatsoftware.com/downloads/download-systat/ List of Free Statistics Software: http://statpages.org/javasta2.html