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

2. Types of Variables Categorical Variables n Organized into category n No necessary order n No quantitative measure n Examples F male, female F race F marital status F treatment A and treatment B

3. Types of Variables Continuous Variables n Have specific order n Examples: u weight u temperature u blood pressure u Age u Test score n May be converted to categorical or ordinal

4. Descriptive Statistics n Measures of central tendency u mean (average) n Measures of variability u range u standard deviation

5. Results of Memory Test AgeGenderAge Group Student or Parent Total Score 17MHSS52 16MHSS49 30FAdultP50 16MHSS47 43FAdultP41 36MAdultP51 16FHSS43 FAdultP41 36FAdultP33

6. Descriptive Statistics for Memory Test AgeTotal Score Number of Cases196 Minimum712 Maximum7254 Mean24.937.4 SD168

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

8. Probability and p Values n p < 0.05 u 1 in 20 or 5% chance groups are not different when we say groups are significantly different n p < 0.01 u 1 in 100 or 1% chance of error n p < 0.001 u 1 in 1000 or.1% chance of error

9. Type of Statistical Test to Use n Continuous variable as end point u 2 groups: t-test u 3 or more groups: ANOVA n Relation between 2 categorical variables: u Chi-square test u Fisher’s Exact test (2 x 2) n Relation between 2 continuous variables: u Regression analysis or correlation

10. T-test n When comparing 2 groups and end- point variable is continuous n Purpose is determine if the difference between the 2 groups is unlikely due to chance

11. T-test n Examples: n Blood pressure before and after exercise program n Would parents do better on a memory test than students

12. Results of Memory Test AgeGenderAge Group Student or Parent Total Score 17MHSS52 16MHSS49 30FAdultP50 16MHSS47 43FAdultP41 36MAdultP51 16FHSS43 FAdultP41 36FAdultP33

13. T-test results comparing Parents and Students Total Score NumberMeanSD Students11736.37.5 Parents7939.18.1 p < 0.02 Parents had higher scores than students

14. Analysis of Variance (ANOVA) n When comparing 3 or more groups and end-point is continuous n Example: Compare score on memory test among: u Grade school students u Middle school students u High school students u Parents

15. Analysis of Variance p < 0.03 High School Students and Adults scored better than Grade School or Middle School Students Total Score

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

17. Chi-square Gender and Parent vs Student StudentParentTotal Female6548113 Male523183 Total11779139 p = 0.5 There was no significant gender difference between students and parents

18. Correlation or Regression n When determining if there is a linear relationship between 2 continuous variables n Ranges from -1 to 1

19. Pearson’s Correlation Coefficient Is Diastolic BP related to Weight? r = 0.805 p < 0.01

20. Correlation of Age and Score on Memory Test r = 0.6 No correlation of age and score on memory test

21. Illustrations: Use Graphs Label axes Include brief description Figure 1: Patients that failed the exercise test had a higher mortality than patients that passed p < 0.01

22. Free Statistics Software Mystat: http://www.systat.com/MystatProducts.aspx List of Free Statistics Software: http://statpages.org/javasta2.html