1. Statistical Analysis KSE966/986 Seminar Uichin Lee Oct. 19, 2012

2. Overview Preparing data for statistical analysis Descriptive statistics Comparing means T tests Analysis of variance (ANOVA) Assumptions of t tests and F tests Identifying relationships Regression Nonparametric statistical tests

3. Preparing data for analysis Cleaning up data – Detect errors – Formatting Coding – Types of data that need to be coded – Be consistent Organizing the data – Accommodate to the requirements of statistical software

4. Descriptive statistics Measures of central tendency – Mean – Median – Mode Measures of spread – Range – Variance – Standard deviations

5. Recap: basic design structure

6. Comparing means Summary of methods

7. Comparing 2 means: T tests Independent-samples t test: between-group design 9 10 11 12 13 14 15 16 Results: t = 2.1688, df = 15, p-value = 0.04781 How to report? An independent-samples t test suggests that there is significant difference in the task completion time between the group who used the standard word processing s/w and the group who used the prediction software (t(15) = 2.169, p<0.05)

8. Comparing 2 means: T tests Paired-sample t test: within-group design Results: t = 2.6313, df = 7, p-value = 0.03385 How to report? A paired t test suggests that there is significant difference in the task completion time between the standard word processing s/w and the prediction software (t(7) = 2.631, p<0.05)

9. Comparing 2 or more means: Analysis of variance (ANOVA) Also called F tests One-way ANOVA: for between-group design Data layout: Table 4.6 Results summary:

10. 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

11. Factorial ANOVA For between-group design 2 or more independent variables involved Data layout: table 4.9

13. Factorial ANOVA Summary results

14. Repeated measures ANOVA For within-group design Can investigate one or more variables One-way ANOVA

15. Repeated measures ANOVA One way ANOVA summary report:

16. Repeated measures ANOVA Two way ANOVA experiment design:

17. Two way ANOVA data layout Repeated measures ANOVA

18. Two way ANOVA summary report:

19. Split-plot ANOVA Involves both between-group and within-group factors Experiment design

20. Split-plot ANOVA data layout

21. Split-plot ANOVA summary report

22. Assumptions of t tests and F tests Errors should be independent of each other Errors should be identically distributed Errors should be normally distributed

23. Identify relationships Correlation: Two factors are correlated if there is a relationship between them Most commonly used test for correlation is the Pearson’s product moment correlation coefficient test Pearson’s r: ranges between -1 to 1 Pearson’s r square represents the proportion of the variance shared by the two variables

24. Identify relationships Correlation does not imply causal relationship

25. Identify relationships Regression: can investigate the relationship between one DV and multiple IVs Regression is used for 2 purposes: – Model construction – Prediction Different regression procedures – Simultaneous – Hierarchical

26. Non-parametric tests Non-parametric tests are used when: – The error is not normally distributed – The distances between any two data units are not equal – The variance of error is not equal

27. Non-parametric tests Chi-square test – Used to analyze categorical data – Table of counts (contingency table) – Assumptions of the test Data points need to be independent The sample size should not be too small

28. Non-parametric tests Two groups of data – For between-group design: Mann–Whitney U test or the Wald–Wolfowitz runs test – For within-group design: Wilcoxon signed ranks test Three or more groups of data – For between-group design: Kruskal–Wallis one- way analysis of variance by ranks – For within-group design: Friedman’s two-way analysis of variance test