Chapter 4

1. Chapter 4 Norms, Correlation, And Inference

2. Different types of correlation coefficient • Pearson’s r is applicable to measure the association between two continuous-scaled variables. • Spearman is suitable to rank-order/ordinal data; not affected by sample size.

3. Different types of correlation coefficient • But when you have one binary variable (e.g. “yes/no”, “male/female”) and one continuous-scaled variable, the point biserial correlation (PBC) or biserial correlation (BC) coefficient should be used instead. • In the point biserial correlation coefficient the binary variable should be "naturally" dichotomous, such as gender. • If the binary variable is artificially dichotomized, this variable may be viewed as having an underlying continuity. For example, an instructor may use a cut score to classify the examinees into “pass” and “fail”. In this case, the biserial correlation is the more appropriate approach.

4. Different types of correlation coefficient • If you have a 2X2 table and hence both variables are binary (dichotomous), then you need Phi coefficient. • If you are categorical data and they are binary or multiple levels (e.g., race, academic rank), then you need Cramer’s V.

5. correlation of .83

6. correlation of .83

7. correlation of .83

8. correlation of .83

9. Misconception: small is insignificant • It is important to point out that sometimes even a very low correlation may have clinical significance. For example, Thomas Holmes and Richard Rahe investigated over 5,000 medical patients to see whether stress might cause sickness. Patients were asked to tally a check list of 43 life events. It was found that there was a positive correlation of 0.118 between these two variables. Based on this finding, the Holmes-Rahe Stress Scale was developed and validated. 0.118? What a big deal! But in clinical psychology or medical research, we must pay attention to even such a small correlation.http://www.harvestenterprises-sra.com/The%20Holmes-Rahe%20Scale.htm

10. In-class activity • Download the data set “visualization_data.jmp” from http://www.creative-wisdom.com/teaching/480 /. • In JMP use “matched-pairs” to get the Pearson’s correlation coefficient of scores and GPA. • In JMP use Multivariate statistics to compute Pearson’s coefficient, and the confidence interval. • Use Fit Y by X to run a simple regression model. Use scores as the dependent variable (Y) and GPA as the independent variable (X). Select Fit Line from the red triangle to get the regression result. Can GPA predict test scores? • Use 95% density ellipse to identify the concentration pattern of the data. Are there any outliers? If so, please exclude them and re-run the regression model. Is the result different?

11. Single study vs. meta-analysis • We cannot treat the conclusion based on a single study as the last word. Indeed, different studies on the same topic may yield different and even contradictory results. Meta-analysis is a way of synthesizing diverse results by computing the effect size. • Effect size can be conceptualized as a standardized difference. You cannot compare between apples and organs. In order to compare oranges against oranges, you need to look at the difference in terms of a standard (e.g. SD, variance).

12. Example of how meta-analysis is applied

13. How can we determine effect size?

14. How can we determine effect size? • Today the most popular effect size is Cohen’s d. • Good news: You don’t need to worry about doing a hand-calculation of effect size. There are plenty of online effect size calculators. E.g. http://www.uccs.edu/~lbecker/

15. In-class activity • You want to conduct a meta-analysis of three studies based on the following information: • Use the online effect size calculators to compute the Cohen’s d of each study. Average all three effect sizes. Does the treatment work?