1. CORRELATIONAL RESEARCH II Relations in Observational and Survey Research Lawrence R. Gordon Psychology Research Methods I

2. Brief Review from Last Class n Correlational analysis –Pearson r –Scatterplots –Special problems Restricted range Mixtures of Ss n Regression analysis –Line of “best fit” –Prediction equation –Rsq (r 2 ) as predictable variance n Continuing ….

3. Interpretation and Other Goodies n Causality: e.g. TV watching and violence Directionality Y  X or X  Y ? Third variable Z  X AND Z  Y ? n Major uses Psychological testing and scaling (measurement) Personality and abnormal psychology Psychogenetics -- “nature/nurture” n Correlational research is a methodology and Correlation & regression are statistical tools Corr Res  Corr/Regr E.g. t-test 

4. “HAVING FUN” EXAMPLE n MORE Fun mean time estimated = 8.6 n LESS Fun mean time estimated = 12.5 n ARE THESE MEANS “DIFFERENT”? n YES - more now

5. ANSWERS REVISITED “Having Fun” Example Inferential Statistics

6. Another view of “Having Fun”

7. “Having Fun” with Regression

8. Goodies, cont... n Extensions Multiple regression –Add additional predictors –Predict GPA -- SATs, HS rank, Score on Essay Factor analysis –Look for “structure” among many correlations –E.g. CBCL -- Internalizing/Externalizing n Now let’s move on to a different topic in correlational research – analysis of nominal data 

9. Treating Nominal Data n Surveys and observational studies often produce nominal (categorical) data n Major procedures for its analysis include tabulation and crosstabulation followed by “chi-square” tests n Examples: Views on an editorial (Howell,1999) –Favor vs. Opposed -- single variable tabulation –Favor vs. Opposed BY Respondent’s Own View -- two variable crosstabulation

10. CATEGORICAL DATA n Examples…general, “dichotomies” n Counts (frequencies) in Categories –Mutually exclusive –Exhaustive –“Nominal” data n Often phrased as questions about percentages or proportions, or relationships between variables

11. Treating Nominal Data n Surveys and observational studies often produce nominal (categorical) data n Major procedures for its analysis include tabulation and crosstabulation followed by “chi-square” tests n Examples: Views on an editorial (Howell,1999) –Favor vs. Opposed -- single variable tabulation –Favor vs. Opposed BY Respondent’s Own View -- two variable crosstabulation

12. Chi-Square Formula n Ta da  n Two major cases: –One-variable df = c-1, c is # of categories –Two-variable df = (r-1)(c-1), r is # of rows and c is # of columns {actually r is # of categories of the “row” variable, and c of the “column” variable}

13. Treating Nominal Data n Surveys and observational studies often produce nominal (categorical) data n Major procedures for its analysis include tabulation and crosstabulation followed by “chi-square” tests n Examples: Views on an editorial (Howell,1999) –Favor vs. Opposed -- single variable tabulation –Favor vs. Opposed BY Respondent’s Own View -- two variable crosstabulation

14. Example: Tabulation of a Single Variable A “vaguely worded newspaper editorial” was read by 100 student participants who were asked whether overall it favored or opposed the unrestricted dissemination of birth control information:

15. CASE: Single Variable n If a dichotomy, question is usually proportion or %-age of cases in one of the categories (e.g., Yes, True, Correct, M, Smokes, Head, Hit, etc.) n Null hypothesis - specifies a distribution (“chance,” predicted, earlier findings) n Test - do the data “fit” the null distribution? If not (higher, or p “small enough”), Reject H0.

16. Single Variable Computation A “vaguely worded newspaper editorial” was read by students who were asked whether it favored or opposed unrestricted dissemination of birth control information:

17. Single Variable SPSS Computation Single Variable Chi-Square Test

18. M & M  COLORS EXAMPLE n Fricker (1996) “The mysterious case of the blue M&Ms  ” Chance, 9, 19-22. –Evidence that proportions of colors differed from those publicized by the M&M/Mars Co. n Peanut king-size bag expected colors: 20% for Br Y R Blue, 10% for O, G n Results of personal test …SPSS

19. M & M  COLORS EXAMPLE: SPSS

20. Next Example: Two Variables Now, ALSO ask students about their own view on the issue of the unrestricted dissemination of birth control information...

21. CASE: Two Variables n Cases are “cross-classified” (or “cross- tabulated”) into r rows (categories of the first variable) and c columns (categories of the second variable). Cell entries are counts. Referred to as an “r x c table” (e.g. “2x3”). n df = (r-1) x (c-1) If df=1, what size table? n Null hypothesis -- the two variables are “independent” in that they do NOT predict one another. This is like a zero correlation.

22. Two Variable EXAMPLES n Political “exit” poll -- what is the null hypothesis of “independence”?

23. Two Variable EXAMPLES n Political “exit” poll -- what is the null hypothesis of “independence”?

24. Howell Example: Two Variables Now, ALSO ask students about their own view on the issue of the unrestricted dissemination of birth control information... df = #R-1  #C-1= (2-1)(2-1) = 1

25. Crosstabs --- SPSS

26. Crosstabs --- SPSS (cont…) This is a Pearson r!

27. WRAPUP ON CHI-SQUARE n Assumptions –Sufficient expected frequencies –Independent observations n Statistics used for -- –Test: chi-square or –Description: percentage or proportion n Doolittle (1887) -- the meaning of “association” (“thus and so”) 

28. Doolittle (1887) “Having given the number of instances respectively in which things are both thus and so, in which they are thus but not so, in which they are so but not thus, and in which they are neither thus nor so, it is required to eliminate the general quantitative relativity inhering in the mere thingness of the things, and to determine the special quantitative relativity subsisting between the thus-ness and the so-ness of the things.”