CORRELATIONAL RESEARCH I Lawrence R. Gordon Psychology Research Methods I

“The Two Disciplines…” n Complete that phrase? n What are they? –Experimental psychology –Correlational psychology n These have “typical” stats, but either might use any given statistical test, depending on the questions asked

Two Research “Disciplines”: Experimental vs. Correlational n Manipulated IV n Indiv differences minimized (“error”) n Try to find general laws n Often use “means” and associated statistics (t, F) n Selected variables n Indiv differences studied n Try to find how people differ n Often use correlation and regression Merger -- how indiv diffs (organismic, “P” vars) interact with manipulations (treatment, “E” vars); e.g., PxE designs.

Correlation n Descriptive -- Pearson product-moment correlation coefficient, r n Values: -1 __________ 0 _________ +1 n Visualization: SCATTERPLOTS n Inferential -- is obtained r unlikely from a population with a correlation of 0 (H 0 :  =0)? n EXAMPLE -- our midterm exams

Correlation (cont…) n EXAMPLE… –Our midterm exams: First vs. Second

Correlation (cont…) n Issues: –Restriction of range –Mixtures of subjects –Assumes linearity of relationship n EXAMPLES

Corr: Restriction of range –Relate NC scale and CFC scale –But what if we use only those with NC scores between 50 and 75? (18-90 poss.) Unrestricted Restricted

Corr: Restriction of range (cont…) =Unrestricted r =.40, Range Restricted r =.29, Range 50-75

Corr: Mixtures of subjects n Relate height and weight (r=.67) n But has both females and males For females only, r =.47 For males only, r =.68

REGRESSION ANALYSIS

Regression (cont…) n The “best-fitting” line to predict Y from X: –Nomenclature: Y “criterion”, X “predictor” variables –Y’ = a + bX –a is the intercept (where line crosses Y axis, X=0) –b is the slope (change in Y when X changes by 1) –Y’ is a PREDICTED Y value - may be compared to the actual Y (Y-Y’ deviations) –a and b are those numbers that minimize the sum of all N of these squared deviations -- “least squares” –the line ALWAYS passes though the means of Y and of X –For same data, X’ = a + bY is a different regression n Two points determine a line!

REGRESSION ANALYSIS Y= a + bX II= I

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 but Correlation & regression are statistical tools Corr Res  Corr/Regr E.g. t-test 

“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

ANSWERS REVISITED “Having Fun” Example Inferential Statistics

Another view of “Having Fun”

Goodies, cont... n Extensions Multiple regression Factor analysis n Further information: G9 n More next class!