Correlation Coefficients
Introduce the concepts of positive, zero, and
negative correlations with examples (eating and weight, the number
of notes they take and the price of tea in China, number of suicidal
thoughts and happiness). You can also have them learn about correlation coefficients by using the authors' tutorial called " The Correlator."
Alternatively, you could one or more of the following online tutorials:
Next, have every student state a
relationship between the two variables and then tell us whether this
relationship is positive, zero, or negative. Then, graphically
demonstrate the concepts with scatterplots. Then, give them positively, zero, and negatively related data sets and have them
compute Spearman's rho (because it's simpler to calculate than
Pearson's r). Finally, show how Pearson's r makes better use of the
data than rho when there is continuous interval data.
Once students understand the Pearson r, you could discuss the following three topics:
- The different types of correlation coefficients. These are summarized in table 6-4 (p. 162).
- The coefficient of determination. Begin by showing students that +1 and -1 relationships are perfect, so r-squared for each of them should be (and is) 1.00. Zero correlations indicate no relationship, so knowing one variable shouldn't help at all in knowing the other variable (and zero squared is zero). Having thus reviewed two essential points about correlation coefficients (#1 negative correlations are not weaker than positive correlations and #2 zero correlations indicate no relationship), go on to discuss the r-squared's commonly found in psychology (.09 to .25). Explain that although these r-square's indicate that we fail to account for a great deal of the variabity in human behavior, that's to be expected because (1) we have measurement error, and (2) we wouldn't expect a single variable (e.g., IQ) to account for all the variance in another variable (college performance). From this point, go on to debate the value ot the SATs, the utility or futility of using r-squared to address the nature-nurture controversy (emphasizing the notions of correlation and causality and apparent size of effect and restriction of range); whether r-squared might be more informative than p values, or multiple regression.
- Multiple regression. Two useful references are
Cohen, J. & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
Kachigan, S. K. (1982). Multivariate statistical analysis: A conceptual introduction.
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