Chapter 15 Cousins or Just Good Friends? Testing Relationships Using the Correlation Coefficient Part IV Significantly Different: Using Inferential Statistics

What you will learn in Chapter 15 How to test the significance of the correlation coefficient The interpretation of the correlation coefficient Using SPSS to analyze correlational data…and interpret the results The distinction between significance and meaningfulness (Again!) How to test the significance of the correlation coefficient The interpretation of the correlation coefficient Using SPSS to analyze correlational data…and interpret the results The distinction between significance and meaningfulness (Again!)

The Correlation Coefficient Remember…correlations examine the relationship between variables, they do not attempt to determine causation Examine the “strength” of the relationship Range from -1 to +1 Direct relationships Positive correlations Indirect relationships Negative correlations Remember…correlations examine the relationship between variables, they do not attempt to determine causation Examine the “strength” of the relationship Range from -1 to +1 Direct relationships Positive correlations Indirect relationships Negative correlations

Path to Wisdom & Knowledge

Computing the Test Statistic Use the Pearson formula H 0 : ρ xy = 0 H 1 : r xy ≠ 0 Use the Pearson formula H 0 : ρ xy = 0 H 1 : r xy ≠ 0

So How Do I Interpret… r (27) =.393, p <.05? r is the test statistic 27 is the degrees of freedom.393 is the obtained value p <.05 is the probability r (27) =.393, p <.05? r is the test statistic 27 is the degrees of freedom.393 is the obtained value p <.05 is the probability

Causes and Associations (Again!) Just because two variables are related has no bearing on whether there is a causal relationship. Example: Quality marriage does not ensure a quality parent- child relationship Two variables may be correlated because they share something in common…but just because there is an “association” does not mean there is “causation.” Just because two variables are related has no bearing on whether there is a causal relationship. Example: Quality marriage does not ensure a quality parent- child relationship Two variables may be correlated because they share something in common…but just because there is an “association” does not mean there is “causation.”

Significance Versus Meaningfulness (Again, Again!!) Even if a correlation is significant, it doesn’t mean that the amount of variance accounted for is meaningful. Example Correlation of.393 Variance accounted for:.154 or 15.4% 84.6% remaining!!! “What you see is not always what you get” Even if a correlation is significant, it doesn’t mean that the amount of variance accounted for is meaningful. Example Correlation of.393 Variance accounted for:.154 or 15.4% 84.6% remaining!!! “What you see is not always what you get”

Using the Computer SPSS and the Correlation

SPSS Output What does it all mean?