Interpreting Correlation Coefficients

Correlations Helpful in determining the extent of the relationships between –Ratio variables –Interval variables –Ratio and interval variables Necessary where it must be shown that one variable is a potential “cause” of another variable (concomitant variation).

Correlation Coefficient r xy, “the correlation between x and y” The denominator is always positive. The numerator will be negative when… The numerator will be positive when…

Four possible compuations for the numerator How many possible results for the “average” coefficient, or result?

Correlations Private Label % Folgers % ShareWalMart % Private Label % Pearson Correlation Sig. (2-tailed) N32 Folgers % Share Pearson Correlation Sig. (2-tailed) N32 WalMart % Pearson Correlation Sig. (2-tailed) N32 **Correlation is significant at the 0.01 level (2-tailed).

Using the Correlation with Surveys Correlation coefficients show the correspondence between two questionnaire items, or pairs of variables. Correlation output is presented in a symmetrical matrix of paired analyses. One correlation coefficient can summarize what is shown on an entire crosstab table— very efficient means of communicating a relationship.

Ranges and Significance The coefficient can range between and +1.00, values closer to these values are generally significant. Significance is the probability of incorrectly rejecting a null hypothesis that the coefficient is not different from zero. With larger sample sizes, it’s easier to reject the null. Significance is not dependent on sign, but on sample size. As sample size increases, smaller coefficients can be statistically significant.

Interpreting the Coefficient’s Sign Positive: “Above average values of x are accompanied by above average values of y. Similarly, below average values of x are accompanied by below average values of y.” Negative: “Above average values of x are accompanied by below average values of y. Below average values of x are accompanied by above average values of y.”

R 2 and “Shared Variance” The coefficient can range between and If you squared the correlation coefficient, you create R 2, a “percentage” measure of shared variance. If the correlation coefficient between two items is above.70 (49%), you can claim that the two items share ½ the variance.