Correlation Analyses
Correlation analyses employ the t distribution because this probability distribution adequately mirrors the sampling distribution of r at small and large sample sizes. The method for conducting a correlation analysis is to first calculate r and then test for the statistical significance of r by comparing tcrit and tobt. Keep this two-step procedure in mind so that you understand the analytic technique in Step 4.
For our first example, we will use the Police–Public Contact Survey to find out if there is a relationship between respondents’ ages and the number of face-to-face contacts they have had with police officers in the past year
In a correlation analysis, the null hypothesis is that there is no correlation between the two variables. The null is phrased in terms of ρ , the population correlation coefficient. This is the Greek letter rho (pronounced “roe”). Recall that a correlation coefficient of zero signifies an absence of a relationship between two variables; therefore, the null is
H0: ρ = 0
