Consider the data in the 3 waves:

We can calculate the (linear) correlation coefficients between the waves and test various hypotheses in one operation. To run the test for waves data1 and data2 execute the command:

StatsLinearCorrelationTest/T=1/Q data1,data2

The test results are displayed in the Linear Correlation Test table:

There are 12 data points in each wave. The correlation coefficient r=0.422481 with a standard error sr. For the hypothesis H₀: the correlation coefficient is zero, the t_Value is below the critical value so H₀ can't be rejected. On the other hand, if we test data2 and data3 we get different results. To run the test execute the command:

StatsLinearCorrelationTest/T=1/Q data2,data3

In this case the correlation coefficient r=0.876562 and both t_Value and the F exceed their respective critical values and H₀ must be rejected.

The operation can also test the specific hypothesis ρ=ρ₀ agains the alternative ρ!=ρ₀. Using the same data as in the last example execute the command:

StatsLinearCorrelationTest/T=1/Q/RHO=0.5 data2,data3

Since the Zstatistic=2.43427 exceeds the two-tailed critical value Zc2=1.95996, H₀: ρ=0.5 must be rejected. However, if we test ρ=0.75, we find:

StatsLinearCorrelationTest/T=1/Q/RHO=0.75 data2,data3

In this case Zstatistic=1.16332<Zc2=1.95996 and so H₀ can't be rejected.