Consider the data in the 3 waves:

 data1 data2 data3 9 5.47 8.4 8.78 5.84 8.8 9.02 5.79 9 8.29 5.33 8.3 8.37 5.49 8.4 9.06 5.18 8.3 8.69 5.67 8.7 8.53 5.53 8.5 8.78 5.75 8.8 9.1 5.88 9.1 8.61 5.95 8.6 9.26 6.24 9.2

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:

 n 12 r 0.422481 sr 0.28662 rc1 0.497265 rc2 0.575983 t_Value 1.47401 tc1 1.81246 tc2 2.22814 F 2.46309 Fc1 2.97824 Fc2 3.71679 Power1 0.38787 Power2 0.268562

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`

 n 12 r 0.876562 sr 0.152197 rc1 0.497265 rc2 0.575983 t_Value 5.7594 tc1 1.81246 tc2 2.22814 F 15.2025 Fc1 2.97824 Fc2 3.71679 Power1 0.992761 Power2 0.982695

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`

 n 12 r 0.876562 sr 0.152197 rc1 0.497265 rc2 0.575983 t_Value 5.7594 tc1 1.81246 tc2 2.22814 F 15.2025 Fc1 2.97824 Fc2 3.71679 FisherZ 1.36073 zeta 0.549306 sigmaZ 0.333333 Zstatistic 2.43427 Zc1 1.64485 Zc2 1.95996 Power1 0.787354 Power2 0.679027

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`

 n 12 r 0.876562 sr 0.152197 rc1 0.497265 rc2 0.575983 t_Value 5.7594 tc1 1.81246 tc2 2.22814 F 15.2025 Fc1 2.97824 Fc2 3.71679 FisherZ 1.36073 zeta 0.972955 sigmaZ 0.333333 Zstatistic 1.16332 Zc1 1.64485 Zc2 1.95996 Power1 0.317867 Power2 0.210131

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