In this example we test the equality of the variances of two data sets that belong to a normal distribution. We start this example by creating 3 waves of different statistics. The first pair (data1 and data2) have the same variance but different means. The second pair (data2 and data3) have the same mean but different variance. To create the data execute the commands:

Make/O/N=100 data1=100+gnoise(3)
Make/O/N=80 data2=80+gnoise(3)
Make/O/N=90 data3=80+gnoise(4)

Comparing the variance of two waves using a two-tailed hypothesis

To run the test execute the command:

StatsFTest/T=1/Q  data1,data2

The results of the test appear in the F-Test table:

n1 100
Mean1 99.8754
Stdv1 3.39174
degreesOfFreedom1 99
n2 80
Mean2 79.6029
Stdv2 3.10709
degreesOfFreedom2 79
F 1.19162
lowCriticalValue 0.659763
highCriticalValue 1.53104
P 0.418974
Accept 1

The F statistic is within the critical range so the two-tailed hypothesis of equal variances is accepted.

Testing in the case of unequal variances (two tails test)

To run the test execute the following command:

StatsFTest/T=1/Q  data1,data3

The results of the test appear in the F-Test table:

n1 100
Mean1 99.8754
Stdv1 3.39174
degreesOfFreedom1 99
n2 80
Mean2 80.5489
Stdv2 4.43966
degreesOfFreedom2 79
F 0.583641
lowCriticalValue 0.659763
highCriticalValue 1.53104
P 0.0112429
Accept 0

The rejection of H0 in this case is pretty sensitive to the choice of significance. It is apparent from the P-value that it would have been accepted if alpha was set to 0.01.

One-tail testing for the same data

First H0: the variance of the first sample is greater than the variance of the second. To run the test execute the command:

StatsFTest/T=1/Q/TAIL=1  data1,data3
n1 100
Mean1 99.8754
Stdv1 3.39174
degreesOfFreedom1 99
n2 80
Mean2 80.5489
Stdv2 4.43966
degreesOfFreedom2 79
F 0.583641
Critical 0.70553
P 0.00562143
Accept 0

H0 is rejected here as one would expect. Similarly,

StatsFTest/T=1/Q/TAIL=2  data1,data3
n1 100
Mean1 99.8754
Stdv1 3.39174
degreesOfFreedom1 99
n2 80
Mean2 80.5489
Stdv2 4.43966
degreesOfFreedom2 79
F 0.583641
Critical 1.4289
P 0.00562143
Accept 1

Here the F is smaller than the critical value so the two-tailed hypothesis can't be rejected.

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