## Variances Test Demo

This test examines the equality of variances for multiple waves.

 data1 data2 data3 data4 44.43 26.84 49.56 44.48 47.34 16.93 33.51 37.59 55.17 30.02 37.66 38.68 62.91 27.21 49.57 48.1 49.28 24.86 38.06 44.23 47.01 27.61 50.09 44.43 43.15 23.62 36.02 64.85 17.3 34.62

To execute Bartlett's version of the test, use the following command:

` StatsVariancesTest/T=1/Q data1,data2,data3,data4`

The results are displayed in the Variances Test table:

 N 30 PooledVariance 42.0284 Bartlett_T 3.00346 critical 7.81473

Bartlett's statistic is smaller than the critical value and so we can't reject the equality of the variances of the waves. To execute Levene's test using the means of the waves select the blue line below and type Ctrl-Enter:

` StatsVariancesTest/T=1/Q/METH=1 data1,data2,data3,data4`

The results are displayed in the Variances Test table:

 N 30 zBar 5.32225 W_statistic 2.77329 critical 2.97515

Levene's test statistic is also smaller than the critical value and so H0 can't be rejected. To execute Levene's test using the medians of the waves select the blue line below and type Ctrl-Enter:

` StatsVariancesTest/T=1/Q/METH=2 data1,data2,data3,data4`

The results are displayed in the Variances Test table:

 N 30 zBar 5.119 W_statistic 1.11643 critical 2.97515

To execute Levene's test using 10% trimmed means of the waves select the blue line below and type Ctrl-Enter:

` StatsVariancesTest/T=1/Q/METH=3 data1,data2,data3,data4`

The results are displayed in the Variances Test table:

 N 30 zBar 5.26138 W_statistic 1.37371 critical 2.97515

Both modified Levene's tests agree with the original and with Bartlett's test -- H0 can't be rejected. If we replace the wave data4 with data5:

 data5 46.25 46.25 38.65 56.82 69.51 62.65 28.6 28.92

Perform Bartlett's test:

` StatsVariancesTest/T=1/Q/METH=0 data1,data2,data3,data5`
 N 30 PooledVariance 96.5199 Bartlett_T 8.51987 critical 7.81473

In this case the Bartlett's test statistic is larger than the critical value and H0 is rejected. You will get similar results if you execute any of the modified tests as shown below:

Levene's Test

` StatsVariancesTest/T=1/Q/METH=1 data1,data2,data3,data5`
 N 30 zBar 7.33533 W_statistic 3.7164 critical 2.97515

Modified Levene's test using the median

`StatsVariancesTest/T=1/Q/METH=2 data1,data2,data3,data5`
 N 30 zBar 7.06833 W_statistic 2.64065 critical 2.97515

Modified Levene's test using 10% trimmed mean

` StatsVariancesTest/T=1/Q/METH=3 data1,data2,data3,data5`
 N 30 zBar 7.35938 W_statistic 3.38862 critical 2.97515