45. Test of Equal VarianceOverviewThe Test of Equal Variance is used to compare two sample variances against each other. For example, a Team might need to determine if two operators have the same amount of variation in the time they take to perform a task. For example, a data sample would be taken of 25 points from each operator to make the judgment, and the result would be the likelihood that the variation in the operator's task time (as work continues) is the same. Thus, a sample of data points (lower curves) is taken from the two processes (the populations of all data points, upper curves), as shown in Figure 7.50.1. From the characteristics of the samples (standard deviation s and sample size n), an inference is made on the size of the population variances σ relative to the each other. The result would be a degree of confidence (a p-value) that the samples come from populations with the same variance. RoadmapThe roadmap is as follows.
Interpreting the OutputThe Test of Equal Variance[87] compares the sample data sets' characteristics (standard deviation s and sample size n) to a reference distribution, to determine whether the sample data sets indicate that the populations variances are statistically different or not. Amongst other things the test returns a p-value, the likelihood that for the samples a difference in variances this large could have occurred purely by random chance even if the populations had the same variation.
Based on the p-values, statements can be generally formed as follows:
The output of an example Test of Equal Variance is shown in Figure 7.50.2. Depending on whether the data is normal or non-normal affects which test results to examine. As stated previously, if both sample data sets are normal, then look to the Bartlett's or F-Test. If either or both sample data sets are non-normal then look to the less powerful Levene's Test. Both tests return a p-value that is interpreted in the usual way:
For the example of Bob and Jane shown in Figure 7.50.2, both data sets had previously been determined to be normal, so looking to the F-Test (with a p-value well above 0.05) the conclusion should be that Bob's variance cannot be differentiated from Jane's. |