Section 45. Test of Equal Variance


45. Test of Equal Variance

Overview

The 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.

Roadmap

The roadmap is as follows.

Step 1.

Identify the metric and levels to be examined (two operators or such like). Analysis of this kind should be done in the Analyze Phase at the earliest, so the metric should be well defined and understood at this point (see "KPOVs and Data" in this chapter).

Step 2.

Collect two samples, one from each population (process) following the rules of good experimentation.

Step 3.

Examine stability of both sample data sets using a Control Chart for each, typically an Individuals and Moving Range Chart (I-MR). A Control Chart identifies whether the processes are stable, that is having

  • Constant mean (from the Individuals Chart)

  • Predictable variability (from the Range Chart)

This is important because if the processes do not have predictable variation then it is impossible to sensibly make the call as to whether their variances are the same or not.

Step 4.

Examine normality of the sample data sets using a Normality Test for each. The Test of Equal Variance uses a different statistic depending on normality.

Step 5.

Perform a Test of Equal Variance on the sample data sets. The Test of Equal Variance has hypotheses:

  • H0: Population (process) σ12 = σ22 (variances equal)

  • Ha: Population (process) σ12 22 (variances not equal)

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.

Interpreting the Output

The 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.

[87] The technical details of a Test of Equal Variance are covered in most statistics textbooks; Statistics for Management and Economics by Keller and Warrack makes it understandable to non-statisticians.

Based on the p-values, statements can be generally formed as follows:

  • Based on the data, I can say that there is a difference in variances and there is a (p-value) chance that I am wrong

  • Or based on the data, I can say that there is an important effect on the variance and there is a (p-value) chance the result is just due to chance

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:

  • p less than 0.05reject H0 and conclude that the variances are different

  • p greater than 0.05accept H0 and conclude that the variances are the same

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.




Lean Sigma(c) A Practitionaer's Guide
Lean Sigma: A Practitioners Guide
ISBN: 0132390787
EAN: 2147483647
Year: 2006
Pages: 138

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