Intervals & Tests
The following is an excerpt from The Quality Engineering Handbook by Thomas Pyzdek, © QA Publishing, LLC.
The variance of machine X output, based on a sample of n = 25 taken from a stable process, is 100. Machine Y variance, based on a sample of 10, is 50. The manufacturing representative from the supplier of machine X contends that the result is a mere "statistical fluke." Assuming that a "statistical fluke" is something that has less than 1 chance in 100, test the hypothesis that both variances are actually equal.
The test statistic used to test for equality of two sample variances is the F statistic, which is calculated by the equation
For this data, F = 100/50 = 2.0
Using Table 8 in the Appendix for F.99 we find that for 24 df in the numerator and 9 df in the denominator F = 4.73. Based on this we conclude that the manufacturer of machine X could be right, the result could be a statistical fluke. This example demonstrates the volatile nature of the sampling error of sample variances and standard deviations.
Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).