What is it: An F test is used test whether two samples are drawn from different populations have the same standard deviation, with a specified confidence level. Samples may be of different sizes. The test static should have an F-distribution if the null hypothesis is true. Examples include:

• The hypothesis that the means of multiple normally distributed populations, all having the same standard deviation, are equal. This is perhaps the most well-known of hypotheses tested by means of an F-test, and the simplest problem in the analysis of variance (ANOVA).
• The hypothesis that the standard deviations of two normally distributed populations are equal, and thus that they are of comparable origin.

Note that if it is equality of variances (or standard deviations) that is being tested, the F-test is extremely non-robust to non-normality. That is, even if the data displays only modest departures from the normal distribution, the test is unreliable and should not be used.

Why use it: The F-test investigates whether two populations are equal based on the variances of two samples from those populations.

Where to use it: To confirm that an improvement is truly an improvement and not just common cause variation in the process.

When to use it: F-tests are used when to compare the variances of two samples to determine if the variation between the two populations they represent are likely to be equal.

How to use it: The formula for an F-test in multiple-comparison ANOVA problems is: F = (between-group variability) / (within-group variability). (Note: When there are only two groups for the F-test: F-ratio = t2 where t is the Student's t statistic.)

In many cases, the F-test statistic can be calculated through a straightforward process. Please refer to the included template package for use of the f-Test.

 Name Format Preview (Click to enlarge) f Test sheet 1 Microsoft ExcelFormat f Test sheet 1 with data entered Microsoft ExcelFormat f Test sheet 2, page 1 with data entered Microsoft ExcelFormat f Test sheet 2, page 2 with data entered Microsoft ExcelFormat
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