KNOWLEDGEBASE - ARTICLE #917

The P value reported along with the F ratio testing whether the variance of two groups is identical (part of the unpaired t test results from Prism and InStat) doesn't match another program or book.

Last modified January 1, 2009

The unpaired t test depends on the assumption that the two samples come from populations that have identical standard deviations (and thus identical variances). Both Prism and InStat test this assumption using an F test.

 

First the programs compute the standard deviations of both groups, and square them both to obtain variances. The F ratio equals  the larger variance divided by the smaller variance. So F is always greater than (or possibly equal to) 1.0.

The P value then asks: If the two populations really had identical variances, what is the chance of obtaining an F ratio this big or bigger? The F distribution is known, so the answer can be calculated. The answer depends on the value of F as well as the sample size of each group.

Prism (up to release 4.00 and 4.0a) and InStat (up to 3.05 and 3.0a) computed the P value incorrectly. These releases do not account for the fact that there are two ways to get to the same F ratio (sample A having a larger variance, or sample B having a larger variance). In other words, older versions of Prism and InStat computed the P value for a one-side hypothesis, but should have computed the P value for a two-sided hypothesis. Therefore the P value was half what it should have been.

This bug was fixed in Prism Windows 4.01, Prism Mac 4.0b, InStat Windows 3.06 and InStat Mac 3.0b.

What should you do if the P value (from the F test) is small indicating that the assumption of equal variances is unlikely to be true? There are three answers.

Example (from Zar Biostatistical Analysis, Fourth Edition, Prentice-Hall, 1999) Example 8.8):

Cpn.  Treated

41.0   52.0
34.0   57.0
33.0   62.0
36.0   55.0
40.0   64.0
25.0   57.0
31.0   56.0
37.0   55.0
34.0 
30.0 
38.0 

The F ratio to compare variances equals 1.424. The correct (two-sided) P value is 0.66. The incorrect (one-sided) P value is 0.33.

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