(25) Significance of an Observed F
10-27-2023, 11:03 PM
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 SlideRule Senior Member Posts: 1,442 Joined: Dec 2013
(25) Significance of an Observed F
An excerpt from Determining the significance of an observed F using a pocket calculator, Behavior Research Methods & Instrumentation, 1977. Vol. 9 (6). 557-558, WILLIAM F. KAEMMERER

"   The F test is the procedure for determining the significance of differences among samples of populations which is perhaps the most frequently used by behavioral scientists, and tables of critical values for this test are widely available. However, occasionally an investigator may find the tabled values inadequate for his or her purposes. If an observed F is marginally significant, an investigator may have to interpolate among tabled values to conduct the test precisely. Furthermore, multivariate procedures may yield F statistics with noninteger degrees of freedom, which are rarely tabled. Finally, when calculating the power of an F test, it is necessary to determine the probability density function of a noncentral F, yet the available tables of noncentral F distributions are limited in scope.
The availability of sophisticated pocket calculators at a reasonable cost has made it possible for researchers to readily determine the significance of an observed F, in these cases and in others, with a high degree of precision. The keystroke program presented below yields a unit normal value with a significance equivalent to the observed F, given the numerator and denominator degrees of freedom, and the noncentrality parameter, λ. …
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The program is presented in Table 1. Although it was developed on a Hewlett-Packard HP-25 programmable calculator, it may also be used with nonprogrammable calculators that use Reverse Polish Notation and have at least four memory locations and the necessary data handling capabilities by following the keystroke routine manually.
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Table 1
Program to Determine the Significance of an Observed F

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