01-29-2019, 05:02 PM
An extract from Determining the significance of an observed F using a pocket calculator, Behavior Research Methods & Instrumentation, 1977. Vol. 9 (6). 557-558.
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, A. (In the case of the central F, the program is used with A= 0.) The program is based on National Bureau of Standards approximation formulas (Abramowitz & Stegun, 1966, Formulas 26.6.15 and 26.6.26), which yield a maximum error in the significance level of .0005 in the case of the central F, and an error generally less than .005 in the noncentral case. The z value that results from the program may be entered into programs for calculating the corresponding probability, generally supplied with such calculators (e.g., Hewlett-Packard, 1975), or compared to the critical values for z. (The two or three commonly used critical z values may be committed to memory, eliminating reliance on tables.)
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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SlideRule
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, A. (In the case of the central F, the program is used with A= 0.) The program is based on National Bureau of Standards approximation formulas (Abramowitz & Stegun, 1966, Formulas 26.6.15 and 26.6.26), which yield a maximum error in the significance level of .0005 in the case of the central F, and an error generally less than .005 in the noncentral case. The z value that results from the program may be entered into programs for calculating the corresponding probability, generally supplied with such calculators (e.g., Hewlett-Packard, 1975), or compared to the critical values for z. (The two or three commonly used critical z values may be committed to memory, eliminating reliance on tables.)
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.
BEST!
SlideRule