# Appendix A. Computational Forms

If the value you need is not in the statistical table, it is possible to estimate the value by *linear interpolation.* For example, suppose you want the critical value of a test statistic, *C*, corresponding to ν degrees of freedom, and this value of degrees of freedom is not in the table. Find the values of degrees of freedom that are in the table that bracket *v*, denoted *a* and *b.* Determine the fraction of the way between *a* and *b* that *v* lies, *f* = (ν − *a*)/(*b* − *a*). Therefore, the desired critical value is *C* = *C**a* + *f* (*C**b* − *C**a*), where *C**a* and *C**b* are the critical values that correspond to *a* and *b* degrees of freedom.

A similar approach can be used to interpolate between two *P* values at a given degrees of freedom. For example, suppose you want to estimate the *P* value that corresponds to *t* = 2.620 with 20 degrees of freedom. From Table 4–1 with 20 degrees of freedom *t*.01 = 2.845 and *t*.02 = 2.528, *f* = (2.620 − 2.845)/(2.528 − 2.845) = 0.7098, and *P* = .01 + .07098 × (.02 − .01) = .0171.

These formulas can be used for equal or unequal sample sizes.

For treatment group *t*: *n**t* = size of sample, = mean, *s**t* = standard deviation. There are a total of *k* treatment groups.

Subscript *t* refers to treatment group; subscript *s* refers to experimental subject.

Degrees of freedom and *F* are computed as above.

where

Use

in the equation for *t* above.

The contingency table is

where *N* = *A* + *B* + *C* + *D.*

where *B* and *C* are the numbers of people who responded to only one of the treatments.

Interchange the rows and columns of the contingency table so that the smallest observed frequency is in position *A*. Compute the probabilities associated with the resulting table, and all more-extreme tables obtained by reducing *A* by 1 and recomputing the table to maintain the row and column totals until *A* = 0. Add all these probabilities to get the first tail of the test. If either the two-row sums or two-column sums ...