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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.

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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.

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

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Given Sample Means and Standard Deviations

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For treatment group *t*: *n**t* = size of sample,

= mean,

*s**t* = standard deviation. There are a total of

*k* treatment groups.

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

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

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Given Sample Means and Standard Deviations

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in the equation for *t* above.

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

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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 ...