Skip to Main Content

++

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)/(ba). Therefore, the desired critical value is C = Ca + f (CbCa), where Ca and Cb 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.

++

Image not available.

++

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

++

Given Sample Means and Standard Deviations

++

For treatment group t: nt = size of sample, Image not available. = mean, st = standard deviation. There are a total of k treatment groups.

++

Image not available.

++

Given Raw Data

++

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

++

Image not available.

++

Degrees of freedom and F are computed as above.

++

Given Sample Means and Standard Deviations

++

Image not available.

++

where

++

Image not available.

++

Given Raw Data

++

Use

++

Image not available.

++

in the equation for t above.

++

The contingency table is

++

Image not available.

++

Chi Square

++

Image not available.

++

where N = A + B + C + D.

++

McNemar's Test

++

Image not available.

++

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

++

Fisher Exact Test

++

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 ...

Pop-up div Successfully Displayed

This div only appears when the trigger link is hovered over. Otherwise it is hidden from view.