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# Knowledge Base

## Solution 11929: Calculating P-value on the TI-83 Plus Family, TI-84 Plus C Silver Edition, TI-84 Plus Family, or TI-Nspire™ in TI-84 Plus Mode.

### How do I calculate the p-value on a TI-83 Plus family, TI-84 Plus C Silver Edition, TI-84 Plus family, or TI-Nspire in TI-84 Plus mode?

First the TI-83 Plus family, TI-84 Plus family, or TI-Nspire in TI-84 Plus mode will compute all the one-variable statistics (mean of x, s, n, etc.). Then the standard error is computed (s/n). After computing the standard error, the t-value is computed, (mean of x-m)/standard error, where m is the hypothesis mean. The algorithm used for this computation is given below.

Using the t-value, the integral of the distribution function is calculated with the appropriate upper and lower limits depending on which alternative hypothesis is tested (m<m0, m9m0, m>m0). This integral does not have a closed form so an incomplete Beta Function is used.

To arrive at the incomplete Beta Function, begin with the Student's Distribution Probability Function:

A(t|v) = (1/(v^(1/2)*B(1/2,v/2))) * integral(1+ (x^2)/v)^(-(v+1)/2)) dx) from -t to t where, B is the Beta function.

This function (A(t|v)) is related to the Beta Function by the following relationship:

A(t|v) = 1- I (v/(v+t^2) (v/2,1/2)

and the Incomplete Beta Function is (in continued fraction form):

Ix(a,b) = (x^a (1-x)^b)/(a*B(a,b)) * (1/(1+d1/(1+d2/(1+d3/(......)))))

References:
Handbook of Mathematical Function, by Abromowitz and Stegun, formula 26.5.3 for additional information.

Numerical Recipes in C, 2nd Edition, Pg 226-229