= How do I use cumulative distribution functions to compute p-values in SPSS, EXCEL and R? =

P-values may be computed for an observed sample statistics, x, using the ''cumulative distribution function'' (CDF) of a particular distribution.

{{{
For x < 0 (1-sided) p-value = CDF(x) = P(X <= x) 
For x > 0 (1-sided) p-value = 1- CDF(x) = P(X >= x)
}}}

A list of CDFs for various distributions is available in SPSS by clicking transform>compute and choosing CDF and noncentral CDFs.

In EXCEL the normdist(x,mean,standard_dev,cumulative) function will give P(X < -x) + P(X > x) for a z-score, x, coming from a Normal distirbution with given mean and s.d. Placing "False" as the cumulative gives a two-tailed p-value. For example typing in a spreadsheet cell

{{{
=normdist(1.96,0,1,FALSE) 
}}}

and pressing the enter button gives a (two-tailed) p of 0.05.

In R information on the implementation of commonly used cdfs can be obtained by typing at the R prompt help(dt) for the t distribution, help(dnorm) for the Normal distribution, help(dchisq) for the chi-square distribution and help df for the F distribution.

* Programs to obtain p-values using EXCEL and SPSS are available [:FAQ/pvalues:here.]