Calculating P values from statistical ratios

Free web calculators 

  The easiest way to compute a P value from a statistical ratio is to use this free GraphPad QuickCalc page.  It can compute a P value from a z, t, F, chi-square or r value you enter. 

Calculations with older versions of Excel

If you want to compute P values using older (pre 2010) Excel, use these functions:

P value from F	=FDIST (F, DFn, DFd) The order of the two degrees of freedom matters. Dfn is the degree of freedom for the numerator of the F ratio, and DFd is for the denominator.
P value from t (two tailed)	=TDIST (t, df, 2) (The third argument, 2, specifies a two-tail P value.)
P value from Chi Square	=CHIDIST (ChiSquare, DF)
P value from z (two tailed)	=2*(1.0-NORMSDIST(z))

    

Calculations with newer versions of Excel

If you want to compute P values using newer (2010 and later) Excel, use these functions:

 

P value from F	=F.DIST.RT (F, DFn, DFd) The order of the two degrees of freedom matters. Dfn is the degree of freedom for the numerator of the F ratio, and DFd is for the denominator.
P value from t (two tailed)	=T.DIST.2T(t, df)
P value from Chi Square	=CHISQ.DIST.RT(ChiSquare, DF)
P value from z (two tailed)	=2*(1.0-NORM.S.DIST(z,TRUE))

Algorithms used in Prism

GraphPad Prism (and InStat) report exact P values with most statistical calculations. It computes a P value from an F ratio using these algorithms, adapted from section 6.14 of the third edition of Numerical Recipes, which is available on line. 

PFromF(F_Value, DF_Numerator, DF_Denominator) =
BetaI(DF_Denominato /2, DF_Numerator/2, DF_Denominator / (DF_Denominator + DF_Numerator * F_Value))

PFromT(T_Value, DF) = BetaI(DF /2, 1/2, DF / (DF + T_Value^2))

PFromZ(Z_Value) = PFromT(Z_Value, Infinity)

PFromR(R_Value) = PFromT(|R_Value| / SQRT((1 - R_Value^2)/DF) , DF)

PFromChi2(Chi2_Value, DF) = GammaQ(DF / 2, Chi2Value /2)

 

Note that BetaI is the incomplete beta function, and GammaQ is the incomplete gamma function.