Statistics Knowledge Base - p-Value for the Chi-Square Test

Friday, March 12, 2010

p-Value for the Chi-Square Test

The p-value for a one-tailed chi-square test is the probability that a value chosen at random from a particular chi-square distribution would be greater than or equal to the value of an observed value (the chi-square value) from the same distribution.

PROPERTIES

Some of the important properties of the chi-square distribution include:

Because the chi-square distribution is a probability distribution, the p-value for a one-tailed chi-square test also refers to the total area under a particular chi-square distribution from the chi-square value to infinity.
The shape of a chi-square distribution depends upon its degrees of freedom. As the degrees of freedom increase, the shape of the chi-square distribution approaches the normal distribution.
The chi-square distribution is directly related to the Fisher F-distribution, insofar as the F-distribution is a function of the ratio of two independent chi-square variates which have been divided by their respective degrees of freedom.
The chi-square distribution is a special case of the gamma distribution.

ONLINE CALCULATOR

To calculate a p-Value for the Chi-Square Test, please click here.

FORMULAE

The formula involved in the computation of a p-Value for the Chi-Square test is detailed below.

Chi-square distribution probability density function:
Where k is the degrees of freedom, and Γ is the Gamma function.

REFERENCES

Kenney, J.F. and Keeping, E.S. (1951), "The Chi-Square Distribution." in Mathematics of Statistics, Pt. 2, (2nd edition), Van Nostrand, Princeton, NJ.

Abramowitz, M. and Stegun, I.A., eds. (1965), "Handbook of Mathematical Functions", Dover, New York, NY.