Chi-Square Disribution

Pronounced "Kai-squared"
This is a special case of the gamma distribution
This can be used to calculate confidence interval estimates for population variances and standard deiations na din testing hypothesis involving the same parameters.
This type of distribution is also relevant when testing for goodness of fit, homogeneity and independence

Products and Squares of approximately normal distributed tend to have chi-squared distributions
This type of distribution consists of a whole family distinguised by a single whole number parameter v, called the number of degress of freedom

Examples

Properties

mean = v
variance = 2v
Continuous
right tail
Skewed
Has a family specified by the degrees of freedom "v"

Assumptions

Probability Distribution Graph

For values of v larger than 30 this type of distribution can be well approximated as a normal distribution.

Cumulative Distribution Graph

Excel Functions

Returns the probability of getting "less than" or "equal to" a specific random variable x
CHISQ.DIST - (left tail) The cumulative beta probability density function

Returns the random variable where the probability of getting less than it is P.
CHISQ.INV - (left tail) The inverse

CHISQ.DIST.RT - (2010 - CHIDIST) (right tail)

CHISQ.INV.RT

CHITEST(observed freq range, expected freq range) - return p-value for testing observed versus expected frequencies. Does not compute expected frequencies