
Chisquare distribution
The chisquare distribution has one
parameter k, the degrees of freedom.
The chi squared distribution becomes more symmetric as k increases.
The mean and variance of the chi square^{ }distribution also increase
as k increases and the mean = k and variance = 2k. 

Chisquare test explained Chisquare test is based on the chi square^{ }distribution. It is used for the goodnessoffit test because it asks whether there is a good fit between the data (O = Observed frequency) and the theory (E = Expected frequency). Chisquare determines whether the differences between the observed and expected scores can be attributed to some actual difference in behavior or if this difference between the scores is caused by chance using the formula chi square = sum{ (OE)^2) / E}. 

Determining significance of chi square If we wish to reject
H_{o} at the .05 level, we will determine if our value of
chi square^{ }is greater than the critical
value of chi square^{ } that cuts
off the upper 5% of the distribution at our particular degrees of freedom
value. If our value of chi
square^{ }from the formula is greater than the critical
value of chi square, we reject H_{o}
and conclude that the obtained frequencies differ from the expected frequencies
more than would be predicted by chance. 

Two variable chi square The two variable chisquare is used to determine whether one variable is contingent on a second variable. So, we construct a contingency table that shows the distribution of one variable at each level of the other variable. For a contingency table, the expected frequency for a given cell is obtained by multiplying the totals for the row and column in which the cell is located and dividing by total sample size. 
