11.88 Likelihood-ratio chi-squared For testing independence, most software also reports another chi-squared statistic, called likelihood-ratio chi-squared. It equals

a. Show that G2 = X2 = 0 when each observed count = expected count.

b. Explain why in practice you would not expect to get exactly G2 = X2 = 0, even if the variables are truly independent.

G = 2 observed count log ( observed count)]. It has similar properties as the X statistic, such as df (r-1) x (c-1).