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For testing independence most software also reports another chi squared statistic

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

G2 = 2 ∑ [observed count × log (observed count / expected count)]

It has similar properties as the X2 statistic, such as

df = (r - 1) × (c - 1).

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.

G2 = 2 ∑ [observed count × log (observed count / expected count)]

It has similar properties as the X2 statistic, such as

df = (r - 1) × (c - 1).

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.

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