The Hosmer-Lemeshow is a goodness of fit statistic computed using the 2 x g table of observed and expected frequencies, where g is the number of groups. This statistic is compared to a chi-square distribution with g-2 degrees of freedom.

Where Nj is the number of observations in the jth group, Oj is the number of responses in the jth group, and is the average of the predicted probabilities in the jth group.