Goodness-of-fit tests for multinomial models with many parameters can be simplified using power-divergence statistics. These tests can be applied to models with large degrees of freedom, even when the data is sparse. By increasing the number of independent multinomials while keeping the number of classes and parameters fixed, the tests can be made more accurate. For binomial data, the tests can be seen as score tests within an expanded model. The results show that the tests' expectations and variances align closely with the estimated parameters, especially when the sizes of the multinomials are large.