### 8.9: Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (*n*) to the number of categories (*k*).

Hence, the expected frequency of any number appearing when casting a die will be 1/6.

However, suppose the expected frequencies of the dataset are unequal; the expected frequency is obtained by multiplying the total number of observations *n *and the probability *p *for the category.