The Chi-Square Goodness of Fit Statistic . This statistic enables us to test whether observed frequencies are close to . those we would expect. ... Expected frequencies . ... For example, if we . have an honest die we would expect 1/6 of all cases to show any of . ... So, for example, if we roll a die 60 times we would expect : . ... If we actually roll a die 60 times we wouldn't expect each of the faces . ... times each face actually comes up is the observed frequency for that face. ...