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What is the impact in terms of reliability of having low expected frequencies (less than 5)...

What is the impact in terms of reliability of having low expected frequencies (less than 5) when doing chi-square test?

and why is that?

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Answer #1

The chi- square is unreliable for low expected frequencies.No theoretical cell frequency should be less than 5. The chi- square distribution is continuous distribution if frequency is less than five it can't maintenans the property of continuity so we use pooled frequency to maintain the continuity. If any frequency is less than five then application of chi square test is it is pooled with preceding or succeeding frequency so pooled frequency is more than five. And adjust degree freedom lost in pooling.

Chi-Squre distribution only depends on observed and expected frequencies on degree of freedom.

When frequency is very low the theoretical and observed distribution is plotted the observed distribution is very irregular.

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