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I am proposing this question for a chi-squared test of association between party and voting. The following table is based on how (R)-Republican and (D)-Democrats voted on a specific bill

     yes no
   R  99 11
   D   1 48

Since the (D, yes) cell is 1, could I be violating Cochran's rules for a chi-squared test?

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  • $\begingroup$ What is the expected count for D-yes? $\endgroup$ – Alexis Dec 5 '17 at 22:48
  • $\begingroup$ 30.817 found from (100*49/159) $\endgroup$ – Nathgun Dec 5 '17 at 22:57
  • $\begingroup$ Isn't the rule that the $\chi^{2}$ contingency table test should not be used when expected counts in any cell are less than 5? $\endgroup$ – Alexis Dec 5 '17 at 23:04
  • $\begingroup$ @Alexis I should have specified that the table listed here is the observed counts. None of the expected count cells are less than 5 $\endgroup$ – Nathgun Dec 5 '17 at 23:28
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    $\begingroup$ Cochran's main point under this heading was that a rule such as all expected counts being at least 5 was over-cautious. $\endgroup$ – Nick Cox Dec 6 '17 at 2:35
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Answer: contingency table $\chi^{2}$ tests with expected counts less than 5 were deemed inappropriate by Cochran, but your example is of observed counts.

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