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Chi square test for association: Yates' correction

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7 (i) When should Yates' correction be applied when carrying out a Chi-square test?
Two vaccines against typhoid fever, A and B, were tested on a total of 700 people in Nepal during a particular year. The vaccines were allocated randomly and whether or not typhoid had developed was noted during the following year. The results are shown in the table.
Vaccines
A B

Developed typhoid 19 4

Did not develop typhoid 310 367

(ii) Carry out a suitable Chi-square test at the 1% significance level to determine whether the outcome depends on the vaccine used. Comment on the result.

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The solution provides step by step method for the calculation of chi square test for association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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(i) Yates' correction
Yates' correction is applied when at least one cell of the contingency table has an expected frequency less than 5 (some statistics books set that value at 10).
(ii)
The null hypothesis tested is
H0: The outcome independent of the vaccines used.
The alternative hypothesis is
H1: The outcome depends on the vaccines used.
The test statistic used is where O is the observed frequency and E ...

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