What is the definition of expected counts in chi square tests?

Just wondering whether anyone could define expected counts in regards to a chi square test.

Answer

Expected counts are the projected frequencies in each cell if the null hypothesis is true (aka, no association between the variables.)

Given the follow 2×2 table of outcome (O) and exposure (E) as an example, a, b, c, and d are all observed counts:

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The expected count for each cell would be the product of the corresponding row and column totals divided by the sample size. For example, the expected count for O+E+ would be:

(a+b)×(a+c)a+b+c+d

(see red arrows for the meaning of “corresponding”)

Then the expected counts will be contrast with the observed counts, cell by cell. The more the difference, the higher the resultant statistics, which is the χ2.

Attribution
Source : Link , Question Author : Joanna , Answer Author : time

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