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With the chi-square test, does the magnitude of the observed and expected values make a difference?

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See the following example, in both data sets (A and B) the observed and expected vary by 30%, however in sample A the test result means we infer they are different, but in sample B we infer they are not:

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Am I missing something?

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  • $\begingroup$ Surely the test should be impacted by the relative distance between observed and expected rather than the actual. A difference of 1 is much greater when the actual value is 5 rather than 500. In the example both series differ by 30%, why should it matter that the values are larger or smaller? $\endgroup$
    – Laurence_jj
    May 18, 2021 at 10:46

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The observed counts in your table represents observations. So, if you divide all counts by 100, like you did in your example, you have effectively reduced your sample size. In smaller samples it is harder to find deviations from the null hypothesis. So that is why your pattern is not significant in panel B and significant in panel A.

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  • $\begingroup$ ok, so I can only use the test for observation counts rather than observation values. I see the floor in my understanding thanks! $\endgroup$
    – Laurence_jj
    May 18, 2021 at 10:49

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