Undergrad Understanding Yates' correction

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Yates' correction is discussed in the context of approximating the probability of a calculated chi-squared value, particularly when degrees of freedom (df) equals one. The approximation may not align perfectly with the alpha level set, leading to potential misinterpretations of results. While Yates' correction is recommended for df=1 to account for continuity, some argue against its use, suggesting that the chi-squared distribution is not appropriate for fixed counts in contingency tables. The debate centers on whether Yates' correction is necessary, with some asserting it should never be applied. The discussion highlights the complexities of statistical approximations and their implications for biostatistical analysis.
Tyto alba
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I was studying Biostatistics by Zar, the Yates' correction part and stumbled upon this:

... Our need to determine the probability of a calculated X2 can be met only approximately by consulting Appendex Table B.1, and our conclusions are not taking place exactly at the level of alpha which we set. This situation would be unfortunate were it not for the fact that the approximation is a very good one, except when df=1. In the case of df=1, it is usually recommended to use Yates correction for continuity.

My doubts:

  1. The conculsions are not taking place exactly at the level of alpha- what does this mean?
Do the values of Chi square mentioned in table not correspond to the alpha(probability) indicated? Is the corresponding value actually a range?

  1. I also don't understand what it means by 'This situation would be unfortunate were it not for the fact that the approximation is a very good one, except when df=1. In the case of df=1, it is usually recommended to use Yates correction for continuity.'
Why is Yates' correction specifically done when df=1?
 
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The statistics for the table simply do not have a chi squared distribution. We have a fixed count and hence a discrete distribution whereas the chi-squared is continuous. Nevertheless the chi-squared distribution is a reasonable approximation for the contingency table. I don't agree that you should use Yates correction when the degrees of freedom is one. I argue that you should never use Yates correction.
 
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