Understanding Yates' correction

In summary, when using the Yates' correction for continuity in Biostatistics, it is important to note that the conclusions may not exactly match the set level of alpha. This is because the approximation is generally accurate, except in cases where the degrees of freedom is one. In these cases, it is recommended to use Yates' correction to obtain a more accurate result. However, some experts argue that Yates' correction should never be used, as the contingency table has a fixed count and a discrete distribution, making the chi-squared distribution a reasonable approximation.
  • #1
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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  • #2
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.
 

1. What is Yates' correction?

Yates' correction is a statistical method used to adjust for continuity in 2x2 contingency tables. It is named after its creator, Frank Yates.

2. When is Yates' correction used?

Yates' correction is used when analyzing categorical data with a binary outcome, such as yes or no responses. It is commonly used in chi-square tests to account for potential bias introduced by small sample sizes.

3. How does Yates' correction work?

Yates' correction involves subtracting 0.5 from the absolute value of the difference between observed and expected values in a contingency table. This adjustment reduces the chi-square statistic, making it more conservative and accounting for potential errors in small sample sizes.

4. What are the limitations of Yates' correction?

Yates' correction is only appropriate for 2x2 contingency tables and does not work well for larger tables. It also assumes that the expected values are at least 5, which may not always be the case. Additionally, it may not be necessary for larger sample sizes.

5. Is Yates' correction always necessary?

No, Yates' correction is not always necessary. It is most useful when dealing with small sample sizes and when the expected values are less than 5. For larger sample sizes, the correction may not make a significant difference and may not be necessary.

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