Undergrad Understanding Yates' correction

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SUMMARY

The discussion centers on Yates' correction in the context of Biostatistics, specifically as outlined in the textbook by Zar. It highlights that while the approximation of Chi-square values using Appendix Table B.1 is generally reliable, it fails when the degrees of freedom (df) equals 1. In such cases, Yates' correction is recommended to address continuity issues, although some participants argue against its necessity. The conversation emphasizes the distinction between discrete and continuous distributions, particularly in relation to Chi-square tests.

PREREQUISITES
  • Understanding of Chi-square tests and their applications
  • Familiarity with degrees of freedom in statistical analysis
  • Knowledge of continuity corrections in statistics
  • Basic concepts of discrete versus continuous distributions
NEXT STEPS
  • Research the implications of using Yates' correction in Chi-square tests
  • Explore the differences between discrete and continuous probability distributions
  • Study the Chi-square distribution and its properties in depth
  • Examine alternative continuity corrections and their applications
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Statisticians, biostatisticians, and students studying statistical methods who seek to understand the application and implications of Yates' correction in Chi-square tests.

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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