Yates Correction Calculator

Historical Background

Yates' correction, introduced by Frank Yates in 1934, is applied to Pearson's chi-squared test for 2x2 contingency tables to reduce the error caused by small sample sizes. It adjusts the observed differences between frequencies by subtracting 0.5 from the absolute difference between observed and expected frequencies, which prevents overestimation of statistical significance.

Calculation Formula

The Yates-corrected chi-squared formula is:

\[ \chi^2_{\text{Yates}} = \sum \frac{(|O - E| - 0.5)^2}{E} \]

Where:

• \(O\) = Observed frequency
• \(E\) = Expected frequency

Example Calculation

Suppose you have an observed value \(O_A = 10\), \(O_B = 12\) and expected values \(E_A = 15\), \(E_B = 10\):

\[ \chi^2_{\text{Yates}} = \left(\frac{(|10 - 15| - 0.5)^2}{15}\right) + \left(\frac{(|12 - 10| - 0.5)^2}{10}\right) = 0.9167 \]

Importance and Usage Scenarios

Yates' correction is particularly important when analyzing small datasets in 2x2 contingency tables. It helps avoid inflated chi-squared values and prevents incorrect rejection of the null hypothesis, which would imply significance when none exists. This correction is primarily used in biological and social sciences research.

Common FAQs

1. When should I apply Yates' correction?

   • Yates' correction is typically applied to chi-squared tests with small sample sizes, particularly when the expected frequency in any cell is below 5.

2. Does Yates' correction always improve accuracy?

   • While it helps in small samples, Yates' correction can be overly conservative in larger samples, potentially reducing the test's power.

3. Can Yates' correction be applied to contingency tables larger than 2x2?

   • No, Yates' correction is specifically for 2x2 tables. For larger tables, other adjustments may be more appropriate.