Description: Yates’ correction is a statistical adjustment applied to the chi-squared test, designed to reduce bias that can arise in small samples. This correction is primarily used in 2×2 contingency tables, where the relationship between two categorical variables is assessed. The chi-squared test, in its original form, can overestimate statistical significance when expected counts are low, leading to erroneous conclusions. Yates’ correction, introduced by British statistician Maurice Yates in 1934, involves subtracting 0.5 from each observed count before calculating the chi-squared statistic. This adjustment helps provide a more conservative estimate of significance, especially in situations where data is scarce or unbalanced. Yates’ correction is fundamental in categorical data analysis, as it allows researchers to obtain more reliable and accurate results, minimizing the risk of Type I errors, that is, incorrectly rejecting the null hypothesis.
History: Yates’ correction was introduced by British statistician Maurice Yates in 1934. Its development arose from the need to improve the accuracy of the chi-squared test in situations where sample sizes were small and expected counts were low. Yates observed that the original test could lead to erroneous conclusions in these contexts, which motivated the creation of this adjustment. Since its introduction, Yates’ correction has been widely adopted in applied statistics, especially in fields such as biology, medicine, and social sciences, where researchers often work with limited categorical data.
Uses: Yates’ correction is primarily used in the analysis of contingency tables, especially in studies comparing two categorical groups. It is common in medical research to assess the effectiveness of treatments, as well as in market studies to analyze consumer preferences. It is also applied in epidemiological studies to investigate the relationship between risk factors and diseases. Its use is crucial in situations where sample sizes are small, as it helps avoid erroneous conclusions about the relationship between variables.
Examples: A practical example of Yates’ correction can be found in a study evaluating the relationship between the consumption of a new medication and the occurrence of side effects. If it is observed that 5 patients experience side effects out of a total of 20 who took the medication, and 1 patient out of 20 who did not take it, applying Yates’ correction would adjust the counts to provide a more accurate assessment of statistical significance. Another example could be in a survey analysis comparing the preferences of two consumer groups, where sample sizes are unequal.
