test

Two common statistical tests, one developed by R.A. Fisher, and the other a chi-squared test of independence, are employed to assess the association between two categorical variables. However, their suitability varies based on sample size. The first test provides an accurate p-value for small sample sizes, particularly when any cell in a contingency table has an expected count less than 5. The second relies on a chi-squared distribution approximation, which becomes less reliable with small samples. For instance, if examining the relationship between a new drug and patient improvement with a small group of participants, and if few are expected to improve regardless of treatment, the first test becomes more appropriate.

The value of using the correct test lies in obtaining statistically sound conclusions. In situations where data are limited, relying on the chi-squared approximation may lead to inaccurate inferences, potentially resulting in false positives or negatives. Fisher’s approach, though computationally intensive in the past, now provides a more precise and trustworthy result, especially when dealing with sparse data or small sample sizes. This precision enhances the validity of research findings and informs better decision-making across various fields, from medicine to social sciences.

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