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Fisher's Exact Test vs. Chi-Square Test

Introduction

Both Fisher's Exact Test and the Chi-Square Test are statistical tests used to analyze categorical data and determine if there is a significant association between two categorical variables. While they serve similar purposes, there are differences in their applications, assumptions, and interpretations. This article compares Fisher's Exact Test and the Chi-Square Test to highlight their similarities and differences.

Fisher's Exact Test

• Application: Suitable for small sample sizes and 2x2 contingency tables.
• Assumptions: No assumptions about sample size or expected cell frequencies.
• Interpretation: Provides an exact p-value, making it more reliable for small sample sizes.
• Limitation: Less practical for larger sample sizes and tables larger than 2x2 due to computational complexity.

Chi-Square Test

• Application: Commonly used for larger sample sizes and contingency tables of any size.
• Assumptions: Assumes that the sample size is sufficiently large and that expected cell frequencies are not too small.
• Interpretation: Provides an approximate p-value based on the chi-square distribution.
• Advantage: More practical for larger datasets and can handle tables larger than 2x2.

Conclusion

Fisher's Exact Test and the Chi-Square Test are both valuable tools for analyzing categorical data and assessing associations between variables. Fisher's Exact Test is particularly useful for small sample sizes and 2x2 tables, while the Chi-Square Test is more practical for larger datasets and can handle tables of any size. Choosing the appropriate test depends on the nature of the data and the specific research question at hand.