The Fine Print: Exploring the Limitations of Fisher’s Exact Test

Question:

Could you elucidate on the constraints one might encounter when applying Fisher’s exact test to a 2×2 contingency table?

Answer:

Fisher’s exact test is ideal for small sample sizes. However, as the sample size increases, the test becomes computationally intensive, making it less practical for large datasets.

Data Requirements:

The test requires the data to be categorical and placed into a 2×2 matrix. It’s not suitable for continuous data or data that doesn’t fit into this format.

Fixed Margins:

Fisher’s test assumes that the marginal totals of the table are fixed, either by design or by the nature of the data collection process. This may not always be the case in observational studies.

Sensitivity to Sparse Data:

The test can be overly sensitive when dealing with sparse data, especially when one or more cells of the table have very small counts or zero counts.

Interpretation of Results:

While Fisher’s exact test provides a p-value indicating the probability of observing the data given the null hypothesis of no association, it does not measure the strength of the association or its practical significance.

One-Tailed vs. Two-Tailed Tests:

Deciding between a one-tailed or two-tailed version of Fisher’s test can be challenging. The choice affects the p-value and can lead to different conclusions about the significance of the results.

Assumption of Independence:

The test assumes that the observations are independent. If there is a hidden pairing or clustering within the data, the test may not be appropriate.

Multiple Testing:

If Fisher’s exact test is used multiple times on different tables or subsets of data, the risk of Type I error (false positives) increases. Adjustments for multiple comparisons may be necessary.

In conclusion, while Fisher’s exact test is a powerful tool for analyzing categorical data, it’s important to be aware of its limitations and ensure that its assumptions are met before applying it to a dataset.

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