mariposa (version 0.7.3)

fisher_test: Fisher's Exact Test for Small Samples

Description

fisher_test() performs Fisher's exact test for independence in a contingency table. Use this instead of chi_square() when your sample is small or when expected cell frequencies are below 5.

Think of it as:

• An exact alternative to the chi-square test of independence

• Best for small samples where the chi-square approximation may be inaccurate

• SPSS automatically reports Fisher's Exact Test for 2x2 tables

The test tells you:

• Whether two categorical variables are related (exact p-value)

• The contingency table of observed frequencies

• Results that are valid even with very small samples

Usage

fisher_test(data, row, col, weights = NULL, ...)

Value

Test results showing whether two categorical variables are related, including:

• Exact p-value (two-sided)

• Contingency table of observed frequencies

• Sample size (N)

Arguments

data

Your survey data (data frame or tibble)

row

The row variable (categorical)

col

The column variable (categorical)

weights

Optional survey weights for population-representative results

...

Additional arguments (currently unused)

Details

Understanding the Results

P-value: If p < 0.05, the variables are likely related (not independent)

• p < 0.001: Very strong evidence of relationship

• p < 0.01: Strong evidence of relationship

• p < 0.05: Moderate evidence of relationship

• p >= 0.05: No significant relationship found

Unlike the chi-square test which uses a large-sample approximation, Fisher's exact test computes the exact probability of observing the given table (or a more extreme one) under the null hypothesis of independence.

For tables larger than 2x2, the Fisher-Freeman-Halton extension is used.

When to Use This

Use Fisher's exact test when:

• Any expected cell frequency is less than 5

• Your total sample size is small (typically N < 30)

• You have a 2x2 table (Fisher's exact is standard here)

• You want an exact p-value rather than an approximation

Relationship to Other Tests

• For large samples with all expected frequencies >= 5: Use chi_square() instead

• For paired binary data (before/after): Use mcnemar_test() instead

• For testing a single proportion: Use binomial_test() instead

SPSS Equivalent

SPSS: CROSSTABS /STATISTICS=CHISQ (Fisher's exact test is automatically reported for 2x2 tables)

References

Fisher, R. A. (1922). On the interpretation of chi-square from contingency tables, and the calculation of P. Journal of the Royal Statistical Society, 85(1), 87-94.

Freeman, G. H., & Halton, J. H. (1951). Note on an exact treatment of contingency, goodness of fit and other problems of significance. Biometrika, 38(1/2), 141-149.

See Also

chi_square for chi-square test of independence (large samples).

mcnemar_test for paired proportions.

Other hypothesis_tests: ancova(), binomial_test(), chi_square(), chisq_gof(), factorial_anova(), friedman_test(), kruskal_wallis(), mann_whitney(), mcnemar_test(), oneway_anova(), t_test(), wilcoxon_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Basic 2x2 Fisher test
survey_data %>%
  fisher_test(row = gender, col = region)

# Fisher test for larger table
survey_data %>%
  fisher_test(row = gender, col = interview_mode)

# With weights
survey_data %>%
  fisher_test(row = gender, col = region, weights = sampling_weight)

# Grouped analysis
survey_data %>%
  group_by(education) %>%
  fisher_test(row = gender, col = region)