mariposa (version 0.7.3)

binomial_test: Test Whether a Proportion Matches an Expected Value

Description

binomial_test() tests whether the observed proportion of a binary variable differs from a hypothesized proportion. It uses the exact binomial test, making it valid for any sample size.

Think of it as:

• Testing whether a coin is fair (proportion of heads = 50 percent)

• Checking if your sample's gender ratio matches the population

• Verifying if satisfaction rates meet a target proportion

The test tells you:

• Whether the observed proportion differs significantly from the expected

• The exact p-value (based on the binomial distribution)

• A confidence interval for the true proportion

Usage

binomial_test(data, ..., p = 0.5, weights = NULL, conf.level = 0.95)

Value

Test results showing whether the proportion differs from expected, including:

• Category counts and observed proportions

• Test proportion (null hypothesis)

• Exact p-value (two-sided)

• Confidence interval for the true proportion

Arguments

data

Your survey data (a data frame or tibble)

...

One or more binary variables to test. Each must have exactly 2 categories (e.g., Yes/No, Male/Female, 0/1, TRUE/FALSE)

p

The hypothesized proportion to test against (Default: 0.50 = 50 percent). This refers to the proportion of the first category (first factor level, or the lower numeric value).

weights

Optional survey weights for population-representative results

conf.level

Confidence level for intervals (Default: 0.95 = 95 percent)

Details

Understanding the Results

P-value: If p < 0.05, the proportion differs significantly from the test proportion

• p < 0.001: Very strong evidence the proportion differs

• p < 0.01: Strong evidence the proportion differs

• p < 0.05: Moderate evidence the proportion differs

• p > 0.05: No significant difference from expected proportion

Observed Proportion: The actual proportion in your data. Compare this with the test proportion to see the direction of any difference.

Confidence Interval: The range likely to contain the true population proportion. If the test proportion falls outside this range, the result is significant.

When to Use This

Use the binomial test when:

• You want to compare an observed proportion to a known value

• Your variable has exactly 2 categories

• You need an exact test (not relying on normal approximation)

• Sample size is small (where chi-square may not be reliable)

Relationship to Other Tests

• For testing association between two categorical variables: Use chi_square() instead

• For comparing proportions between groups: Use chi-square or z-test for proportions

• For larger samples with normal approximation:

Weighted variants

SPSS NPAR TESTS ignores WEIGHT BY, so weighted results have no SPSS reference. The weighted variant is an R-only frequency-weight extension that reduces exactly to the unweighted test when all weights equal 1 (enforced by an internal invariance suite); see vignette("spss-compatibility") for validation status.

Results will be very similar to a one-sample z-test for proportions

References

Conover, W. J. (1999). Practical nonparametric statistics (3rd ed.). John Wiley & Sons.

See Also

binom.test for the base R exact binomial test.

chi_square for testing associations between categorical variables.

Other hypothesis_tests: ancova(), chi_square(), chisq_gof(), factorial_anova(), fisher_test(), 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)

# Test whether gender split is 50/50
survey_data %>%
  binomial_test(gender, p = 0.50)

# Test whether East region proportion is 50%
survey_data %>%
  binomial_test(region, p = 0.50)

# Multiple variables at once
survey_data %>%
  binomial_test(gender, region, p = 0.50)

# Weighted analysis
survey_data %>%
  binomial_test(gender, p = 0.50, weights = sampling_weight)

# Grouped analysis (separate test per region)
survey_data %>%
  group_by(region) %>%
  binomial_test(gender, p = 0.50)