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
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)
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
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()insteadFor comparing proportions between groups: Use chi-square or z-test for proportions
For larger samples with normal approximation: Results will be very similar to a one-sample z-test for proportions
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)
#>
#> Binomial Test Results
#> ---------------------
#>
#> - Test proportion: 0.5
#> - Confidence level: 95.0%
#>
#> gender
#> ------
#> Categories:
#> ------------------------------------
#> N Observed Prop.
#> Group 1: Male 1194 0.478
#> Group 2: Female 1306 0.522
#> Total 2500 1.000
#> ------------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0.026 0.458 0.497 *
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Test whether East region proportion is 50%
survey_data %>%
binomial_test(region, p = 0.50)
#>
#> Binomial Test Results
#> ---------------------
#>
#> - Test proportion: 0.5
#> - Confidence level: 95.0%
#>
#> region
#> ------
#> Categories:
#> ----------------------------------
#> N Observed Prop.
#> Group 1: East 485 0.194
#> Group 2: West 2015 0.806
#> Total 2500 1.000
#> ----------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0 0.179 0.21 ***
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Multiple variables at once
survey_data %>%
binomial_test(gender, region, p = 0.50)
#>
#> Binomial Test Results
#> ---------------------
#>
#> - Test proportion: 0.5
#> - Confidence level: 95.0%
#>
#> gender
#> ------
#> Categories:
#> ------------------------------------
#> N Observed Prop.
#> Group 1: Male 1194 0.478
#> Group 2: Female 1306 0.522
#> Total 2500 1.000
#> ------------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0.026 0.458 0.497 *
#> -----------------------------------------
#>
#> region
#> ------
#> Categories:
#> ----------------------------------
#> N Observed Prop.
#> Group 1: East 485 0.194
#> Group 2: West 2015 0.806
#> Total 2500 1.000
#> ----------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0 0.179 0.21 ***
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Weighted analysis
survey_data %>%
binomial_test(gender, p = 0.50, weights = sampling_weight)
#>
#> Weighted Binomial Test Results
#> ------------------------------
#>
#> - Test proportion: 0.5
#> - Confidence level: 95.0%
#> - Weights variable: sampling_weight
#>
#> gender
#> ------
#> Categories:
#> ------------------------------------
#> N Observed Prop.
#> Group 1: Male 1194 0.478
#> Group 2: Female 1306 0.522
#> Total 2500 1.000
#> ------------------------------------
#>
#> Weighted Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0.026 0.458 0.497 *
#> -----------------------------------------
#>
#> Note: Weighted analysis uses rounded frequency weights.
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Grouped analysis (separate test per region)
survey_data %>%
group_by(region) %>%
binomial_test(gender, p = 0.50)
#>
#> Binomial Test Results
#> ---------------------
#>
#> - Test proportion: 0.5
#> - Confidence level: 95.0%
#>
#>
#> Group: region = East
#> --------------------
#>
#> gender
#> ------
#> Categories:
#> -----------------------------------
#> N Observed Prop.
#> Group 1: Male 238 0.491
#> Group 2: Female 247 0.509
#> Total 485 1.000
#> -----------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0.716 0.445 0.536
#> -----------------------------------------
#>
#>
#> Group: region = West
#> --------------------
#>
#> gender
#> ------
#> Categories:
#> ------------------------------------
#> N Observed Prop.
#> Group 1: Male 956 0.474
#> Group 2: Female 1059 0.526
#> Total 2015 1.000
#> ------------------------------------
#>
#> Test Statistics:
#> -----------------------------------------
#> Test Prop. p value CI lower CI upper sig
#> 0.5 0.023 0.452 0.497 *
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05