mcnemar_test() tests whether paired proportions have changed between
two dichotomous measurements. Use this for before/after comparisons of
categorical outcomes.
Think of it as:
A paired comparison test for binary (yes/no) data
The categorical equivalent of a paired t-test
Tests whether the proportion of "changers" is symmetric
The test tells you:
Whether paired proportions changed significantly
Both asymptotic and exact p-values for maximum reliability
The number of discordant pairs (who actually changed)
Arguments
- data
Your survey data (data frame or tibble)
- var1
First dichotomous variable (0/1 or two-level factor)
- var2
Second dichotomous variable (0/1 or two-level factor)
- weights
Optional survey weights for population-representative results
- correct
Logical, whether to apply continuity correction (default: TRUE)
- ...
Additional arguments (currently unused)
Value
Test results showing whether paired proportions changed, including:
McNemar chi-square statistic (with continuity correction)
Asymptotic p-value
Exact binomial p-value (two-sided)
2x2 contingency table
Discordant pair counts (b and c)
Details
Understanding the Results
P-value: If p < 0.05, the paired proportions are significantly different
p < 0.001: Very strong evidence of change
p < 0.01: Strong evidence of change
p < 0.05: Moderate evidence of change
p >= 0.05: No significant change found
Exact vs Asymptotic: The exact binomial p-value is more reliable for small samples. For large samples, both p-values will be very similar.
Discordant Pairs: Only pairs where the two measurements differ (b and c) contribute to the test. If b approximately equals c, there is no evidence of systematic change.
When to Use This
Use McNemar's test when:
You have paired or matched binary data
You're comparing before/after proportions
Both variables must be dichotomous (exactly 2 levels)
The McNemar Statistic
For a 2x2 table with discordant cells b and c: $$\chi^2 = \frac{(|b - c| - 1)^2}{b + c}$$ (with continuity correction)
The exact test uses a binomial test on the discordant pairs.
Relationship to Other Tests
For unpaired categorical data: Use
chi_square()insteadFor paired ordinal/continuous data: Use
wilcoxon_test()insteadFor paired data with more than 2 levels: Consider the Bowker test of symmetry
References
McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157.
See also
chi_square for independence tests.
wilcoxon_test for paired non-parametric tests on ordinal data.
Other hypothesis_tests:
ancova(),
binomial_test(),
chi_square(),
chisq_gof(),
factorial_anova(),
fisher_test(),
friedman_test(),
kruskal_wallis(),
mann_whitney(),
oneway_anova(),
t_test(),
wilcoxon_test()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Create dichotomous variables
test_data <- survey_data %>%
mutate(
trust_gov_high = as.integer(trust_government >= 4),
trust_media_high = as.integer(trust_media >= 4)
)
# McNemar test
test_data %>%
mcnemar_test(var1 = trust_gov_high, var2 = trust_media_high)
#> McNemar Test Results
#> --------------------
#>
#> - Variable 1: trust_gov_high
#> - Variable 2: trust_media_high
#>
#> 2x2 Contingency Table:
#> ----------------------------------------
#> v2
#> v1 0 1
#> 0 1342 338
#> 1 448 99
#> ----------------------------------------
#>
#> Test Results:
#> -----------------------------------------
#> Chi-Sq (cc) p (asymp) p (exact) N Sig
#> 15.116 <.001 <.001 2227 ***
#> -----------------------------------------
#>
#> Discordant pairs: b = 338, c = 448
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Grouped analysis
test_data %>%
group_by(region) %>%
mcnemar_test(var1 = trust_gov_high, var2 = trust_media_high)
#> McNemar Test Results
#> --------------------
#>
#> - Variable 1: trust_gov_high
#> - Variable 2: trust_media_high
#>
#>
#> Group: region = East
#> --------------------
#> -----------------------------------
#> Chi-Sq p (asymp) p (exact) N Sig
#> 8.255 0.0041 0.0039 435 **
#> -----------------------------------
#>
#>
#> Group: region = West
#> --------------------
#> ------------------------------------
#> Chi-Sq p (asymp) p (exact) N Sig
#> 8.242 0.0041 0.0041 1792 **
#> ------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05