chisq_gof() tests whether observed frequencies of a categorical
variable match expected frequencies. By default, it tests against equal
proportions (uniform distribution). You can also specify custom expected
proportions.
Think of it as:
Testing whether categories are equally distributed
Comparing observed distribution to a theoretical distribution
The one-sample version of the chi-square test
The test tells you:
Whether observed frequencies differ from expected frequencies
How strong the deviation is (chi-square statistic)
A frequency table with observed, expected, and residual counts
Arguments
- data
Your survey data (data frame or tibble)
- ...
One or more categorical variables to test (tidyselect supported)
- expected
Optional numeric vector of expected proportions (must sum to 1). Only used when a single variable is tested. If NULL (default), equal proportions are assumed.
- weights
Optional survey weights for population-representative results
Value
Test results showing whether observed frequencies match expected, including:
Chi-square statistic and p-value for each variable
Degrees of freedom
Frequency table with observed, expected, and residual counts
Sample size (N)
Details
Understanding the Results
P-value: If p < 0.05, the distribution differs from expected
p < 0.001: Very strong evidence the distribution differs
p < 0.01: Strong evidence the distribution differs
p < 0.05: Moderate evidence the distribution differs
p >= 0.05: No significant deviation from expected distribution
Residuals: The difference between observed and expected counts. Large positive residuals indicate a category has more cases than expected; large negative residuals indicate fewer cases than expected.
When to Use This
Use this test when:
You want to check whether a categorical variable follows a specific distribution
You want to test if categories are equally distributed (uniform)
You have a single categorical variable and a hypothesised distribution
The Chi-Square Goodness-of-Fit Statistic
$$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$
where O_i = observed frequency, E_i = expected frequency.
Degrees of freedom = number of categories - 1.
Relationship to Other Tests
For testing association between two categorical variables: Use
chi_square()insteadFor testing a single binary proportion: Use
binomial_test()insteadFor small samples where expected frequencies are below 5: Use
fisher_test()instead
References
Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50(302), 157-175.
See also
chi_square for chi-square test of independence (two variables).
binomial_test for testing a single proportion.
Other hypothesis_tests:
ancova(),
binomial_test(),
chi_square(),
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 is equally distributed
survey_data %>%
chisq_gof(gender)
#> Chi-Square Goodness-of-Fit Test Results
#> ---------------------------------------
#>
#> - Variables: gender
#> - Expected: Equal proportions
#>
#> gender - Frequency Table:
#> ------------------------------------
#> category observed expected residual
#> Male 1194 1250 -56
#> Female 1306 1250 56
#> ------------------------------------
#>
#> ----------------------------------------
#> Variable Chi-Square df p-value N Sig
#> gender 5.018 1 0.0251 2500 *
#> ----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Test multiple variables at once
survey_data %>%
chisq_gof(gender, region, education)
#> Chi-Square Goodness-of-Fit Test Results
#> ---------------------------------------
#>
#> - Variables: gender, region, education
#> - Expected: Equal proportions
#>
#> gender - Frequency Table:
#> ------------------------------------
#> category observed expected residual
#> Male 1194 1250 -56
#> Female 1306 1250 56
#> ------------------------------------
#>
#> region - Frequency Table:
#> ------------------------------------
#> category observed expected residual
#> East 485 1250 -765
#> West 2015 1250 765
#> ------------------------------------
#>
#> education - Frequency Table:
#> --------------------------------------------------
#> category observed expected residual
#> Basic Secondary 841 625 216
#> Intermediate Secondary 629 625 4
#> Academic Secondary 631 625 6
#> University 399 625 -226
#> --------------------------------------------------
#>
#> -----------------------------------------
#> Variable Chi-Square df p-value N Sig
#> gender 5.018 1 0.0251 2500 *
#> region 936.360 1 <.001 2500 ***
#> education 156.454 3 <.001 2500 ***
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Custom expected proportions
survey_data %>%
chisq_gof(interview_mode, expected = c(0.5, 0.3, 0.2))
#> Chi-Square Goodness-of-Fit Test Results
#> ---------------------------------------
#>
#> - Variables: interview_mode
#> - Expected: 0.5, 0.3, 0.2
#>
#> interview_mode - Frequency Table:
#> ----------------------------------------
#> category observed expected residual
#> Face-to-face 1485 1250 235
#> Telephone 655 750 -95
#> Online 360 500 -140
#> ----------------------------------------
#>
#> ----------------------------------------------
#> Variable Chi-Square df p-value N Sig
#> interview_mode 95.413 2 <.001 2500 ***
#> ----------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# With weights
survey_data %>%
chisq_gof(gender, weights = sampling_weight)
#> Weighted Chi-Square Goodness-of-Fit Test Results
#> ------------------------------------------------
#>
#> - Variables: gender
#> - Expected: Equal proportions
#> - Weights variable: sampling_weight
#>
#> gender - Frequency Table:
#> ------------------------------------
#> category observed expected residual
#> Male 1195 1258 -63
#> Female 1321 1258 63
#> ------------------------------------
#>
#> ----------------------------------------
#> Variable Chi-Square df p-value N Sig
#> gender 6.31 1 0.0120 2516 *
#> ----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
# Grouped analysis
survey_data %>%
group_by(region) %>%
chisq_gof(education)
#> Chi-Square Goodness-of-Fit Test Results
#> ---------------------------------------
#>
#> - Variables: education
#> - Expected: Equal proportions
#>
#>
#> Group: region = East
#> --------------------
#> ----------------------------------------
#> Variable Chi-Square df p-value N Sig
#> education 34.645 3 <.001 485 ***
#> ----------------------------------------
#>
#>
#> Group: region = West
#> --------------------
#> -----------------------------------------
#> Variable Chi-Square df p-value N Sig
#> education 122.888 3 <.001 2015 ***
#> -----------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05