mariposa (version 0.7.3)

chisq_gof: Chi-Square Goodness-of-Fit Test

Description

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

Usage

chisq_gof(data, ..., expected = NULL, weights = NULL)

Value

Test results showing whether observed frequencies match expected, including:

• Chi-square statistic (chi_squared) and p-value for each variable

• Degrees of freedom

• Frequency table with observed, expected, and residual counts

• Sample size (N)

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

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() instead

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

• For small samples where expected frequencies are below 5: Use fisher_test() instead

SPSS Equivalent

SPSS: NPAR TESTS /CHISQUARE=variable /EXPECTED=EQUAL or: NPAR TESTS /CHISQUARE=variable /EXPECTED=50 30 20

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)

# Test multiple variables at once
survey_data %>%
  chisq_gof(gender, region, education)

# Custom expected proportions
survey_data %>%
  chisq_gof(interview_mode, expected = c(0.5, 0.3, 0.2))

# With weights
survey_data %>%
  chisq_gof(gender, weights = sampling_weight)

# Grouped analysis
survey_data %>%
  group_by(region) %>%
  chisq_gof(education)