mariposa (version 0.7.3)

normality_test: Test Variables for Normality

Description

normality_test() checks whether numeric variables follow a normal distribution, producing the two tests SPSS prints in its EXAMINE "Tests of Normality" table:

• Kolmogorov-Smirnov with Lilliefors significance correction (the "Kolmogorov-Smirnov(a)" column in SPSS)

• Shapiro-Wilk (computed for n between 3 and 5000, matching the SPSS convention)

Use it before a t-test, ANOVA, or Pearson correlation to check the normality assumption, together with levene_test for the equal-variances assumption.

Usage

normality_test(data, ...)

Value

An object of class "normality_test" whose $results

tibble holds one row per variable (and group combination) with:

n

Number of valid (non-missing) cases

ks_statistic, ks_df, ks_p

Kolmogorov-Smirnov statistic with Lilliefors-corrected p-value (Dallal-Wilkinson approximation); df equals n as in SPSS

shapiro_w, shapiro_p

Shapiro-Wilk W and p-value (NA when n < 3 or n > 5000)

Arguments

data

Your survey data (a data frame or tibble). If grouped (via dplyr::group_by()), the tests are run separately per group — matching SPSS EXAMINE ... BY factor.

...

Variables to test (unquoted, supports tidyselect). All selected variables must be numeric.

Details

Understanding the Output

For both tests the null hypothesis is "the variable is normally distributed":

• p >= 0.05: No significant deviation from normality detected.

• p < 0.05: The variable deviates significantly from a normal distribution.

With large survey samples these tests flag even tiny, practically irrelevant deviations. Combine them with the skewness and kurtosis from describe before deciding against a parametric test.

When to Use This

• Before t_test, oneway_anova, or pearson_cor to check the normality assumption

• Grouped (via group_by()) to check normality within each comparison group — the form of the assumption that actually matters for group comparisons

If normality is clearly violated, consider the rank-based alternatives: mann_whitney, kruskal_wallis, or spearman_rho.

Technical Details

The Lilliefors-corrected p-value uses the Dallal-Wilkinson (1986) approximation, the same correction SPSS applies in EXAMINE ("Lilliefors Significance Correction"). Shapiro-Wilk uses stats::shapiro.test() and is reported for 3 <= n <= 5000, as in SPSS. Cases with missing values are excluded per variable.

Weights: normality_test() deliberately takes no weights argument. Normality checks are a diagnostic of the sample distribution, and neither Shapiro-Wilk nor the Lilliefors correction has a well-defined fractional-frequency-weight form. Run the test on the unweighted sample.

An SPSS v29 EXAMINE reference run is pending; until it lands the statistics are verified against independent R implementations of the same published formulas (see the SPSS compatibility vignette).

References

Dallal, G. E., & Wilkinson, L. (1986). An analytic approximation to the distribution of Lilliefors's test statistic for normality. The American Statistician, 40(4), 294-296.

See Also

levene_test for the equal-variances assumption.

describe for skewness and kurtosis.

summary.normality_test for detailed output.

Other descriptive: crosstab(), describe(), frequency(), multiple_response()

Examples

library(dplyr)
data(survey_data)

# Test a single variable
normality_test(survey_data, age)

# Several variables at once
normality_test(survey_data, age, income, life_satisfaction)

# Within comparison groups (SPSS: EXAMINE ... BY gender)
survey_data %>%
  group_by(gender) %>%
  normality_test(age, income)

# --- Three-layer output ---
result <- normality_test(survey_data, age, income)
result              # compact overview
summary(result)     # full SPSS-style table