mariposa (version 0.7.3)

t_test: Test If Two Groups Differ

Description

t_test() helps you determine if two groups have different average values. For example, do men and women have different satisfaction scores? Does Region A spend more than Region B? Is this year better than last year?

The test tells you:

• Whether the difference is statistically significant

• How big the difference is (effect sizes)

• The likely range of the true difference (confidence interval)

Usage

t_test(
  data,
  ...,
  group = NULL,
  weights = NULL,
  var.equal = FALSE,
  mu = 0,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)

Value

Test results showing whether groups differ, including:

• t-statistic and p-value for statistical significance

• Mean difference and confidence interval

• Effect sizes (Cohen's d, Hedges' g, Glass' Delta)

• Group statistics (mean, SD, sample size) Use summary() for the full SPSS-style output with toggleable sections.

Arguments

data

Your survey data (a data frame or tibble)

...

The numeric variables to test. List multiple variables or use tidyselect helpers like starts_with("trust").

group

The variable that defines your two groups (e.g., gender, region). Must have exactly two categories. Leave empty for one-sample tests.

weights

Optional survey weights for population-representative results

var.equal

Should we assume equal variances? (Default: FALSE)

• FALSE: Safer, works even if groups vary differently (Welch's test)

• TRUE: Traditional approach, assumes equal spread (Student's test)

mu

Comparison value (Default: 0). For two-sample tests, usually 0. For one-sample tests, your benchmark value.

alternative

Direction of the test:

• "two.sided" (default): Any difference

• "greater": First group is higher

• "less": First group is lower

conf.level

Confidence level for intervals (Default: 0.95 = 95%)

Details

Understanding the Results

P-value: Is the difference statistically significant?

• p < 0.001: Very strong evidence of a difference

• p < 0.01: Strong evidence of a difference

• p < 0.05: Moderate evidence of a difference

• p >= 0.05: No significant difference found

Effect Sizes (How big is the difference?):

• Cohen's d: The standard measure

  • |d| < 0.2: Negligible difference

  • |d| = 0.2-0.5: Small difference

  • |d| = 0.5-0.8: Medium difference

  • |d| > 0.8: Large difference

• Hedges' g: Corrected for small samples

• Glass' Delta: Uses control group SD only

Confidence Interval: Range where the true difference likely falls

• If it includes 0, groups may not differ

• Width indicates precision (narrower = more precise)

When to Use This

Use t-test when:

• You have exactly two groups to compare

• Your outcome variable is numeric (continuous)

• Groups are independent (different people in each)

• Data is roughly normally distributed (or n >= 30 per group)

Don't use when:

• You have more than two groups (use ANOVA)

• Data is severely skewed with small samples (use Mann-Whitney)

• Groups are paired/matched (use paired t-test - coming soon)

• Variables are categorical (use chi-square)

Reading the Output

The results show both variance assumptions:

• Welch's test (var.equal = FALSE): Safer, doesn't assume equal variances

• Student's test (var.equal = TRUE): Traditional, assumes equal variances

A result with t = 2.45, p = 0.015, d = 0.62 means:

• Groups are 2.45 standard errors apart (t-statistic)

• 1.5% chance this is due to random variation (p-value)

• Medium-sized practical difference (Cohen's d)

Tips for Success

• Always check sample sizes (aim for 30+ per group)

• Consider both statistical significance AND effect size

• Use weights for population-level conclusions

• Plot your data first to check assumptions

• Report confidence intervals along with p-values

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107-128.

Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5(10), 3-8.

Welch, B. L. (1947). The generalization of "Student's" problem when several different population variances are involved. Biometrika, 34(1-2), 28-35.

See Also

t.test for the base R t-test function.

print.t_test for printing results.

group_by for grouped analyses.

summary.t_test for detailed output with toggleable sections.

Other hypothesis_tests: ancova(), binomial_test(), chi_square(), chisq_gof(), factorial_anova(), fisher_test(), friedman_test(), kruskal_wallis(), mann_whitney(), mcnemar_test(), oneway_anova(), wilcoxon_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Basic two-sample test
survey_data %>%
  t_test(life_satisfaction, group = gender)

# With survey weights
survey_data %>%
  t_test(life_satisfaction, group = gender, weights = sampling_weight)

# Multiple variables
survey_data %>%
  t_test(age, income, life_satisfaction, group = region, weights = sampling_weight)

# One-sample test against a benchmark
survey_data %>%
  t_test(life_satisfaction, mu = 5, weights = sampling_weight)

# Grouped analysis
survey_data %>%
  group_by(region) %>%
  t_test(life_satisfaction, group = gender, weights = sampling_weight)

# Equal variance assumption
survey_data %>%
  t_test(life_satisfaction, group = gender, var.equal = TRUE)

# One-sided test
survey_data %>%
  t_test(income, group = gender, alternative = "greater")

# Using tidyselect helpers
survey_data %>%
  t_test(starts_with("trust"), group = gender, weights = sampling_weight)

# Store results for further analysis
result <- survey_data %>%
  t_test(life_satisfaction, group = gender, weights = sampling_weight)
print(result)

# --- Three-layer output ---
result <- t_test(survey_data, life_satisfaction, group = gender)
result              # compact one-line summary
summary(result)     # full detailed output with all sections
summary(result, effect_sizes = FALSE)  # hide effect sizes