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
)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%)
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.
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)
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)
#> t-Test: life_satisfaction by gender
#> t(2384.1) = -1.018, p = 0.309 , g = -0.041 (negligible), N = 2421
# With survey weights
survey_data %>%
t_test(life_satisfaction, group = gender, weights = sampling_weight)
#> t-Test: life_satisfaction by gender [Weighted]
#> t(2390.8) = -1.069, p = 0.285 , g = -0.043 (negligible), N = 2436
# Multiple variables
survey_data %>%
t_test(age, income, life_satisfaction, group = region, weights = sampling_weight)
#> t-Test: age by region [Weighted]
#> t(763.8) = 2.551, p = 0.011 *, g = 0.130 (negligible), N = 2516
#> t-Test: income by region [Weighted]
#> t(712.5) = 0.299, p = 0.765 , g = 0.016 (negligible), N = 2200
#> t-Test: life_satisfaction by region [Weighted]
#> t(721.0) = -0.031, p = 0.975 , g = -0.002 (negligible), N = 2437
# One-sample test against a benchmark
survey_data %>%
t_test(life_satisfaction, mu = 5, weights = sampling_weight)
#> t-Test: life_satisfaction [Weighted]
#> t(2436.0) = -58.925, p < 0.001 ***
# Grouped analysis
survey_data %>%
group_by(region) %>%
t_test(life_satisfaction, group = gender, weights = sampling_weight)
#> [region = 1]
#> t-Test: life_satisfaction by gender [Weighted]
#> t(484.9) = 0.641, p = 0.522 , g = 0.058 (negligible), N = 488
#> [region = 2]
#> t-Test: life_satisfaction by gender [Weighted]
#> t(1902.0) = -1.548, p = 0.122 , g = -0.070 (negligible), N = 1949
# Equal variance assumption
survey_data %>%
t_test(life_satisfaction, group = gender, var.equal = TRUE)
#> t-Test: life_satisfaction by gender
#> t(2419.0) = -1.019, p = 0.308 , g = -0.041 (negligible), N = 2421
# One-sided test
survey_data %>%
t_test(income, group = gender, alternative = "greater")
#> t-Test: income by gender
#> t(2169.3) = 0.690, p = 0.245 , g = 0.030 (negligible), N = 2186
# Using tidyselect helpers
survey_data %>%
t_test(starts_with("trust"), group = gender, weights = sampling_weight)
#> t-Test: trust_government by gender [Weighted]
#> t(2322.7) = -0.682, p = 0.495 , g = -0.028 (negligible), N = 2371
#> t-Test: trust_media by gender [Weighted]
#> t(2350.2) = -2.196, p = 0.028 *, g = -0.090 (negligible), N = 2382
#> t-Test: trust_science by gender [Weighted]
#> t(2360.9) = -1.421, p = 0.156 , g = -0.058 (negligible), N = 2414
# Store results for further analysis
result <- survey_data %>%
t_test(life_satisfaction, group = gender, weights = sampling_weight)
print(result)
#> t-Test: life_satisfaction by gender [Weighted]
#> t(2390.8) = -1.069, p = 0.285 , g = -0.043 (negligible), N = 2436
# --- Three-layer output ---
result <- t_test(survey_data, life_satisfaction, group = gender)
result # compact one-line summary
#> t-Test: life_satisfaction by gender
#> t(2384.1) = -1.018, p = 0.309 , g = -0.041 (negligible), N = 2421
summary(result) # full detailed output with all sections
#> t-Test Results
#> --------------
#>
#> - Grouping variable: gender
#> - Groups compared: Male vs. Female
#> - Confidence level: 95.0%
#> - Alternative hypothesis: two.sided
#> - Null hypothesis (mu): 0.000
#>
#>
#> --- life_satisfaction ---
#>
#> Male: mean = 3.603, n = 1149.0
#> Female: mean = 3.651, n = 1272.0
#>
#> t-test Results:
#> --------------------------------------------------------------------------------
#> Assumption t_stat df p_value mean_diff conf_int sig
#> Equal variances -1.019 2419.000 0.308 -0.048 [-0.140, 0.044]
#> Unequal variances -1.018 2384.147 0.309 -0.048 [-0.140, 0.044]
#> --------------------------------------------------------------------------------
#>
#> Effect Sizes:
#> ------------
#> Variable Cohens_d Hedges_g Glass_Delta Effect_Size
#> life_satisfaction -0.041 -0.041 -0.041 negligible
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation:
#> - Cohen's d: pooled standard deviation (classic)
#> - Hedges' g: bias-corrected Cohen's d (preferred)
#> - Glass' Delta: control group standard deviation only
#> - Small effect: |effect| ~ 0.2
#> - Medium effect: |effect| ~ 0.5
#> - Large effect: |effect| ~ 0.8
summary(result, effect_sizes = FALSE) # hide effect sizes
#> t-Test Results
#> --------------
#>
#> - Grouping variable: gender
#> - Groups compared: Male vs. Female
#> - Confidence level: 95.0%
#> - Alternative hypothesis: two.sided
#> - Null hypothesis (mu): 0.000
#>
#>
#> --- life_satisfaction ---
#>
#> Male: mean = 3.603, n = 1149.0
#> Female: mean = 3.651, n = 1272.0
#>
#> t-test Results:
#> --------------------------------------------------------------------------------
#> Assumption t_stat df p_value mean_diff conf_int sig
#> Equal variances -1.019 2419.000 0.308 -0.048 [-0.140, 0.044]
#> Unequal variances -1.018 2384.147 0.309 -0.048 [-0.140, 0.044]
#> --------------------------------------------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05