Intermediate10 min readSource-backed

T-Tests: Comparing Means Between Groups

Master the one-sample, independent samples, and paired t-tests: when to use each, what assumptions to check, and how to interpret the output.

You'll learn

When and how to compare two group means and check your assumptions.

Use this when

You want to compare blood pressure, BMI, or test scores between two groups.

Try this in VibeResearch

The t-Test Family

T-tests compare means and quantify whether observed differences are likely due to chance. All t-tests produce a t-statistic, degrees of freedom (df), and a p-value. There are three common variants:

●One-sample t-test: Compare a sample mean to a known or hypothesized value
●Independent samples t-test: Compare means of two unrelated groups
●Paired (dependent) samples t-test: Compare means of the same subjects under two conditions

Independent Samples t-Test

Use this when you have two distinct, unrelated groups and want to compare their means on a continuous outcome.

●Example: Compare mean HbA1c between diabetic patients who received Drug A vs. Drug B (different patients in each group)
●H₀: μ₁ = μ₂ (no difference in means)
●H₁: μ₁ ≠ μ₂ (two-tailed) or μ₁ > μ₂ (one-tailed)
●Report: Mean ± SD for each group, t(df) = X.XX, p = 0.XXX, 95% CI for difference, Cohen's d

Always use Welch's t-test (which adjusts for unequal variances) unless you have strong evidence of equal variances. Most software defaults to Welch's version.

Paired Samples t-Test

Use this when the same subjects (or matched pairs) provide two measurements. The paired design eliminates between-subject variability, giving more statistical power.

●Example: Measure blood pressure before and after a 12-week intervention in the same patients
●Example: Compare scores from left eye and right eye in the same patients
●The test is performed on the within-subject differences (d = post - pre)
●H₀: The mean of differences = 0
●Report: Mean difference ± SD of differences, t(df), p, 95% CI for the mean difference

Checking Assumptions

1.Continuous outcome: The dependent variable must be measured on an interval or ratio scale
2.Normality: For independent t-test, each group should be approximately normal. For paired t-test, the differences should be normal. Check with Shapiro-Wilk.
3.Independence: Observations within each group must be independent (unless using paired test)
4.No extreme outliers: Outliers can distort the mean and inflate variance. Examine with boxplots.

If normality is violated and sample size is small (n < 30), use Mann-Whitney U (independent) or Wilcoxon signed-rank (paired) instead.

Interpreting t-Test Output

Typical software output includes:

●t-statistic: Larger absolute values → stronger evidence against H₀
●df (degrees of freedom): Related to sample size; larger df → results closer to normal distribution
●p-value: Probability of this result assuming H₀ is true
●95% CI for the difference: If it excludes 0, result is significant at p < 0.05
●Cohen's d: Effect size. d = 0.2 (small), 0.5 (medium), 0.8 (large)

Example interpretation: "The treatment group had significantly lower HbA1c (7.2 ± 0.8%) compared to the control group (8.1 ± 1.0%), t(58) = 4.12, p < 0.001, d = 1.05 (large effect)."

Practice with your own dataset

Upload a dataset with a continuous variable and a two-category grouping variable, then run the T-Test to compare means between the groups.

Required variables

• One continuous outcome variable
• One binary grouping variable

1.Upload your dataset with a numeric outcome and a 2-group variable
2.Select "T-Test" from the analysis menu
3.Assign the continuous variable to "Outcome" and the grouping variable to "Group"
4.Review t-statistic, p-value, 95% CI for the difference, and Cohen's d

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