Unpaired t test: vitamin C and tooth growth
Compare tooth length under two vitamin C supplements.
T-Test Calculator
FigranPaste two groups to get the p value, effect size and a graph with the significance bracket.
- Welch, paired or Mann–Whitney
- Effect size with 95% CI
- Graph with p value bracket
Data
Test
Options
p = 0.0064
Welch t (14.97) = 3.17 · mean difference 5.25 (95% CI 1.72 to 8.78) · g = 1.36
Descriptive statistics
| Group | n | Mean | SD | SEM | Median | Q1–Q3 | Min–max |
|---|---|---|---|---|---|---|---|
| OJ | 10 | 13.23 | 4.46 | 1.41 | 12.25 | 9.70–16.18 | 8.20–21.50 |
| VC | 10 | 7.98 | 2.75 | 0.87 | 7.15 | 5.95–10.90 | 4.20–11.50 |
Test results
| t | 3.17 |
|---|---|
| df | 14.97 |
| p | p = 0.0064 |
| 95% CI | 1.72 – 8.78 |
| Hedges' g | 1.36 [0.39, 2.29] |
| p < α (0.05) | Yes |
Assumption checks
| Shapiro–Wilk OJ | W = 0.89, p = 0.18 |
|---|---|
| Shapiro–Wilk VC | W = 0.89, p = 0.17 |
| SD ratio (larger / smaller) | 1.62 |
Use these as a description, not as a gate for choosing the test.
Report
Results
OJ (M = 13.23, SD = 4.46, n = 10); VC (M = 7.98, SD = 2.75, n = 10). Welch t(14.97) = 3.17, p = .0064; mean difference = 5.25, 95% CI [1.72, 8.78], Hedges' g = 1.36, 95% CI [0.39, 2.29].
Methods
Groups were compared with Welch's t test (two-sided, α = 0.05).
T-test calculator examples
Explore real datasets and load one to try the calculator.
Paired t test example: two sleep drugs
Compare extra sleep after the same participants take two sleep drugs.
Mann–Whitney U test: skewed ozone levels
Compare the distributions of ozone in May and August.
Wilcoxon signed-rank test: depression scores
Compare paired scores at two visits after treatment begins.
One-sample t test example: Michelson’s speed of light
Compare measurements with a reference value.
From mean, SD and n: chick weights by feed
Compare two groups from summary statistics.
Bar graph with significance stars: insect sprays
Compare insect counts after two sprays.
Student’s t test: plant dry weight
Compare treatment and control plant weights.
How to do a t test
Compare your data and make a figure in four steps.
1Choose a design
Paste the values for each group.
2Choose a test
Welch is the default for two independent groups.
3Read the results
Review the p value, interval and effect size.
4Export your work
Choose a graph style and download or copy the results.
Which t test should I use?
Choose a test that matches your design and data.
| Design | Data / assumptions | Test | Effect size | Plot |
|---|---|---|---|---|
| Two groups | Continuous data; equal variances not assumed | Welch t test | g | Dots |
| Two groups | Continuous data; equal variances assumed | Student t test | g | Dots |
| Paired | Paired continuous differences | Paired t test | dz | Paired lines |
| One group | Continuous values versus a reference mean | One-sample t test | d | Dots |
| Two groups | Independent ordinal or non-normal data | Mann–Whitney U (Wilcoxon rank-sum) | rrb | Box + dots |
| Paired | Paired or one-sample differences; symmetric distribution | Wilcoxon signed-rank | rrb | Paired lines |
| One group | Paired or one-sample differences; symmetric distribution | Wilcoxon signed-rank | rrb | Dots |
Welch's t test by default
Welch’s test accommodates unequal variances and is a practical default for independent groups.
Normality and equal variances
Assumption checks describe the data; avoid using a preliminary normality test as an automatic gate for choosing a test.
References: Delacre et al. (2017) · Ruxton (2006) · Rochon et al. (2012)
T test formulas
These formulas connect the estimates with their uncertainty.
Welch t test
Student t test
Paired t test / One-sample t test
Hedges’ g
For the default example, (13.23 − 7.98) / √(4.46²/10 + 2.75²/10) ≈ 3.17.
Rank tests
U is the first group’s rank sum minus n₁(n₁ + 1)/2. The displayed V and effect size use ranks after removing zero differences. For exact p values, zeros are included in ranking and excluded from sign assignments, matching R 4.6; larger samples use a continuity-corrected normal approximation.
References: Student (1908) · Welch (1947) · Mann & Whitney (1947) · Wilcoxon (1945)
T-test calculator FAQ
Which t test should I use?
Use Welch for independent groups, a paired test for repeated measurements, and a one-sample test against a fixed value. For three or more groups, consider ANOVA. ANOVA calculator.
Should I use Welch’s or Student’s t test?
Welch is a useful default because it accommodates unequal variances while remaining effective when variances are similar. R uses Welch by default; GraphPad QuickCalcs also offers it.
What is the difference between paired and unpaired tests?
A paired test analyzes matched differences. Group summaries alone do not preserve the pairing.
When should I use Mann–Whitney or Wilcoxon?
Consider rank tests for ordered or markedly skewed data. They compare ranks and distributions rather than means. A log transform may be appropriate for fold-change data.
Do I need to test normality before a t test?
No; a preliminary normality test should not be an automatic gate for choosing a test. Avoid post-hoc power based on a nonsignificant p value; plan sample size before collecting data. Power analysis calculator.
One-tailed or two-tailed?
Use a two-sided test unless a direction was specified before collecting the data.
How do I report a t test result?
Report the group summaries, statistic, degrees of freedom, p value, confidence interval and effect size.
What do the asterisks on the graph mean?
One, two, three and four stars indicate p below 0.05, 0.01, 0.001 and 0.0001, respectively. State the thresholds and test in the legend. To add labels manually to an existing figure, use: Bar graph maker · Box plot maker.
Do the results match R, GraphPad Prism and Excel?
The t tests follow standard formulas used by R, Prism and Excel; Excel T.TEST types 1, 2 and 3 select paired, Student and Welch tests. Small-sample rank tests use the R 4.6 exact conditional distribution; SPSS and older R approximations may differ. For exact signed-rank p values, zero differences are included when ranking but excluded from the sign distribution, as in R. The displayed V and effect size use ranks after removing zeros, so R may display a different V. Data stay in your browser. For additional effect sizes, use: Effect size calculator.