Online t-Test Calculator (One-sample, Paired & Independent)

When to use this test

• •You want to compare a sample mean against a known reference value (one-sample t-test).
• •You have two related measurements on the same subjects — before/after, left/right, matched pairs (paired t-test).
• •You have two independent groups and want to know whether their means differ (independent t-test).
• •Your outcome variable is continuous (metric) and roughly normally distributed.
• •Your sample size is small-to-moderate and the underlying variance is unknown.

How to use it

1. 1

   Upload or paste your data

   Open the analyzer and drag a CSV or XLSX file into the upload area, or paste rows directly into the spreadsheet grid. One column should hold the outcome values; if you are running an independent t-test, a second column should hold the group label.

2. 2

   Pick the t-test variant from the catalog

   Open Hypothesis Tests in the sidebar. Choose One-sample, Paired or Independent t-test depending on your design. The catalog only enables variants that match the column types you have assigned.

3. 3

   Assign variables to roles

   Drag the outcome column into the Dependent slot. For an independent test, drag the group label into the Group slot. For a paired test, assign the two paired columns. For a one-sample test, enter the reference value (mu) you are comparing against.

4. 4

   Review the results table and chart

   You get the t-statistic, degrees of freedom, two-tailed p-value, mean difference, 95% confidence interval for the difference, and Cohen's d. A boxplot or paired-difference plot is generated automatically.

5. 5

   Export or save

   Download the results table as CSV, copy the plain-English interpretation into your report, or save the whole analysis to your DeepStats history if you are logged in.

Example with sample data

Below is a minimal dataset for an independent t-test. Two study groups, eight observed test scores. Paste the block into the analyzer grid.

Group,Score
A,85
A,92
A,91
A,88
B,78
B,72
B,80
B,75

With this sample the analyzer reports t ≈ 4.6, df = 6, p ≈ 0.0036, mean difference ≈ 10.25 and Cohen's d ≈ 2.3. Because p is below 0.05 you would reject the null hypothesis of equal means; the effect size is very large, so the difference is not just detectable but substantively big.

How to interpret the results

You will see: t-statistic, degrees of freedom, p-value (two-tailed), mean difference, 95% confidence interval, Cohen's d.

t-statistic

The ratio of the observed effect to its standard error. For the classical formula t = (x̄ − μ) / (s / √n) in a one-sample test, larger absolute values of t indicate the sample mean sits further from the reference than sampling noise alone would explain.

Degrees of freedom (df)

Controls which t-distribution is used to compute the p-value. df = n − 1 for one-sample and paired tests; for independent tests with Welch correction, df is computed from the Welch-Satterthwaite formula.

p-value

The probability of observing a test statistic at least as extreme as yours under the null hypothesis. A common threshold is 0.05: below it you reject the null, above it you do not. A p-value is not the probability that the null is true.

95% confidence interval for the mean difference

A range of plausible values for the true mean difference. If the interval excludes zero, the result is significant at the 0.05 level. The width of the interval tells you how precisely you estimated the effect.

Cohen's d

Standardised effect size. Conventional benchmarks: 0.2 small, 0.5 medium, 0.8 large. Always report d alongside the p-value — a tiny effect can be statistically significant in a huge sample without being practically meaningful.

Assumptions

• Normality.Each sample should be roughly normally distributed. Moderate departures are tolerated thanks to the central limit theorem once n is above ~30 per group. For small, skewed samples, switch to the Mann-Whitney U test (independent design) or the Wilcoxon signed-rank test (paired design).
• Independence.Observations within and between groups must be independent. Time-series data, nested designs (students within classes) or repeated measurements require a different test — paired t, repeated-measures ANOVA or a mixed model.
• Equal variances (Student version only).Classical Student's t-test assumes the two groups share the same variance. Levene's test is run automatically; when variances differ, DeepStats applies Welch's correction so you still get a valid p-value.
• Measurement scale.The outcome must be at least interval-scaled. Ordinal data (Likert ranks) should be analysed with a rank-based alternative like Mann-Whitney or Wilcoxon.

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Frequently asked questions