Calculator Form
Example Data Table
| Scenario | Test choice | Sample A | Sample B | Null value |
|---|---|---|---|---|
| Class score versus target | One sample | 82, 79, 85, 88, 81 | Not used | 80 |
| Before and after training | Paired samples | Before values | After values | 0 |
| Two independent groups | Welch unequal variance | Group one values | Group two values | 0 |
Formula Used
One sample: t = (x̄ - μ0) / (s / √n), df = n - 1.
Paired samples: t = (d̄ - d0) / (sd / √n), df = n - 1.
Independent equal variance: t = [(x̄1 - x̄2) - Δ0] / [sp √(1/n1 + 1/n2)].
Welch test: t = [(x̄1 - x̄2) - Δ0] / √(s1²/n1 + s2²/n2).
Decision: reject the null hypothesis when p value is less than alpha.
How To Use This Calculator
- Select the correct t test type.
- Choose raw data or summary statistics.
- Enter the null mean or null difference.
- Choose the tail, alpha, and confidence level.
- Press Calculate to view the result above the form.
- Use CSV or PDF buttons to save the report.
Understanding T Test Results
Purpose
A t test helps compare a sample result against a target. It also compares two sample means. The method is useful when sample sizes are limited. It works best when observations are independent. The data should be roughly normal, especially for small groups.
Choosing The Test
This calculator supports common t test layouts. Use one sample testing when one group is compared with a known value. Use paired testing when two measurements belong to the same subject. Use independent testing when groups are separate. Choose Welch testing when spreads are unequal.
Main Output
The main output is the t statistic. It measures how far the observed estimate is from the null value. The distance is scaled by standard error. A larger absolute t value gives stronger evidence against the null claim. The degrees of freedom define the curve used for probability.
P Value
The p value shows how unusual the result is under the null claim. A small p value means the observed difference is unlikely by random sampling alone. Compare it with alpha. If the p value is below alpha, reject the null claim. If it is not below alpha, do not reject it.
Confidence Interval
Confidence intervals give a practical range for the true mean or difference. A narrow interval means the estimate is precise. A wide interval means more uncertainty remains. The interval is built with the critical t value and standard error.
Effect Size
Effect size adds meaning beyond significance. Cohen style values show the size of the difference in standard deviation units. This helps compare studies with different units. It also helps avoid overreading tiny effects from large samples.
Assumptions
Always review assumptions before using results. Check for outliers. Check whether groups are paired or independent. For skewed data, consider larger samples or a nonparametric method. For unequal variances, Welch testing is usually safer.
Reporting
Use the report as a decision aid, not a final judgment. Statistical evidence should be paired with subject knowledge. Good input data matters most. Clear hypotheses also matter. Document the test type, alpha level, and tail choice. Then keep the downloaded file with your notes for future review.
Final Note
When reporting, state sample sizes, means, standard deviations, test statistic, degrees of freedom, p value, confidence interval, and final interpretation in plain language for readers.
FAQs
What is a t test?
A t test checks whether a sample mean or mean difference is statistically different from a chosen null value.
When should I use a one sample t test?
Use it when one sample mean is compared with a known target, standard, or hypothesized population mean.
When should I use a paired t test?
Use it when both measurements come from the same subjects, matched pairs, or before and after observations.
What is Welch testing?
Welch testing compares two independent means without assuming equal variance. It is often safer for unequal spreads.
What does the p value mean?
The p value shows how likely the observed result is under the null hypothesis and selected test direction.
What does alpha mean?
Alpha is the rejection threshold. Common choices are 0.05, 0.01, and 0.10.
Can I enter raw values?
Yes. Enter comma, space, or line separated values. The calculator computes sample means and standard deviations.
What does effect size show?
Effect size shows practical difference in standard deviation units. It helps judge importance beyond statistical significance.