Calculator
Formula Used
t statistic: t = (x̄ - μ0) / (s / √n)
Degrees of freedom: df = n - 1
Right tail p value: P(T ≥ t)
Left tail p value: P(T ≤ t)
Effect size: d = (x̄ - μ0) / s
How to Use This Calculator
Enter the sample mean, hypothesized mean, sample standard deviation, sample size, alpha, and tail direction.
Use right tail when your claim is greater than the hypothesized mean. Use left tail when your claim is less than it.
You may paste raw values instead. Separate values with commas, spaces, or line breaks. Then press Calculate.
Review the p value, critical value, effect size, and decision. Export the result as CSV or PDF when needed.
Example Data Table
| Case | Mean | Test Mean | SD | n | Tail | Alpha | t | One Tail p | Decision |
|---|---|---|---|---|---|---|---|---|---|
| Training score | 52 | 50 | 5 | 25 | Right | 0.05 | 2.000 | 0.028 | Reject H0 |
| Defect weight | 47 | 50 | 6 | 36 | Left | 0.05 | -3.000 | 0.002 | Reject H0 |
| Process time | 101 | 100 | 12 | 40 | Right | 0.05 | 0.527 | 0.301 | Do not reject H0 |
Understanding a One Tail T Test
A one tail t test checks one directed claim. It compares a sample mean with a claimed population mean. The test is useful when the question has one clear direction. You may test whether a mean is greater than a value. You may also test whether it is less than a value.
When to Use It
Use this test when the population standard deviation is unknown. Use a sample standard deviation instead. The observations should be independent. The sample should come from a roughly normal population. Larger samples can handle mild non normality better. The test is common in quality checks, surveys, finance studies, and experiments.
How the Result Works
The calculator finds the t statistic first. It then uses the degrees of freedom. The degrees of freedom equal sample size minus one. A positive t statistic means the sample mean is above the test mean. A negative t statistic means it is below. The p value measures tail evidence. A small p value supports the selected direction.
Right Tail and Left Tail Choices
Choose right tail when the alternative claim says greater than. Choose left tail when the claim says less than. The tail choice must be made before looking at results. Changing the tail after seeing data weakens the analysis. This is because it can favor a wanted conclusion.
Interpreting the Decision
Compare the p value with alpha. Alpha is the chosen significance level. A common alpha is 0.05. If the p value is less than or equal to alpha, reject the null hypothesis. Otherwise, do not reject it. This does not prove the null is true. It only means the sample did not give enough directed evidence.
Practical Notes
Always review the mean difference and effect size. A result can be statistically significant but still small in practice. A large effect can also fail significance with a small sample. Report the t statistic, degrees of freedom, p value, alpha, and tail. Include the sample details. Clear reporting helps readers judge both evidence and meaning. Use graphs only as support. Do not replace the test with a chart. Keep raw data available. It lets another reviewer repeat your work exactly later.
FAQs
What is a one tail t test?
It is a test for a directional claim about a population mean. It checks whether a sample mean is significantly greater than or less than a hypothesized mean.
When should I choose a right tail test?
Choose right tail when your alternative hypothesis says the population mean is greater than the hypothesized mean. Make this choice before viewing the result.
When should I choose a left tail test?
Choose left tail when your alternative hypothesis says the population mean is less than the hypothesized mean. The p value will use the left side of the t distribution.
What does the p value mean?
The p value shows how unusual the sample result is under the null hypothesis. Smaller p values give stronger evidence for the selected directional claim.
What is alpha?
Alpha is the significance level. It is the cutoff used for the decision. Common values are 0.05, 0.01, and 0.10.
Can I use raw data?
Yes. Paste at least two values in the raw data box. The calculator will compute the sample mean, standard deviation, and sample size from those values.
What is Cohen d?
Cohen d is an effect size. It divides the mean difference by the sample standard deviation. It helps show practical size, not just statistical evidence.
Does rejecting H0 prove the claim?
No. It means the sample gives enough evidence at the selected alpha level. Statistical results should still be judged with data quality and study design.