Calculator Form
Example Data Table
| Case | Test type | Tail | Null value | Sample evidence | Alpha |
|---|---|---|---|---|---|
| Mean increase | Z mean | Right | 100 | Mean 105, n 40, sigma 15 | 0.05 |
| Mean decrease | T mean | Left | 80 | Mean 76, n 25, s 10 | 0.01 |
| Proportion increase | Z proportion | Right | 0.50 | 64 successes from 100 | 0.05 |
Formula Used
Z test for one mean: z = (x̄ - μ₀) / (σ / √n)
T test for one mean: t = (x̄ - μ₀) / (s / √n), with df = n - 1
Z test for one proportion: z = (p̂ - p₀) / √((p₀(1 - p₀)) / n)
Right tailed p value: p = P(T ≥ test statistic)
Left tailed p value: p = P(T ≤ test statistic)
Decision rule: reject H₀ when p value is less than alpha.
How To Use This Calculator
Select the test type first. Choose right tailed for greater than claims. Choose left tailed for less than claims.
Enter alpha, sample data, and null value. Use the population standard deviation for a z mean test. Use the sample standard deviation for a t mean test.
For a proportion test, enter successes, total trials, and null proportion. Press calculate. Review the statistic, p value, critical value, and final decision.
Understanding One Tailed Tests
A one tailed hypothesis test checks direction. It asks whether evidence is greater than a null value. It can also ask whether evidence is lower. This makes it different from a two sided test. The test uses one rejection area only. That area sits in the selected tail.
When To Use It
Use a right tailed test for claims about increases. Use a left tailed test for claims about decreases. The direction must be chosen before looking at results. This protects the analysis from bias. It also keeps the decision rule clear.
Inputs That Matter
The calculator supports common test forms. A mean test can use a known population standard deviation. It can also use a sample standard deviation. A proportion test uses successes and trials. Direct statistic mode is useful when your statistic is already known. Alpha sets the allowed Type I error risk.
How Results Are Read
The test statistic measures distance from the null value. It uses standard error units. A large positive statistic supports a right tailed claim. A large negative statistic supports a left tailed claim. The p value shows how rare the evidence is under the null hypothesis.
Critical Value Logic
The critical value marks the boundary of rejection. For a right tail, reject when the statistic is larger. For a left tail, reject when the statistic is smaller. The p value rule gives the same conclusion. Reject the null when p is less than alpha.
Practical Interpretation
A rejected null does not prove a claim with certainty. It means the data gives strong directional evidence. A non rejected null does not prove no effect. It means the evidence is not strong enough at the chosen alpha. Always report the test type, tail, statistic, p value, alpha, and sample details.
Good Practice
Choose the tail from the research question. Check sample quality before testing. Use a t test when the population standard deviation is unknown. Use a z test for known standard deviation or one proportion cases. Keep assumptions visible in reports. Clear assumptions make decisions easier to review. For publication, add a sentence explaining why a directional alternative was justified. This improves transparency and prevents result driven tail selection.
FAQs
What is a one tailed hypothesis test?
It is a test that checks evidence in one direction only. The claim is either greater than or less than the null value. It does not test both directions at once.
When should I use a right tailed test?
Use a right tailed test when the alternative hypothesis claims an increase. Common wording includes greater than, higher than, above, more than, or improved.
When should I use a left tailed test?
Use a left tailed test when the alternative hypothesis claims a decrease. Common wording includes less than, lower than, below, reduced, or worse.
What does the p value mean?
The p value is the probability of getting evidence this extreme, assuming the null hypothesis is true. Smaller p values show stronger evidence against the null.
What is alpha?
Alpha is the chosen significance level. It is the maximum Type I error risk you accept before testing. Common values are 0.05, 0.01, and 0.10.
Should I use z or t for a mean?
Use z when the population standard deviation is known. Use t when it is unknown and you only have the sample standard deviation.
Can I test a sample proportion?
Yes. Select the one proportion option. Enter successes, total trials, and the null proportion. The calculator then uses the one sample proportion z statistic.
Does rejection prove the alternative hypothesis?
No. Rejection means the data gives enough statistical evidence at the selected alpha. It does not prove certainty or practical importance.