What This Calculator Does
A standardized test statistic turns sample evidence into one comparable score. It tells how far an estimate sits from a null value. The distance is measured in standard error units. That simple idea supports many hypothesis tests. This calculator handles means, proportions, variances, and two sample cases. It also reports the distribution, degrees of freedom, p value, critical value, and decision.
Why Standardization Helps
Raw differences can mislead. A mean difference of five may be large in one study. It may be small in another study. The standard error adjusts that difference for sample size and spread. Large samples usually create smaller standard errors. Higher variation creates larger standard errors. The test statistic combines these effects in one number. A larger absolute statistic often shows stronger evidence against the null claim.
Choosing the Right Test
Use a one mean z test when the population standard deviation is known. Use a one mean t test when it is unknown and the sample standard deviation is used. Use proportion tests when the measurement is a count of successes. Use Welch t for two independent means when spreads differ. Use the chi square option for one variance. Use the F option for comparing two variances.
Reading the Result
The p value shows how unusual the statistic is under the null hypothesis. A small p value means the sample result would be rare if the null claim were true. The alpha level is your cutoff. Common choices are 0.10, 0.05, and 0.01. If the p value is not greater than alpha, reject the null. Otherwise, fail to reject it. This does not prove the null. It only says evidence is not strong enough.
Good Practice
Check assumptions before trusting any result. Samples should be random. Observations should be independent. Extreme outliers can distort mean based tests. Proportion tests need enough expected successes and failures. Variance tests are sensitive to nonnormal data. Use the export buttons to keep a record. Include inputs, formulas, and interpretation in reports. Review context before making business, research, or classroom decisions. Store each run with its date. Compare exports when assumptions or sample sizes change during sensitivity checks later for better review trails.