Understanding Test Statistics
A test statistic turns sample evidence into one standardized number. It helps compare data with a null hypothesis. This calculator follows a StatCrunch style workflow. You choose the test, enter values, and review each computed step.
Why the Value Matters
The statistic shows distance from the null value. A large absolute z or t value suggests stronger evidence. A large chi-square value shows larger disagreement between observed and expected counts. An F value compares two variances. The p-value then measures how unusual the statistic is under the null model.
Supported Test Choices
The tool supports one mean z tests, one mean t tests, one proportion z tests, two mean tests, paired t tests, two proportion z tests, chi-square tests, and F variance tests. This range covers classroom and reporting cases. It also helps users check answers before entering work in statistical software.
Reading the Output
The result panel shows the test name, estimate, standard error, statistic, degrees of freedom, p-value, alpha, and decision. The decision uses the p-value approach. When the p-value is less than or equal to alpha, reject the null hypothesis. Otherwise, do not reject it.
Good Input Practice
Use summary statistics from reliable data. Match the test to the sampling plan. Use paired t only when observations are matched. Use two sample methods when groups are independent. For chi-square tests, expected counts should be at least five. For proportions, success and failure counts should be large enough.
Exporting Results
The download buttons save the result. CSV works well for spreadsheets. PDF is useful for homework records or audit notes. Keep exported reports with the original data source. This makes your conclusion easier to verify later.
Common Mistakes
Do not mix sample standard deviation with population standard deviation. That choice changes the test type. Do not enter percentages as whole numbers unless the field asks for counts. Review the tail setting before judging significance. A left tail, right tail, and two tail test can give different p-values from the same statistic.
Final Notes
A calculator cannot decide study design quality. It only applies formulas to the entered values. Always check assumptions, sample selection, and measurement methods. Those details affect the trustworthiness of every statistical conclusion.