Understanding Test Statistics
A test statistic turns sample evidence into one standard number. It compares what you observed with what the null hypothesis expects. Large absolute values often show stronger disagreement. The correct statistic depends on the data type, sample design, and known information.
Common Choices
Use a z statistic when the population standard deviation is known, or when a large sample supports a normal approximation. Use a t statistic when the population standard deviation is unknown and the sample standard deviation estimates spread. Use a proportion z statistic for success rates. Use chi square for variance tests. Use an F statistic for comparing two variances.
Why the Value Matters
The value helps locate your result on a reference distribution. From that location, you can estimate a p value. The p value shows how unusual the evidence is under the null model. It does not prove the alternative. It only measures compatibility with the chosen null assumption.
Inputs and Assumptions
Good results need careful inputs. Enter sample means, sample sizes, standard deviations, proportions, hypothesized values, and degrees of freedom where needed. Keep units consistent. Check that samples are random and independent. For proportions, expected successes and failures should usually be large enough. For t tests, strong skew or extreme outliers can distort conclusions.
Interpreting Results
A positive statistic means the observed estimate is above the hypothesized value. A negative statistic means it is below it. Two tailed tests use the magnitude in both directions. Right tailed tests focus on high values. Left tailed tests focus on low values. Compare the p value with alpha. When p is less than alpha, reject the null hypothesis.
Practical Use
This calculator shows formulas, substitutions, degrees of freedom, p values, and a decision. It also creates exportable records. Use the example table to understand entry patterns. Use the reports for homework notes, audit trails, or classroom checking. The calculator supports fast exploration, but conclusions still require sound study design and context.
Limits and Care
Rounded inputs can change the final statistic slightly. Always keep the raw study record when possible. Report the chosen test, tail direction, alpha level, and assumption checks with the final number. This makes the calculation easier to review by readers.