Test Statistic Calculator for Hypothesis Tests

Hypothesis test type

Alternative hypothesis

Alpha level

Null difference, delta0

One mean: sample mean

One mean: null mean

One mean: known population SD

One mean: sample SD

One mean: sample size

Group 1 mean

Group 2 mean

Group 1 sample SD

Group 2 sample SD

Group 1 sample size

Group 2 sample size

Group 1 known population SD

Group 2 known population SD

Paired test: mean difference

Paired test: difference SD

Paired test: pair count

One proportion: successes

One proportion: sample size

One proportion: null proportion

Two proportions: group 1 successes

Two proportions: group 1 size

Two proportions: group 2 successes

Two proportions: group 2 size

Variance test: sample variance

Variance test: null standard deviation

Variance test: sample size

Formula Used

The calculator chooses the formula from the selected hypothesis test.

One mean z: z = (xbar - mu0) / (sigma / sqrt(n))
One mean t: t = (xbar - mu0) / (s / sqrt(n))
Welch t: t = ((xbar1 - xbar2) - delta0) / sqrt(s1^2/n1 + s2^2/n2)
Pooled t: t = ((xbar1 - xbar2) - delta0) / (sp sqrt(1/n1 + 1/n2))
Paired t: t = (dbar - delta0) / (sd / sqrt(n))
One proportion z: z = (phat - p0) / sqrt(p0(1 - p0) / n)
Two proportions z: z = ((p1 - p2) - delta0) / sqrt(pc(1 - pc)(1/n1 + 1/n2))
Variance chi-square: chi-square = (n - 1)s^2 / sigma0^2

How to Use This Calculator

Select the hypothesis test type.
Choose the alternative hypothesis direction.
Enter alpha, such as 0.05 or 0.01.
Fill only the fields needed for the selected test.
Press the calculate button.
Review the statistic, p value estimate, and decision.
Use CSV or PDF download after a result appears.

Example Data Table

Test type	Sample input	Null value	Use case
One sample mean t	xbar = 52, s = 8, n = 36	mu0 = 50	Compare one sample average with a target.
Welch two mean t	xbar1 = 82, xbar2 = 78, s1 = 10, s2 = 9	delta0 = 0	Compare two independent averages.
One proportion z	x = 62, n = 100	p0 = 0.50	Test one observed success rate.
Variance chi-square	sample variance = 16, n = 20	sigma0 = 3.5	Test whether variance differs from a claim.

Understanding Hypothesis Test Statistics

A test statistic turns sample evidence into one standardized number. It shows how far your sample result sits from the null value. Large distance often means stronger evidence against the null hypothesis. The correct statistic depends on the data type, sample size, known variation, and study design.

Why the Statistic Matters

Hypothesis testing compares an observed effect with random sampling noise. The statistic joins both pieces. A mean test uses a difference divided by a standard error. A proportion test uses a count based standard error. A variance test uses a chi square ratio. Each method gives a scale that matches a reference distribution.

Supported Test Choices

This calculator handles one sample mean tests, two sample mean tests, paired mean tests, one proportion tests, two proportion tests, and variance tests. It can use a z statistic when the population standard deviation is known. It uses a t statistic when standard deviation is estimated from sample data. For two independent means, it can apply Welch's method or a pooled method.

Reading the Output

The output shows the statistic, standard error, degrees of freedom when needed, p value estimate, and a decision based on alpha. A positive statistic means the sample estimate is above the null value. A negative statistic means it is below. For two tailed tests, distance matters more than direction.

Better Inputs Give Better Tests

Enter raw counts for proportions. Enter sample means, sample standard deviations, and sample sizes for mean tests. Use paired testing when the same subjects are measured twice. Do not use independent two sample testing for matched data. Check assumptions before trusting the result. Samples should be independent unless a paired design is selected. Numeric data should be reasonable for the selected method. Very small samples may need more careful review.

Exporting Work

CSV export helps you save the calculation for spreadsheets. PDF export creates a compact record for reports. Use the example table to confirm input style before entering your own study data. The calculator does not replace study design. It helps organize common computations. Review sampling plan, missing data, outliers, and measurement method. When results affect policy, finance, or health, confirm conclusions with a qualified analyst before publishing decisions.

FAQs

What is a test statistic?

A test statistic is a standardized value. It compares your sample result with the null hypothesis. Larger absolute values often show stronger evidence against the null claim.

Which test should I select?

Select a mean test for numeric averages. Select a proportion test for counts or success rates. Select paired t when the same subjects have matched measurements.

When should I use a z test?

Use a z test when the population standard deviation is known, or when testing proportions with suitable sample sizes. Otherwise, use a t test for means.

What is alpha?

Alpha is the significance level. It is the chosen cutoff for rejecting the null hypothesis. Common values are 0.05, 0.01, and 0.10.

What does a two tailed test mean?

A two tailed test checks for a difference in either direction. It tests whether the sample result is significantly above or below the null value.

Why is degrees of freedom shown?

Degrees of freedom define the reference curve for t and chi-square tests. They usually depend on sample size and the selected formula.

Can I export the result?

Yes. After calculating, use the CSV button for spreadsheet records. Use the PDF button for a compact report copy.

Does the result prove the hypothesis?

No. A hypothesis test gives evidence under assumptions. It does not prove truth. Good sampling, valid data, and correct test choice still matter.