Stats Hypothesis Testing Calculator

Calculator Inputs

Test type

Alternative hypothesis

Alpha

Confidence level

Null value

Use mean, difference, proportion, or hypothesized standard deviation.

Sample mean 1

Sample standard deviation 1

Sample size 1

Sample mean 2

Standard deviation 2

Sample size 2

Known standard deviation

Use this for one sample z or as known deviation 1.

Successes 1

Trials 1

Successes 2

Trials 2

Example Data Table

Scenario	Inputs	Expected Use
One sample mean	Mean 52, null 50, known deviation 10, n 40	Check whether a process average differs from target.
Two sample mean	Means 52 and 49, deviations 8 and 7.5	Compare two independent groups with Welch or pooled logic.
One proportion	64 successes, 100 trials, null proportion 0.60	Test whether a success rate differs from a claim.
Variance check	Sample deviation 8, null deviation 10, n 40	Test population spread under normality assumptions.

Formula Used

One sample z: z = (x̄ - μ0) / (σ / √n).

One sample t: t = (x̄ - μ0) / (s / √n), with df = n - 1.

Two sample z: z = ((x̄1 - x̄2) - Δ0) / √((σ1² / n1) + (σ2² / n2)).

Welch t: t = ((x̄1 - x̄2) - Δ0) / √((s1² / n1) + (s2² / n2)).

Pooled t: sp² = ((n1 - 1)s1² + (n2 - 1)s2²) / (n1 + n2 - 2).

One proportion: z = (p̂ - p0) / √(p0(1 - p0) / n).

Two proportions: z = ((p̂1 - p̂2) - Δ0) / pooled standard error.

Variance test: χ² = (n - 1)s² / σ0².

How to Use This Calculator

Select the test type that matches your data and claim.
Choose a two sided, left tailed, or right tailed alternative.
Enter alpha, confidence level, null value, and sample values.
Use the result box to read the statistic, p value, and decision.
Download the CSV or PDF report for your records.

Understanding Hypothesis Testing

Hypothesis testing helps you judge a statistical claim. It compares sample evidence with a null assumption. The result does not prove truth. It measures how unusual the sample looks.

Why This Calculator Helps

Manual testing can be slow. You must choose a test, compute a statistic, find a p value, and compare it with alpha. This calculator keeps those steps organized. It supports mean, proportion, variance, and two sample studies. It also shows confidence limits when the selected method allows them.

Choosing the Right Test

Use a one sample z test when the population standard deviation is known. Use a one sample t test when it is unknown. Use two sample tests for comparing two groups. Choose Welch when group spreads may differ. Choose pooled only when equal variance is reasonable. Use proportion tests for success rates. Use the variance test for one normal population spread.

Reading the Results

The test statistic shows distance from the null value. A larger absolute value gives stronger evidence. The p value is the probability of results at least this extreme, assuming the null is true. If the p value is at or below alpha, reject the null. Otherwise, do not reject it. This is not proof that the null is true. Best practice is to report the chosen tail before viewing results. This prevents convenient decisions and keeps analysis transparent for readers. State your alpha before formal testing.

Good Input Practices

Enter sample sizes carefully. Avoid zero or negative values. Use raw units consistently. For proportions, enter successes and trials. For means, enter standard deviations, not variances. For two sample work, confirm both groups measure the same outcome. Small samples need careful interpretation. Outliers can affect means and standard deviations.

Using Exports

The CSV download gives a simple spreadsheet record. The PDF download creates a compact report. These exports help with homework, audit trails, classroom examples, and recurring quality checks. Keep notes about data source, sampling method, and assumptions beside the exported results.

Limitations

This tool is educational. It does not replace professional statistical review. Real projects may need randomization checks, power analysis, multiple testing correction, or nonparametric methods. Use judgment, especially with biased samples, missing values, or unusual distributions.

FAQs

What is a hypothesis test?

It is a method for comparing sample data with a stated claim. The calculator estimates a test statistic and p value, then gives a decision using your alpha level.

Which alpha should I use?

Many studies use 0.05. Stricter work may use 0.01. Exploratory work may use 0.10. Choose alpha before reviewing results.

What does p value mean?

It is the probability of seeing evidence this extreme, or more extreme, when the null hypothesis is assumed true.

When should I use a t test?

Use a t test for mean data when the population standard deviation is unknown. It is common with sample standard deviations.

When is a z test useful?

Use a z test when the population standard deviation is known, or when testing large sample proportions with suitable counts.

What is a two sided test?

A two sided test checks for a difference in either direction. It is useful when you only want to know whether values differ.

Can I export my result?

Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple report that records the main outputs.

Does this replace statistical advice?

No. It is a learning and reporting tool. Complex studies may require expert review, better models, or additional diagnostics.