Which hypothesis test should I use for before and after data?

Use a paired t-test when each before value is linked to a matching after value from the same person, object, or matched pair.

What is the difference between a t-test and a z-test?

A t-test is usually used for mean tests when the population standard deviation is unknown and the sample standard deviation is used. A z-test is used for proportions and for mean tests when the population standard deviation is known.

Does a statistically significant result mean the effect is important?

Not always. Statistical significance means the result is unlikely under the null hypothesis, but effect size helps show whether the difference is large enough to matter in practice.

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Hypothesis Testing Calculator

Calculate p-values, test statistics, confidence intervals, and conclusions for common hypothesis tests.

Background

Hypothesis testing helps you decide whether sample data gives enough evidence to reject a null hypothesis. This calculator shows the test statistic, p-value, decision, assumptions, effect size, and a plain-English conclusion so students can understand the result, not just copy a number.

Run a hypothesis test

Choose test type

Use the helper when you are not sure which test fits your homework problem.

Which test should I use?

Outcome type

Study design

Known population σ?

Hypothesis settings

Significance level α

Alternative hypothesis

Confidence level

One-sample mean test

Enter summary statistics, or paste raw sample data and click “Use pasted data.”

Sample mean x̄

Null mean μ₀

Sample standard deviation s

Sample size n

Optional raw sample data

Two-sample mean test

Default uses Welch's t-test, which is safer when standard deviations differ.

Group 1 mean

Group 1 SD

Group 1 n

Group 2 mean

Group 2 SD

Group 2 n

Method

Optional group 1 raw data

Optional group 2 raw data

Paired t-test

Paste paired values or enter summary statistics for the differences.

Mean difference d̄

SD of differences s_d

Number of pairs n

Null mean difference

Before / group A data

After / group B data

One-proportion test

Successes x

Sample size n

Null proportion p₀

Two-proportion test

Group 1 successes x₁

Group 1 n₁

Group 2 successes x₂

Group 2 n₂

Chi-square goodness-of-fit

Enter observed counts and expected counts or expected proportions. Use the same order for both lists.

Observed counts

Expected counts or proportions

Chi-square test of independence

Paste a two-way table. Separate cells with commas or spaces, and rows with new lines.

One-way ANOVA

Paste one group per line. Numbers can be separated by commas or spaces.

Quick examples (click to see result)

Result

No result yet. Choose a test type, enter your data, then click Calculate Hypothesis Test.

How to use this calculator

Choose the test type or use the “Which test should I use?” helper.
Enter summary statistics, raw data, category counts, or a two-way table.
Choose α and the alternative hypothesis: left-tailed, right-tailed, or two-tailed.
Click Calculate Hypothesis Test.
Read the p-value, reject/fail-to-reject decision, confidence interval, assumptions, effect size, and plain-English conclusion.

How this calculator works

Mean tests use t or z style test statistics depending on the test and available information.
Proportion tests use normal approximation z tests and pooled proportions for hypothesis testing.
Chi-square tests compare observed counts with expected counts.
ANOVA compares between-group variation with within-group variation using an F statistic.
The calculator converts the test statistic into a p-value and compares it with α.

Formula & Equations Used

One-sample t: t = (x̄ − μ₀) / (s / √n)

Two-sample t: t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

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

Chi-square: χ² = Σ (O − E)² / E

ANOVA: F = MS_between / MS_within

Example Problems & Step-by-Step Solutions

Example 1: One-sample mean test

A class sample has mean 72.4, standard deviation 8.1, and n = 36. Test whether the true mean differs from 70.

Use a two-tailed one-sample t-test with H₀: μ = 70 and H₁: μ ≠ 70.

Example 2: Two-proportion test

Compare whether two groups have different success rates using x₁/n₁ and x₂/n₂.

The calculator uses the pooled proportion for the z test and an unpooled standard error for the confidence interval.

Example 3: One-way ANOVA

Paste each group on its own line to test whether at least one group mean is different.

ANOVA gives an F statistic and p-value, but a significant result does not say which exact groups differ.

Common mistakes to avoid

Do not say “accept H₀.” In most intro stats courses, say “fail to reject H₀.”
Do not confuse statistical significance with practical importance. Check the effect size too.
Do not use a two-sample test for paired before/after data.
Do not use chi-square tests with expected counts that are too small without caution.
Make sure the alternative hypothesis direction matches the wording of the problem.

FAQ

What does the p-value mean?

The p-value is the probability of getting a result at least as extreme as your sample result, assuming the null hypothesis is true.

When do I reject the null hypothesis?

Reject H₀ when the p-value is less than or equal to α. Otherwise, fail to reject H₀.

Which test should I use for before/after data?

Use a paired t-test because each before value is linked to a matching after value.