What is the difference between a Student's t-test and a Welch's t-test?

A Student's t-test assumes both groups have equal variances, while a Welch's t-test does not. This makes the Welch test more reliable for real-world data where variances often differ.

Can I use this calculator without raw data?

Yes, you can leave the raw data fields blank and input the mean, standard deviation, and sample size for both groups to run the test.

What does the alpha value represent?

The alpha value (commonly 0.05) is the significance level. It represents the probability of rejecting the null hypothesis when it is actually true.

How do I interpret the p-value?

If the calculated p-value is less than your chosen alpha level, the difference between the groups is considered statistically significant, and you reject the null hypothesis.

What alternative hypotheses are supported?

You can test if the means are simply different (two-sided), or if one mean is specifically greater than or less than the other (one-sided).

Elysia Tools

Navigation

Math & Numbers

Welch t Test Calculator

Run Welch two-sample t tests for independent groups with unequal variances from raw data or summary statistics

Execution

Run this tool

Fill in the form, run the tool, and review the result in one place.

Prepared example runs

Click an example to fill the form automatically. File inputs still need an upload.

1 examples

Compare two groups with unequal variances

Run Welch t test for two independent samples without assuming equal variances

{"result":{"tStatistic":3.4669,"pValue":0.0096,"degreesOfFreedom":7.3855,"rejectNull":true}}

Inputs

Options are grouped so long tools stay easier to scan.

12 options

ContentPaste or type the main input values.2

Group 1 ValuestextareaOptionalGroup 2 ValuestextareaOptional

SettingsAdjust formats, ranges, numbers, and modes.10

Group 1 Mean (Optional)numberOptionalGroup 2 Mean (Optional)numberOptionalGroup 1 Standard Deviation (Optional)numberOptionalGroup 2 Standard Deviation (Optional)numberOptionalGroup 1 Size (Optional)numberOptionalGroup 2 Size (Optional)numberOptionalHypothesized DifferencenumberOptionalAlternative HypothesisselectOptionalAlphanumberOptionalDecimal PlacesnumberOptional

Result

Ready for a run

Run the tool to preview files, text, structured data, or streamed output here.

Samples

Welch t Test Calculator

Run this tool

Prepared example runs

Inputs

Result

Examples that match this tool

Continue with connected tools and hubs

Prepared example runs

Inputs

Result

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Comparing Website Conversion Rates

2. Evaluating Drug Efficacy from Published Data

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

Web Image Processing Rust Samples

Effect Size Calculator

Fatigue Limit Calculator (Goodman / Gerber / Soderberg)

Half-Life Calculator

Margin of Error Calculator

Barcode, QR Code, and Label Tools

Audio Encoding and Format Conversion Tools

Image Format Conversion and Animated Export Tools

JSON Interchange and Format Translation Tools