Chi-Square Goodness of Fit

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Determine if observed data matches an expected distribution.

Frequency Data

Observed Frequencies

Expected Frequencies

Statistical Analysis

Chi-Square Stat (χ²)1

Degrees of Freedom2

Observed vs Expected comparison

About this calculator

Overview

The Chi-Square goodness of fit test is a statistical hypothesis test used to determine whether a variable is likely to come from a specified distribution. It is often used to see if observed data matches what was expected according to a specific theory.

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Pro Tips

All expected frequencies should be at least 5 for the test results to be highly reliable.
The degrees of freedom is simply the number of categories minus one.
A large χ² value suggests that the observed data significantly differs from the expected model.

Fun Facts

"Gregor Mendel, the father of genetics, used principles similar to Chi-Square to analyze the traits of pea plants."
"The Chi-Square test was developed by Karl Pearson in 1900, the same person who developed the Pearson correlation."
"A Chi-Square value of zero would mean the observed and expected data are a perfect, 100% match."

Formula: χ² = Σ [ (O - E)² / E ]