Chi-Square Test (χ²)

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Example: a die was rolled 60 times and faces 1 to 6 came up 8, 12, 9, 11, 6 and 14 times. Is it fair? Change the values to test your own case.

Observed frequencies O_i One per category, separated by spaces or commas. Expected frequencies E_i Counts that add up to the same as the observed ones, or proportions that add up to 1.

Step by step

What each term means

Chi-Square (χ²): The test statistic. A high value means a large gap between the observed and the expected data.
Summation: Adds the result of the calculation over every category or group in your data.
Squared Difference: The difference between the observed frequency (Oᵢ) and the expected frequency (Eᵢ), squared so that negative values don't cancel out.
Expected Frequency (Eᵢ): The frequency you would expect in a category if the null hypothesis were true. It normalizes the squared difference.