How Do I Calculate Chi Square

Chi-Square Goodness of Fit Calculator

Determine if your observed data fits the expected distribution

Category Label	Observed (O)	Expected (E)

Calculation Results

Chi-Square (χ²) 0.00

Degrees of Freedom (df) 0

How Do You Calculate Chi-Square?

The Chi-Square Goodness of Fit test is a statistical method used to determine how well observed data fits a specific distribution. It is widely used in genetics, marketing, and social sciences to compare categorical data.

The Chi-Square Formula

χ² = Σ [ (O – E)² / E ]

• O: The Observed value (the actual count recorded).
• E: The Expected value (the theoretical count predicted).
• Σ: Summation symbol (add up the results for all categories).

Step-by-Step Calculation Example

Imagine you roll a six-sided die 60 times. You expect each number to appear 10 times (Expected = 10). However, you observe the number '1' appeared 15 times.

1. Calculate (O – E): 15 – 10 = 5
2. Square the result: 5² = 25
3. Divide by Expected: 25 / 10 = 2.5
4. Sum: Repeat for all other numbers (2-6) and add the results together.

Understanding Degrees of Freedom (df)

Degrees of freedom represent the number of categories that are free to vary. For a goodness of fit test, the formula is df = n – 1, where 'n' is the number of categories. If you have 4 categories, your df is 3.

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