Free Chi-Square Statistic Calculator
Calculate the chi-square statistic by summing squared differences between observed and expected frequencies divided by expected frequencies.
Chi-Square Statistic
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Chi-Square Statistic vs Observed 1
How to Calculate the Chi-Square Statistic
Formula
chi-square = Sum of [(Oi - Ei)^2 / Ei]
For each category, compute the squared difference between observed (O) and expected (E) frequencies, divided by the expected frequency. Sum these components. Larger values indicate greater discrepancy between observed and expected. Degrees of freedom = number of categories - 1.
Example Calculation
Three categories with observed frequencies 30, 20, 50 and expected 25, 25, 50.
- 01Component 1: (30-25)^2/25 = 25/25 = 1.0
- 02Component 2: (20-25)^2/25 = 25/25 = 1.0
- 03Component 3: (50-50)^2/50 = 0/50 = 0.0
- 04Chi-square = 1.0 + 1.0 + 0.0 = 2.0
- 05df = 3 - 1 = 2
Frequently Asked Questions
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