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
2.000000
Chi-Square Statistic vs Observed 1
Formule
## 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.
Exemple Résolu
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
Questions Fréquentes
What is a large chi-square value?
The chi-square statistic must be compared to the chi-square distribution with the appropriate degrees of freedom. For df=2, a value above 5.991 is significant at the 5% level. The larger the statistic, the more the data departs from expected.
What are the assumptions of the chi-square test?
Expected frequencies should be at least 5 in each category. Observations must be independent. The data should be frequency counts, not percentages or means.
Can chi-square be zero?
Yes. Chi-square = 0 means observed frequencies exactly match expected frequencies in every category. In practice, some discrepancy is expected due to random sampling variation.
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