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Chi-Square Statistic
2.708333
Chi-Square Statistic vs Observed 1
Formule
## How to Perform a Chi-Square Test ### Formula **chi-square = Sum of [(Oi - Ei)^2 / Ei]** Compare the computed chi-square statistic to the chi-square distribution with k-1 degrees of freedom (where k is the number of categories). If the statistic exceeds the critical value, reject the null hypothesis that the observed distribution matches the expected distribution.
Exemple Résolu
Four categories: observed 45, 35, 25, 45; expected 40, 40, 30, 40.
- 01c1 = (45-40)^2/40 = 25/40 = 0.625
- 02c2 = (35-40)^2/40 = 25/40 = 0.625
- 03c3 = (25-30)^2/30 = 25/30 = 0.8333
- 04c4 = (45-40)^2/40 = 25/40 = 0.625
- 05Chi-square = 0.625 + 0.625 + 0.8333 + 0.625 = 2.7083
- 06df = 4 - 1 = 3
- 07Critical value at alpha=0.05, df=3 is 7.815
- 08Since 2.7083 < 7.815, do not reject H0
Questions Fréquentes
What is the null hypothesis for a chi-square test?
For a goodness-of-fit test, H0 is that the observed frequencies match the expected distribution. For a test of independence, H0 is that the two categorical variables are independent.
What if expected frequencies are less than 5?
The chi-square approximation is unreliable when expected frequencies are below 5. Consider combining categories or using Fisher's exact test instead.
Can chi-square detect the direction of the difference?
No. Chi-square only detects that a difference exists, not the direction. To understand which categories differ, examine the individual components (residuals).
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