Chi-Square Calculator
Run a chi-square goodness-of-fit test comparing observed vs expected frequencies.
Inputs
χ² Statistic
2.0000
P-value
0.849145
Degrees of Freedom
5
Step by step
Values used
Observed frequencies (comma separated) = 16, 18, 16, 14, 12, 12; Expected frequencies (comma separated) = 15, 15, 15, 15, 15, 15
Formula applied
χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ
χ² Statistic
= 2.0000
P-value
= 0.849145
Degrees of Freedom
= 5
How it works
The chi-square goodness-of-fit test measures how well observed categorical data match an expected distribution. Large χ² values (small p-values) indicate the observed data differ significantly from what was expected.
Formula
χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ
- Oᵢ
- Observed frequency
- Eᵢ
- Expected frequency
Frequently Asked Questions
What are the assumptions of the chi-square test?
Observations must be independent, all expected frequencies should be at least 5, and the data must be counts (not proportions or means).
What does a small p-value mean?
A p-value below your significance level (commonly 0.05) means you reject the hypothesis that the data follow the expected distribution.