Chi-Square Test Calculator
Test goodness of fit or independence using the chi-square distribution.
Goodness of Fit
Contingency Table
Chi-Square Statistic
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Enter data and calculate
χ² Value
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Degrees of Freedom
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p-Value
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Critical Value
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Decision
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Cramér\'s V
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Chi-Square Test
The chi-square test compares observed frequencies to expected frequencies to test hypotheses about categorical data.
Chi-Square Formula
χ² = Σ [(O - E)² / E]
Where O = observed frequency, E = expected frequency
Types of Chi-Square Tests
| Test | Purpose | df |
|---|---|---|
| Goodness of Fit | Test if data fits a distribution | k - 1 |
| Independence | Test relationship between variables | (r-1)(c-1) |
Assumptions
- Data are counts/frequencies
- Observations are independent
- Expected frequency ≥ 5 for each cell
- Sample size is sufficiently large
Frequently Asked Questions
When should I use chi-square test?
Use chi-square when testing relationships between categorical variables or comparing observed data to expected distributions. Not for continuous data.
What if expected frequencies are too small?
If any expected frequency is less than 5, consider using Fisher's Exact Test for contingency tables or combining categories.