2.72
3
100
100
7.815
-5.095
1
2.72
3
100
100
7.815
-5.095
1
The Chi-Square Test Calculator performs a goodness-of-fit test for up to 4 categories. The chi-square (χ²) test is one of the most commonly used statistical tests in biology, particularly in genetics for testing Mendelian ratios, in ecology for comparing habitat use to availability, and in any field where observed counts are compared to expected frequencies.
This calculator computes the χ² statistic for 4 categories and compares it to the critical value at α = 0.05 (95% confidence) with 3 degrees of freedom. If χ² exceeds 7.815, the difference between observed and expected is statistically significant.
The chi-square statistic is:
χ² = Σ((O - E)² / E)
For 4 categories:
χ² = (O₁-E₁)²/E₁ + (O₂-E₂)²/E₂ + (O₃-E₃)²/E₃ + (O₄-E₄)²/E₄
If χ² is greater than 7.815, reject the null hypothesis that observed values fit the expected distribution.
Inputs
Results
χ² = 0.267 is far below 7.815 (critical value). The data are consistent with a 9:3:3:1 Mendelian ratio. Do not reject the null hypothesis.
Inputs
Results
χ² = 30 greatly exceeds 7.815. The animal uses habitats non-randomly, showing strong preference for habitat 1.
Use the chi-square goodness-of-fit test when you have categorical data (counts in discrete categories) and want to test whether the observed distribution matches an expected distribution. Common applications include testing Mendelian inheritance ratios, comparing species distributions, and evaluating survey responses. Requirements: expected counts should be at least 5 per category.
This calculator is set up for exactly 4 categories (df = 3). For 2 categories, set categories 3 and 4 to observed = 0 and expected = 0.01 (a minimal value). For more categories, you would need a calculator with more input fields. The critical value changes with degrees of freedom: for 2 categories (df=1), critical value is 3.841; for 3 (df=2), it is 5.991.
Degrees of freedom (df) equal the number of categories minus 1. With 4 categories, once you know 3 of the values and the total, the fourth is determined. The critical value depends on df: more categories mean more df and a higher critical value. At α = 0.05: df=1 gives 3.841, df=2 gives 5.991, df=3 gives 7.815.
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