Enter your significance level (α), then fill in each category name, its observed count, and expected count — up to three categories — and the Chi-Square (χ²) Test Calculator returns your χ² value, degrees of freedom, p-value, critical value, and a plain-language result telling you whether to reject the null hypothesis.
Chi-Square (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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Result
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A chi-square test is a statistical method used to determine if observed frequencies in biological data significantly differ from expected frequencies. It's commonly used in genetics, ecology, and experimental biology to test hypotheses about population distributions.
Expected frequencies can be based on theoretical ratios (like Mendelian genetics ratios), equal distribution assumptions, historical data, or null hypothesis predictions. For genetic crosses, use Punnett square ratios as expected values.
The p-value indicates the probability of obtaining your observed results (or more extreme) if the null hypothesis is true. A p-value less than your significance level (typically 0.05) suggests your observed data significantly differs from expected patterns.
Chi-square tests can handle multiple categories. This calculator supports up to 4 categories, but the test can be extended to more. Each additional category increases the degrees of freedom, affecting the critical value for significance.
Key assumptions include: data must be in frequency counts (not percentages), observations must be independent, expected frequency in each category should be at least 5, and the total sample size should be reasonably large (typically >20).
Degrees of freedom equals the number of categories minus 1 (df = k-1). It determines which chi-square distribution to use for finding critical values and calculating p-values. More categories mean higher degrees of freedom.
Use chi-square when analyzing categorical count data to test goodness-of-fit or independence. For continuous data, use t-tests or ANOVA. For comparing proportions between groups, use chi-square test of independence instead of goodness-of-fit.