Chi Square Calculator
Free Chi square Calculator for biostatistics. Enter variables to compute results with formulas and detailed steps. Get results you can export or share.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
ฯยฒ = ฮฃ[(Oแตข - Eแตข)ยฒ / Eแตข] | df = k - 1 (goodness-of-fit)
Chi-square goodness-of-fit test compares observed frequencies to expected frequencies. Large ฯยฒ means observed differs significantly from expected. If no expected values given, assumes equal distribution.
Worked Examples
Example 1: Dice fairness test
Problem:Roll dice 100 times: 50, 30, 20 for three outcomes (expected: 33.3 each)
Solution:ฯยฒ = (50-33.3)ยฒ/33.3 + (30-33.3)ยฒ/33.3 + (20-33.3)ยฒ/33.3 = 13.80
Result:ฯยฒ = 13.80, p โ 0.001 โ Significant (not fair)
Frequently Asked Questions
How do I use a Punnett square?
A Punnett square predicts offspring genotype ratios. Write one parent's alleles across the top and the other's down the side. Fill in each box by combining the row and column alleles. For a monohybrid cross of two heterozygotes (Aa x Aa), you get 1 AA : 2 Aa : 1 aa, or a 3:1 phenotype ratio.
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy