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ChiTest
χ² = Σ((observed − expected)² / expected).
Chi-square sums up, category by category, how far your actual observed counts deviate from what you'd expect if there were no real effect — the bigger the number, the less likely the difference is due to random chance alone.
A/B testing, survey analysis, and checking whether a die or coin is fair all use chi-square to test whether an observed pattern could plausibly be random noise.
χ² statistic
2.9
degrees of freedom: 3
What you entered
Category 1: (observed − expected)² ÷ expected
(18 − 20)² ÷ 20= 0.2Category 2: (observed − expected)² ÷ expected
(22 − 20)² ÷ 20= 0.2Category 3: (observed − expected)² ÷ expected
(15 − 20)² ÷ 20= 1.25Category 4: (observed − expected)² ÷ expected
(25 − 20)² ÷ 20= 1.25Sum across all categories
0.2 + 0.2 + 1.25 + 1.25= 2.9Result
χ² statistic: 2.9
χ² = 2.9 with 3 degrees of freedom — the larger this value, the more your observed counts diverge from what was expected.