GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 308 of 500
Test independence in a contingency table, or goodness of fit of counts against expected counts — the standard test for categorical laboratory and survey data.
Try sample values — fills the form with the worked example below.
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Chi-square (χ²)
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p-value
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Degrees of freedom
Equation: χ² = Σ (O − E)² ÷ E. Independence: E = row total × column total ÷ grand total, df = (rows − 1)(columns − 1). Goodness of fit: df = categories − 1.
Method: Pearson chi-square test per ISO 16269-1. The p-value is computed from the chi-square distribution itself (regularised incomplete gamma function), not read from a table. No continuity correction is applied.
Assumptions: the counts are independent observations; for the approximation to hold, most expected counts should be at least 5 and none should be below 1.
Limitations: with small expected counts the chi-square approximation fails — use Fisher’s exact test (Tool 309) for a 2 × 2 table instead. The test says whether an association exists, not how strong it is.
Rounding: χ² to 4 decimal places; p to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Pearson chi-square test per ISO 16269-1. The p-value is computed from the chi-square distribution itself (regularised incomplete gamma function), not read from a table. No continuity correction is applied.
Assumptions: the counts are independent observations; for the approximation to hold, most expected counts should be at least 5 and none should be below 1.
Limitations: with small expected counts the chi-square approximation fails — use Fisher’s exact test (Tool 309) for a 2 × 2 table instead. The test says whether an association exists, not how strong it is.
Rounding: χ² to 4 decimal places; p to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Table [[10, 20], [20, 10]]: expected counts are all 15, χ² = 6.6667, df = 1, p = 0.0098 — significant at α = 0.05.
Enter values above to see results.
Enter counts, not percentages — the test needs the actual numbers of observations. Tool 308 of 500 — GIFSQ
