Degrees of Freedom
Degrees of freedom (df) is the number of independent pieces of information available for estimation or hypothesis testing. For a single sample, df = n - 1 because one degree of freedom is lost by estimating the mean. For comparing two independent groups, df = n₁ + n₂ - 2. For chi-squared test on a contingency table, df = (rows - 1)(columns - 1).
Real World
A market researcher conducting a chi-squared test on a 3×4 contingency table (3 age groups, 4 product preferences) calculates df = (3−1)(4−1) = 6 before looking up the critical value.
Exam Focus
Calculate and state degrees of freedom explicitly before referencing any table; examiners treat an unsupported critical value as an error.
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