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The 11 pages that link to Degrees of freedom, each with the reason it gives.

• Confidence intervalRelated: They affect critical values in intervals that use estimated variance.

• Analysis of varianceRelated: Each ANOVA component's degrees of freedom determine its mean square and reference F distribution.

• Axis of rotationRelated: A constrained body rotating about one fixed axis has one rotational degree of freedom.

• Student's t-distributionRelated: They control the t-distribution's tail weight and often equal the sample size minus one.

• Prediction intervalRelated: Few studies can make interval critical values larger and predictions less precise.

• Student's t-testRelated: They determine the t-distribution's shape and often depend on sample size.

• Chi-squared distributionRelated: Here, the degrees of freedom count the standard normal squares in the defining sum.

• Sum of squaresRelated: Variance estimates divide a sum of squares by degrees of freedom.

• Chi-squared testRelated: They select the chi-squared distribution used to calculate the p-value.

• F-distributionRelated: The numerator and denominator degrees of freedom determine the F-distribution’s shape.

• Sample mean and covarianceRelated: Estimating the mean constrains centered observations, explaining the n−1 covariance divisor.