Degrees of freedom
Topic of Statistical inference, part of Statistical inference
Degrees of freedom
| Type | Topic |
| Taught in | Statistical inference |
| Part | Statistical inference |
| Questions using it | 28 |
The parameter of the chi-squared, t and F families, and the number of independent pieces of information behind a variance estimate: n-1 for a sample variance, n-p for a regression with p coefficients, (r-1)(c-1) for a test of independence in an r\times c table.
In Statistical inference
If Z_1,\ldots,Z_m are independent standard normal variables, then V=Z_1^2+\cdots+Z_m^2 has the chi-squared distribution with m degrees of freedom, written \chi^2_m. It is the gamma law with shape m/2 and rate 1/2, so \mathbb{E} V=m and \operatorname{Var} V=2m.
Used in
- Taught in Statistical inference
- Also used in Random variables and distributions · Functions of random variables and limit theorems · Confidence intervals · Hypothesis tests · Chi-squared tests · Linear regression · Analysis of variance · Using R · Estimation examples · Testing examples · Analysis of variance examples · Regression examples · Chi-squared examples · Bayesian linear regression · Introduction to generalised linear models · Standard errors, and models for counts · Paired comparisons, and how far a fit is from the data · Smooth means · Additive smooths · Covariance and the multivariate normal · Estimation and inference for the multivariate normal · Statistical classifiers and discriminant analysis · Logistic regression · High-dimensional analysis · Random slopes, and a binary mixed model · Dependence along a series
- Questions that use it (28) — A squared t variable · Lost hours after a safety programme (answer) · Checking equal variances (answer) · A 1:2:1 phenotype ratio (answer) · Is the die fair? (answer) · Counting degrees of freedom · How much do the ads explain? · A Tukey interval for two varieties · Tips and coupons (answer) · Two treatments in blocks (answer) · A contrast among the corn varieties · Two groups (answer) · Steel rod diameters · Haemoglobin and sickle-cell type · Height and age of pine trees · Rain, food, and orange yield · How far sharks swim · Wages, class, and gender · Counting parameters (answer) · Reading the deviance · When ordinary linear discrimination is not defined (answer) · Q24 (answer) · Q34 (answer) · Question 4 · Question 5 · Question 12 (answer) · Question 19 (answer) · Question 22 (answer)
- All 4 questions on Statistical inference
See also
Variance · Chi-squared test of independence · Chi-squared distribution · F distribution · Likelihood-ratio test · Null deviance · One-sample t pivot · Ordinary least squares