Degrees of freedom
The number of observations free to vary once the estimates a statistic relies on are fixed, such as n − 1 for a sample variance. They set which t, chi-square or F distribution applies.
Where you will meet it
Degrees of freedom appears in 7 learning outcomes on the CFA syllabus. A few of them:
- Explain the chi-square, F and Student's t distributions
“Student's t distribution is symmetric like the normal but with fatter tails, governed by its degrees of freedom; it converges on the normal as those grow, and is the right distribution for inference about a mean when the population standard deviation is unknown.”
- Set up tests of whether a multiple regression's coefficients, taken two or more at a time, are jointly significant and explain what the outcome of such joint tests tells you
“A single coefficient is tested with t = (estimate − hypothesised value) ÷ standard error, with n − k − 1 degrees of freedom, and the hypothesised value need not be zero.”
- Choose the right test for a hypothesis concerning a mean
“With an unknown variance — the usual case — a t-test applies, using the sample standard deviation and n - 1 degrees of freedom.”
- Explain how a correlation coefficient is tested
“The null is that the population correlation is zero, and the test statistic follows a t distribution with n - 2 degrees of freedom.”
See also
Practise it
Practise degrees of freedom until it is automatic: questions that explain every wrong option.
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