This degrees of freedom calculator takes the figures you already have and applies the relationship behind degrees of freedom calculations for you, giving degrees of freedom, degrees of freedom between groups and degrees of freedom within groups from number of columns in the table, number of groups (k), sample size (n), sample size (n₁), sample size (n₂), sample size (n), sample size (n₁), sample size (n₂), number of rows in the table, variance (σ₁) and variance (σ₂).
What Is the Degrees of Freedom Calculator?
The degrees of freedom calculator turns a set of measurements into degrees of freedom, degrees of freedom between groups and degrees of freedom within groups, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Degrees of Freedom Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with number of columns in the table set to 10, number of groups (k) set to 5, sample size (n) set to 2, the calculator returns degrees of freedom of 1, and degrees of freedom (df in chi square) of 81, and degrees of freedom (df2) of 108. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out degrees of freedom?
Enter number of columns in the table, number of groups (k), sample size (n), sample size (n₁), sample size (n₂), sample size (n), sample size (n₁), sample size (n₂), number of rows in the table, variance (σ₁) and variance (σ₂). The calculator then works through the relationship and reports degrees of freedom, degrees of freedom between groups and degrees of freedom within groups.
What does the degrees of freedom actually calculate?
It takes number of columns in the table, number of groups (k), sample size (n), sample size (n₁), sample size (n₂), sample size (n), sample size (n₁), sample size (n₂), number of rows in the table, variance (σ₁) and variance (σ₂) and converts them into degrees of freedom, degrees of freedom between groups and degrees of freedom within groups using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter number of columns in the table?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.