Degrees of Freedom Calculator One Sample

Instructions: This Degrees of Freedom Calculator will indicate the number of degrees of freedom for one sample of data, with sample size \(n\):

Sample Size \(n\) (integer) =

Degrees of Freedom Calculator

The first thing we need to understand is the concept of degrees of freedom. The degrees of freedom are defined as the number of values that can independent vary freely to be assigned to a statistical distribution.

Typically, under this definition, the number of degrees of freedom correspond to the sample size minus the number of population parameters that need to be estimated

How To Compute Degrees of Freedom for One Sample?

Based on the definition of degrees of freedom, and considering that we have a sample of size \(n\) and the sample comes from one population, so there is only one parameter to estimate, the number of degrees of freedom is:

\[df = n - 1\]

That is it, at least for the case of one sample. You take the sample size of the data provided, and subtract 1.

Example of computing degrees of freedom

Example: How many degrees of freedom are there for the following sample:

1, 2, 3, 3, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8?

Well, first we compute the sample size. In this case, the sample size is \(n = 14\). Consequently, the degrees of freedom are:

\[df = n - 1 = 14 - 1 = 13\]

Degrees of Freedom calculator t test

Is this only valid for a one-sample t-test ? The answer is yes and no. You can compute the degrees of freedom for a one-sample z-test, but for a z-test the number of degrees of freedom are not required, because the sampling distribution of the associated test statistic has the Z-distribution.

It is for the case of the one-sample t-test where the idea of the degrees of freedom takes relevance, because the sampling distribution of the t-statistic actually depends on the number of degrees of freedom.

Is This Different for the case of two samples?

Yes. For two samples make sure to use the following degrees of freedom calculator for two samples , because in that case the calculation is different, and it can be a little bit more complicated.

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