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Degrees of Freedom Formula

It is the number of values that remains during the final calculation of a statistic that is expected to vary. In simple terms, these are the date used in a calculation. The degrees of freedom can be calculated to help ensure the statistical validity of chi-square tests, t-tests, and even the more advanced f-tests.  Degrees of freedom is commonly abbreviated as ‘df’. Below mentioned is a list of formulas. The number of degrees of freedom refers to the number of independent observations in a sample minus the number of population parameters that must be estimated from sample data.

One Sample T Test Formula

\[\LARGE DF=n-1\]

Two Sample T Test Formula

\[\LARGE DF=n_{1}+n_{2}-2\]

Simple Linear Regression Formula

\[\LARGE DF=n-2\]

Chi Square Goodness of Fit Test Formula

\[\LARGE DF=k-1\]

Chi Square Test for Homogeneity Formula

\[\LARGE DF=(r-1)(c-1)\]

Solved Examples

Question 1: Find the degree of freedom for given sequence:
x = 2, 8, 3, 6, 4, 2, 9, 5

Solution:

Given n= 8
$therefore$ DF = n-1
DF = 8-1
DF = 7

Question 2: Find the degree of freedom for given sequence:

x = 12, 17, 19, 15, 25, 26
y = 18, 21, 32, 43
Solution:

Given:
n1 = 6
n2 = 4

Here, there are 2 sequences, so we need to apply
DF = n1 – n2 – 2
DF = 6 -4 -2
DF =0