Degrees of Freedom Formula

It is the number of values that remain 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 degree of freedom 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.

Formulas to Calculate Degrees of Freedom

  • 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


Given n= 8


DF = n-1

DF = 8-1

DF = 7

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

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


Given: n1 = 6 n2 = 4

Here, there are 2 sequences, so we need to apply DF = n1 + n2 – 2

DF = 6 + 4 -2

DF = 8


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