If a restriction is applied or imposed to the choice that the sum of these number should be 50. Here, we have a choice to select any three numbers, say 10, 15, 20 and the fourth number is 5: [50 – (10 + 15 + 20)]. Thus our choice of freedom is reduced by one, on
the condition that the total be 50. Therefore the restriction placed on the freedom is one and degree of freedom is three. As the restrictions increase, the freedom is reduced. The number of independent variates which make up the statistic is known as the
degrees of freedom and is usually denoted by n (Nu) The number of degrees of freedom for n observations is n – k where k is the number of independent linear constraint imposed upon them.
For the student’ s t-distribution the number of degrees of freedom is the sample sizeminus one. It is denoted by n = n -1 The degrees of freedom plays a very important role in χ2 test of a hypothesis. When we fit a distribution the number of degrees of freedom is (n– k-1) where n is number of observations and k is number of parameters estimated from the data. For e.g., when we fit a Poisson distribution the degrees of freedom is n = n – 1 – 1. In a contingency table the degrees of freedom is (r-1) (c -1) where r refers to number
of rows and c refers to number of columns. Thus in a 3 × 4 table the d.f are (3 – 1) (4 – 1) = 6 d.f. In a 2 × 2 contingency table the
d.f are (2 – 1) (2 – 1) = 1 In case of data that are given in the form of series of variables in a row or column the d.f will be the number of observations in a series less one ie., n = n – 1