Elementary Statistics and Computer Application

One and two tailed test & Degrees of freedom

• The nature of the alternative hypothesis determines the position of the critical region. For example, if H1 is µ1≠µ2 it does not show the direction and hence the critical region falls on either end of the sampling distribution. If H1 is µ1<µ2 or µ1 > µ2 the direction is known. In the first case the critical region falls on the left of the distribution whereas in the second case it falls on the right side.


• One tailed test – When the critical region falls on one end of the sampling distribution, it is called one tailed test.
• Two tailed test – When the critical region falls on either end of the sampling distribution, it is called two tailed test.


• For example, consider the mean yield of new paddy variety (µ1) is compared with that of a ruling variety (µ2). Unless the new variety is more promising that the ruling variety in terms of yield we are not going to accept the new variety. In this case H1 : µ1> µ2 for which one tailed test is used. If both the varieties are new our interest will be to choose the best of the two. In this case H1 : µ1≠ µ2 for which we use two tailed test.

Degrees of freedom

• The number of degrees of freedom is the number of observations that are free to vary after certain restriction have been placed on the data. If there are n observations in the sample, for each restriction imposed upon the original observation the number of degrees of freedom is reduced by one. The number of independent variables which make up the statistic is known as the degrees of freedom and is denoted by (Nu)