Form of t- Distribution

1. The students  t - distribution  like the  normal  distribution has bell shaped frequency  curve which is symmetrical. The only  parameter which  determine the shapes  of the curve  is the  degree of freedom. With a change  in the degrees of freedom the shape of the curve  will also  change.

2.The  mean of the  t- distribution  is zero. This is so  case of normal  curve also.

3.The variance  of t- distribution   is greater than one and  as the sample size increase it  tends to  move towards unity. It is for the reason  that it  has been mentioned above that the  single parameter which change the form of  distribution  are the degrees of freedom or the size of the  sample. If samples  size  becomes  very large  there is no difference  between  distribution and  normal  distribution .

4.T distribution  can be used even in case of large  samples  but the  large sample theory  cannot  be  use for  small  samples.

5. The value  of t ranges from  minus infinity to plus  infinity.

The followings  diagram  gives the steps  of distribution  and a normal  distribution. It would  be noted  that as the  degrees of  freedom  changes  the shapes  of the t- distribution  also  changes.

the  above  diagram  shows two important characteristics of  t- distributions. First a t- distribution  is lower at the mean  and higher  at the  tails  than a normal  distribution. Second  the  distribution  has  proportionately greater area  in its  tails than  the normal  distribution. Interval widths from t- distribution  are therefore wider than  those  based on the normal  distribution.