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.