Elementary Statistics and Computer Application

Student’s t test

• When the sample size is smaller, the ratio will follow t distribution and not the standard normal distribution. Hence the test statistic is given as which follows normal distribution with mean 0 and unit standard deviation. This follows a t distribution with (n-1) degrees of freedom which can be written as t(n-1) d.f.


• This fact was brought out by Sir William Gossest and Prof. R.A Fisher. Sir William Gossest published his discovery in 1905 under the pen name Student and later on developed and extended by Prof. R.A Fisher. He gave a test known as t-test.

Applications (or) uses

• To test the single mean in single sample case.
• To test the equality of two means in double sample case.
• Independent samples(Independent t test)
• Dependent samples (Paired t test)
• To test the significance of observed correlation coefficient.
• To test the significance of observed partial correlation coefficient.
• To test the significance of observed regression coefficient.