Concept of a t- Test
A t-Test is a test of the significance of difference between two means of scores of two samples. For example, suppose the statistics( data of samples) show that boys are more intelligent than girls. Should we generalise this finding for the whole population from where these sample were taken?
To accept this result, Here we need to test the significance of difference between the two samples-Means.
Degree and pattern of variance within group of boys and girls are important in understanding this difference. .
Some girls individually may possess higher level of Intelligence than some boys but when we take mean of Intelligence of the sample of girls, it may fall short of the mean of the intelligence of boys. Conversely , some boys, individually may possess lower level of Intelligence than girls but when averaged in the group /sample, their score may appear to be higher.
A t-Test examines this reality.
Many times, a within group variance( eg 70 to 120) may have mean at 90 where as a within group variance (eg 65 to 110) may have mean at 100. In this case, second group may appear more intelligent at the average level but individually, it may not be true. Average or mean may fool people. It is therefore, required that we understand difference of means under the light of deviation. This is the essence of a test test.
To use a t-test , there are three assumptions about the population parameters:
1. Distribution of the population from where the samples come should be normal.( ie. Mean, mode & median should fall on the same line)
2. Scale of measurement should be at /above interval level
3. variance in the two samples should be almost equal.
Think where such a test is required…