In this article we will discuss about the definition of ‘t’ Test with example.
t-Test is a method to find out whether the difference is quite significant to conclude that the two samples are really different, or the difference in two samples is simply because of some fluctuation, or due to some error or lapses in the experiment. In some cases, it is observed that measurements of two different samples vary.
It can be find out by the following formula:
t = Mean difference/Standard error of differences
In this the “mean difference” and the “standard error of differences” can be determined by the following formulae:
Mean difference = Sum of difference/Number of trials (n)
Standard error of differences = √Sum of square of differences/(n – 1) n – √(Sum of differences)2/n
Example:
Two varieties of maize (variety X and Y) were collected from four different localities. They showed differences in yield in Kg/hectare as mentioned in Table 2.2. With the help of t-test, find out whether yield of variety Y is significantly superior to the yield of variety X.
Table 2.2 Data showing yield of maize varieties, their yield differences and square of differences:
Calculations:
The details of Table 2.2 may be calculated as under:
Mean differences = Sum of differences/Number of trials (n) = 80/4 = 20
In case of some measurements, the average is mentioned as ± standard error.
Therefore t = 20/4.07 = 4.93
The t-value is not true to the expectations, if it is more than 6.