The T Testing is done in order to examine statistically whether the means of the stated two groups are different from each other. The t test analysis is more preferable and accurate to examine the difference in the means of the two groups. For example; in case to examine T Test graphically, consider two groups one is supposed to be the control mean group and other is the treatment mean group.  The graph for both the groups is drawn in order to have the overlapped distribution,  then at this situation the T Test evaluates and explain that whether the means of  both of the groups are statistically different or not. The T Test actually examines the brief relationship between the means of two groups. For example; if there are three different presentations of the various groups with the point that there difference between the mean is actually same put they can be plotted in various ways that they does not give the same view.

First situation is that in the graph the bell shaped curve is drawn with medium or moderate variability , the second situation presents the high level variability and in the second graph the two groups come up with the low level of variability but in three of the cases the two groups overlap each other.  From the various presentation of the graph, the presentation of the two groups in low variability case came up with the different and opposite view because in such case the overlapping is very less. But in high overlapping case there is minimum striking because of high overlapping.  In such case T Test examines and actually defines the distinction of means by analyzing the different aspect of variability between two means.

## Statistical Analysis of the T Test

The T Test is statistically calculated by using a specific formula that is for its evaluation. The formula that is used for T Testing is actually a ratio. In the ration the above portion is the difference calculated between the means or averages of two or more groups. The second part in the formula includes the determination of the dispersion or the variability if the stated values. In actual fact the formula used for T Testing is the example in the research for the signal to noise metaphor.  In this case the evaluation for the mean is considered to be the signal and the second portion of formula that is the measure of dispersion or variability is the noise which is difficult in order to see the difference. The formula in such case is stated as;

Signal =    difference between the group means

Noise             dispersion of groups

= mean (XT) – mean (XC)/ SE [mean (XT) – mean (XC)]

= value of T

In the above stated formula the numerator is very simple to evaluate that is only to calculate the difference of mean between two groups but the denominator that is the standard errors of the difference. It is complicated to evaluate which first requires the evaluation of variance then divided it by the total number of people involved in a group which are further added and their square root is taken. Variance is actually the square of the standard deviation. The value of T is determined in a way that if the first mean value is positive then the value of T is supposed to be positive.

### References

• Richard Mickiewicz, The Story of Mathematics (Princeton University Press), p.158.

• Zimmerman, Donald W. (1997). "A Note on Interpretation of the Paired-Samples t Test". Journal of Educational and Behavioral Statistics 22 (3): 349–360.

• Moore, David S. (1995), The Basic Practice of Statistics, New York: W. H. Freeman.