Question

Discuss how the mean difference, group variability, and sample size are related to statistical significance of the t-statistic.

Answer 1

To understand this let us start with the formula for single t test statisic

t= xbar-mean/ s/ sqrt (n)

So from above formula we can see that t is directly proportional to differennc of means and square root of sample size and inversely proportional to sample s.d.

So to make our t statisic Significance we should have large sample size, small group variability and large mean difference.

For independent two groups

t test= xbar-ybar/ sp*sqrt(1/n1+2/n2)

Where sp is pooled variance. Again same concept will apply that small variability, large mean difference and large sample size will lead to significant t statisic.

I hope this will help.