Question

Discuss how the mean difference, group variability, and sample size are related to

     statistical significance of the t-statistic

Answer 1

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

Answer:

For single t - test statistic:

We know that

The formula of test - statistic (t) is given by

Where

x̄ = Sample mean

= Population mean

S = Sample standard deviation

n = Sample size

Here we can see that t is directly proportional to difference of means and square root of sample size(n) and inversely proportional to sample standard deviation(s).

For independent two groups

We know that

The formula of test statistic (t) is given by

Where

  

Where Sp is the pooled variance. Again same concept will apply that small variability, large mean difference and large sample size will lead to significant test - statistic.