Question

Which set of sample characteristics is most likely to produce a statistically significant value for the independent-samples t statistic?

A) A small mean difference between groups and small sample variances within groups

B) A large mean difference between groups and small sample variances within groups

C) A large mean difference within groups and small sample variances between groups

D) A small mean difference within groups and large sample variances between groups

Answer 1

Here the problem is of Independent sample t-statistics.

In independent sample t-statistics we check whether difference between means of two uncorrelated groups is statistically significant or not.

i.e null hypothesis is "two populations have equal means" and

alternative will be "two populations have different means"

In other words,Both groups are same or different;is the question of interest in independent samples t-test.

Example:- If we want to compare pulse rate peoples living in urban area and rural area.

It is clear that both populations are independent and logically we are interested in rejecting Ho(Both population have same pulse rate)

So here,we go with option(a)

i.e A small mean difference between groups and small sample variances within groups

This sample characteristic is most likely to give statistically significant value for the independent-samples t statistic.

In option(b) large mean difference will not work since (m1-m2) is in numerator of t-statistic and it will given small value of t-test statistic.Which is not favourable for rejecting null hypothesis.

Also option (c) and (d) can not be correct as they are taking about the mean difference between within groups.