t-test for Between Groups and Related Groups

Independent Groups Vs. Repeated or Matched Groups

So far, we have not mentioned how the groups are chosen.

There are two choices:
Independent Groups - Each group is randomly selected

Mary, Bob and Jim in Group 1
Vs.
Phil, Sue and Joan in Group 2

Vs.

Repeated Groups, Within Subjects, Matched Groups -

The Same Folk are tested twice,

You use identical twins,

People are pretested and paired on some characteristic.

Mary, Bob and Jim in Group 1
Vs.
Mary, Bob and Jim tested again in Group 2

Here's the reason to do one versus the other:
Independent Groups:

It is easy to find subjects.

It is the only design that works when you use variables like Gender - you can't change men into women and vice versa for the second trial.
Repeated Groups:

Fewer subjects are needed.

More statistical power because:

These designs reduce experimental error as you reduce the chance that you select wildly different kinds of individuals for each group by luck.

Technically, you subtract a covariance term in the standard error and make it smaller. Thus, you get a bigger t-ratio and this makes it more likely for you to get significance.

Bottom Line:

You get the data.
You calculate the means and standard deviations. If it is a repeated groups design, you also calculate the correlation coefficient.
You calculate the t-ratio.
You look it up.
If the probability of t is less than .05 or .01, you have significance.
You conclude the groups are different.

Remember this:

Big t
Small p
Small p - Significance