T-Test Question

#1
Hi Everyone,

I'm 98% done with my statistics homework, and I'm just stuck on one issue. To make a long story short, I was asked to do a t-test with two groups of data, using a one-sample t-test on SPSS. So, basically, I was assessing change scores. For the next problem, I was asked to use the same data and assume that they were from two independent groups in an independent groups t-test. In the first analysis, the null hypothesis was rejected.. but in the second, it was retained.
The question I'm stuck on is, why do I think this difference occured? I think I have an idea... but I don't know if it's good enough. Can anyone enlighten me? Thanks so much!

Best,
Carrie
 

JohnM

TS Contributor
#2
The first test you did was a dependent-samples t-test (testing whether the average change score was significantly different from 0), which is a more powerful test than an independent-samples t-test (there is a much better chance of rejecting Ho).

The reason for this is that a dependent-samples t-test removes the within-groups variation from the error variation (the denominator of the formula for the t-statistic). With a smaller denominator, the t-statistic becomes larger....

Basically, you're just evaluating change scores and you're not dealing with potentially large variation within each group.