Page 17 - 2023-ml-lewandowski-stats1e

Step 5: Decide and Interpret It is clear from Figure 10.9 that our
sample’s t-score of 0.75 is far below the t-cutoff score of 1.714. We can
also see that our difference in means between our samples of 0.75 is
very close to 0.
Time to make our decision. Because our sample’s results (Step 4) do
not exceed the critical value (Step 3), we fail to reject the null hypoth-
esis (H 0 ) that people who do brain-training will have the same history
quiz score as those who don’t do brain-training ( µµ ≤ µµ 2 ). If we fail
1
to reject the null, we must also say that our research hypothesis (H 1 )
that people who do brain-training will have higher history quiz scores
than those who don’t do brain-training ( µµ > µµ 2) was not supported,
1
because we found no evidence to support the notion that brain-
training resulted in significantly higher test scores. In other words,
we must conclude that these data do not suggest that brain-training
significantly increases history quiz scores.

Hopefully, with the concepts and skills that we have learned in this chap-
ter, performing the t-test for independent means is relatively straightfor-
ward. Before reading on, watch the video associated with this chapter.

HAND CALCULATION VIDEO TUTORIAL: To learn more, check out the video tutorial
Performing the t-Test for Independent Means.

communicating the Result
When we fail to reject the null hypothesis, we should say
that our results were “nonsignificant.” We should not say
that the results were “insignificant,” because this term typi-
cally refers to the effect size (which we will talk about in the Statistics
for Research portion of this chapter).
Also, when we fail to reject the null, we have to be careful not to word
things too harshly. That is, we should not say that our study failed, or
that there is no effect, or that brain-training does not work. The fact is, we
still do not know if brain-training has an impact on college studying and
quiz scores. We have a small piece of evidence that brain-training does
not work, but it is far from definitive. So, much like we avoid being overly
bold in saying things worked when we get statistical significance, we
also avoid beating ourselves up too much when we fail to reject the null.

Forming a conclusion
The results of our t-test were nonsignificant. That is, we
didn’t find that our brain-training group performed dif-
ferently from the non-brain-training group. Now, before

T -TES T F OR TW O INDEPENDENT/UNRELATED S AMPLES • CHAPTER 10 359

Copyright ©2024 Worth Publishers. Distributed by Worth Publishers. Not for redistribution.

11_statsresandlife1e_24717_ch10_343_389.indd 359 29/06/23 5:17 PM