# SPSS from two - to one tailed test

If any of you would like to confirm if my understanding is correct or wrong,
I will be most grateful.

I have done an independent-samples t-test (two-tailed),
for difference between women/men how they see their own skill sett.

In short:
group women,n 76: mean 3,20 - std .980
group men,n 21: mean 3,71 - std .956

df= 95 sig.level set to 0.05

t= - 2.150 sig. (2-tailed) 0.034

(critical value= -1.98 to 1.98)

statistics significant difference between men and women ...
I reject the null hypothesis.

I am going to find out the the results for a one-tailed
test which SPSS do not check for.

H0: There is no difference in drivingskills between women and men.
H1:Women have lower driving skills then men.

I have understood that the principle is the same, but I have to
first be clear on the direction, which is negative (group 2 have a higher mean).
Then I need to divide the significant in 2 which was -2.150/2=-1.075.

The area at 0.05 with 95 df one-tailed test in the
"students distribution" shows me about -1.661.

I conclude therefore that I must accept the null hypothesis
when doing a one-tailed test (since I have the number - 1,075)

Am I very lost here or have I understood it and done it correctly?
(She said with hope).

Thank you.

• The $p$-value for the hypothesis $H_{a}:\mu_{\text{Women}}<\mu_{\text{Men}}$ vs. $H_{0}:\mu_{\text{Women}}\geq\mu_{\text{Men}}$ is about $0.034/2\approx0.017$. So you have evidence against the null hypothesis. But could you explain what you hope to achieve with this? Normally, you decide before the analysis whether you do a two-sided or one-sided test – COOLSerdash Sep 17 '13 at 13:56
• No, since this are questions from my previous exam which I did not do well at all. So I am working through it to learn and get better (I do not have the opportunity to go to lectures, so to get feedback here is really valuable for me). – Heta Sep 17 '13 at 14:23
• Thank you very much for your respond. My english is not perfect as well .. I did not mean no regarding achievemt ... but as you see above. Thanks again. – Heta Sep 17 '13 at 14:32
• Thanks a lot Heta for your comments. Please add the self-study tag in the future whenever the question is about homework or exams. That will help us to give you the right answers. Thanks. – COOLSerdash Sep 17 '13 at 14:38
• Thank you again. I did not know about the self-study tag. I will do that. – Heta Sep 17 '13 at 14:46

You should be dividing the $p$-value (0.034) by two, not the $t$-value.

• I select, and Thank you very so much! That mean when I check in "students ..." that also the one tailed test is significant. One question if you may: the way I have written the one tailed test H1 , is that correct? - Women have lower driving skills then men. I was first thinking to write: H1 Men have better driving skills then women. in writing. (Or maybe this is just artistic logic) – Heta Sep 17 '13 at 14:08
• I do not have a enough rep to select yet.Sigh – Heta Sep 17 '13 at 14:10
• You don't have enough rep to vote, @Heta. Click the check mark below the vote total to accept. You can always accept an answer to your own questions no matter what your rep is. – gung Sep 17 '13 at 14:20

As the two-sided test splits the critical region in two halves, there will always be a mirror region on the side the data did not point towards. It is therefore more likely that a one-sided test will be significant than a two-sided tests (given that you are correct about the direction of the test).

In practice, diviing the obtained p-value is the correct way to go, as the t-value does not change based on the directionality of the hypothesis.

Just some clarifications:

1) Be careful about your hypotheses: The test is a test for difference of population MEANS.

"There is no difference in drivingskills between women and men." does not reflect this accurately. You could say: "The mean of the measure of driving skill is the same in the populations of men and women". Many textbooks are very lax in allowing all sorts of statements here, but the statistical test is solely testing the sense stated.

2) Be careful about the statement "accept the null hypothesis". While this was routinely used by Neyman and Pearson, many modern-day instructors teach not to use it and use "fail to reject H0" instead. Some reasons: The study might be underpowered, failure to show an effect does not directly allow statements about the vaildiity of hypotheses etc.