# Wilcoxon one-tailed signed rank test

It's regarding a one-tailed Wilcoxon sign test.

I am comparing (fictional) ratings of liking before and after an apple is peeled.

The design is complicated. I will do my best to explain.

There are 9 apples. Participants are asked to rate how much they like each apple. After that they are asked if the apple should be peeled. Those who answered yes, are asked to rate how much they like the apple after it was peeled while those who answer no move to rating the next apple. (please remember this is fictional, my actual research is diff. but I don't want to post it here so using a fictional research which is nearly similar).

So basically, I have pre and post peeling ratings.

Participant one may have 5 pre and post ratings while part. 2 has 7 pre and post ratings.

I expect pre peeling ratings to be more than post peeling ratings, hence one-tailed.

This is the output from SPSS:

Descriptive Statistics
N Mean Std. Deviation Minimum Maximum Percentiles
25th 50th (Median) 75th rating1 379 4.000 1.08588 1.00 5.00 3.0000 4.0000 5.0000 rating2 379 3.500 1.70245 1.00 5.00 3.0000 4.0000 5.0000

Ranks
N Mean Rank Sum of Ranks rating2 - rating1 Negative Ranks 135a 63.00 7975.00 Positive Ranks 0b .00 .00 Ties 254c
Total 389
a rating2 < rating1
b rating2 > rating1
c rating2 = rating1

Test Statisticsa

                           rating2 - rating1
Z              -10.331b
Asymp. Sig. (2-tailed)     .000


a Wilcoxon Signed Ranks Test
b Based on positive ranks.

As far as I can see, the difference is signficant p<0.001 (two-tailed).

How about one-tailed? How do I know if it is signficant at one-tailed as my hypothesis is one-tailed...I have predicted that post peeling ratings will be less than pre-peeling.

• If it's significant two-tailed, it's certainly significant one tailed. (More formally, if you wanted the p-value, for most symmetric tests you would simply halve the p-value, since the area in the desired tail is half the area in both tails.) There's probably a way to make SPSS give you the test one tailed. Dec 3, 2013 at 17:39
• Hi Glen. Can you help me further? Is wilcoxon appropriate since each participant is contributing several pairs of data? see above. Thank you! Dec 3, 2013 at 17:41
• So only the ones that vote yes to shaving get to vote the shaved womans? Dec 3, 2013 at 19:44