In using this interactive on-line resource, you'll be able to
enter hypothetical sets of matched data and then see the p-level
that's computed for your data. By varying the nature of
your data sets, you'll come to understand why the Wilcoxon test
sometimes leads to a statistically significant result.
What to Do:
Click on the colored title of this on-line resource: "Wilcoxon's
Matched-Pairs Signed-Ranks Test."
On the screen that pops up, Not that there's a white box
with two columns of scores.
In the white box, imagine that each row of scores corresponds
to a different high school students who wants to go to college.
Further imagine that the specific numbers are SAT scores and
that 2 numbers appear on each row because each of our 9 hypothetical
students took the SAT twice.
Change the last student's second score from 582 to 537.
Click on the "Submit" button, and then examine the p-level
that's presented above the box containing the paired data.
Originally the p-level was 0.0396
Originally the p-level was 0.03906; now, it's equal to .09766.
Think about the one change in the data you made, consider
all 9 pairs of scores, and ask yourself whether it makes sense
that the p-level got larger because of the change you made.
Make other changes in the data, each time checking to see
what happens to the resulting p-level. (To make the original
9 pairs of scores to appear in the white data box, click on
"Return to Statistics" in the upper left-hand corner of the
screen, and then--on the new screen that pops up--click on
"Wilcoxon Matched-Pairs Signed-Ranks Test" under the heading
"One-Sample and Matched-Pairs Tests.")
Sky Huck's Puzzle Question:
If you start with the original 9 pairs of scores (by clicking
on the "Reset" button, you'll note that you can increase the first
student's 2nd score (of 594) by 1 point, by 10 points, or by 100
points, and yet these changes do not alter the p-level. Why does
the p-level remain constant even though this score is changed?
(If you answer this question correctly, you'll probably be able
to sense how extensively you could LOWER 594 without affecting