Re: comparing individuals to groups in the Mann-Whitney test
- From: David Winsemius <doe_snot@xxxxxxxxxxx>
- Date: Sun, 30 Jul 2006 22:30:14 -0500
"Hannah" <hannahdemulder@xxxxxxxxxxx> wrote in
news:1154292922.004843.57590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:
I'm currently trying to do the statistics for my master's thesis and
I'm having some problems, so I'd be really glad if any of you could
give me a helping hand.
Ok, here's the background: in my research I have two experimental
groups (English and Dutch learners of Italian) and one control group
(native speakers of Italian).
What is the intervention? What is the experimental design?
The data consist of reading times which
are not normally distributed (and neither are the variances), so I
can't do parametric tests.
Not necessarily true. How are the times distributed? Log-normally?
Considered any transformations? I just checked and see that Richard
Ulrich suggested the inverse transformation but there may be others such
as log() or square root transformations.
What do you mean when you say the variances are not normally distributed?
I've resorted to Mann-Whitney tests instead.
What was your research question? That question should drive the testing.
Using SPSS, I want to compare the performance of each individual to the
native speaker group to see if any of the individuals fall within the
native speaker range.
You do not need a test to answer that question. Simple descriptive
statistics will get you that.
The way I've done it now is to run a Mann-Whitney
test with reading time as the dependent and group as the independent
variable (the data was filtered so that group 1 consisted of all the
native speakers and group 2 consisted of only one of the English or
Dutch learners). If the outcome of this test was significant, I've
assumed that there is a difference between the one non-native
individual and the native group (i.e. that the non-native individual
did not fall within the native range); if the outcome was not
significant, I've assumed that that particular non-native falls within
the native range.
Now the question: is this a valid way to compare individual performance
to group performance? Or can the Mann-Whitney test not be used in this
way? If not, could any of you give me some alternatives?
(These comments similar to Ulrich's comments regarding the reduced M-W
test strategy, but perhaps you will get a different slant.)
I think not. Your "Mann-Whitney tests" are just some sort of rank score
for an individual vs. a group. The rank score for the individual will
just be equivalenbt to a percentile location. You are examining each
member of the non-native speakers and getting a test score that cannot
really be interpreted. You are also not correcting for multiple
comparisons. You could just as easily describe the 5th-percentile or 2nd-
percentile of times for native speakers and then classify the number of
non-native speakers who performed above or below that level.
I wonder if this "statistical question" could just be window dressing. It
seems blindingly obvious that non-native speakers would not have the same
median reading time as native speakers. It would be more interesting to
identify distinguishing characteristics among the non-native speakers
that would predict facility with acquiring a second language.
--
David Winsemius
.
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