Re: one sample t-test --> nonparamatric equivalent?

On Fri, 14 Nov 2008 16:47:15 EST, Anatol <anatol.sendker@xxxxxxx>
wrote:

Dear all,

this is my first post in this forum. I am working on my MBA thesis,
and while creating my research research
design/hypotheses,/questionnaire, I came across this question:

Is there a nonparametric equivalent to the one sample t-test?

My case: I gathered data on a question such as "At what level do
people "A" exhibit skills compared to the average level exhibited by
all people ("B")?"

It was coded on a 5-point Likert scale, anchored by 1 = extremely
poor and 5 = excellent, with 3 = average. Since this is ordinal data,
I prefer to use nonparametric tests (I know that in spite of this,
parametric tests are sometimes used with such data).

It would be like asking:
1. "From your experience, how good are the CAR driving skills of
people who also have a motor cycle driver's license compared to the
average level of car driving skills for people who do NOT have a motor
cycle license (but of course a car license)?"

1 extremely poor
2 below average
3 about average
4 above average
5 excellent

So I am asking for a comparison of the skills of "A" to the average.
That is why I assumed I know the population mean because I defined it
as the "average".

Unfortunately, I was not able to construct a decent pair of
questions that ask for A and B separately, in which case I would have
been able to use the Mann-Whitney test (right?).

Now I have a known population mean of 3 (set by 3 = average) and
want to test whether the mean of my data about "A" is significantly
different from the known population mean. For parametric data I would
simply use a one sample t-test, and all would be well.

Using the one-sample t-test is probably the most sensible thing.

If you want a test that is strictly non-parametric, with easy-to-state
assumptions, do a sign test. Compare the count of those "below
average" (both groups) to the count of the two groups above average.

If you were to elect to weight the responses differentially, such as,
2 points for each extreme, and 1 point for the moderately above/below,
you are pretty much back to the one-sample t-test.

Doing anything with ranks implicitly entails scoring the groups by
a rank-transform. That will result, most likely, in uneven intervals
between the groups: which is hardly likely to be an improvement
on the original scoring.

Also,rank procedures are not very good when there are too many
ties owing to score categories like these. If you use the
rank-transforms where there are numerous ties, you may be apt to
see a variance estimate (for large samples) which is less accurate
than the computation you would get from doing a t-test on the
rank-transformed scores. -- If you want to perform with a rank
transform, then do the transform and use a one-sample t-test.
But if I were a critic, I would want to see the simple one-sample
t-test on the original data.


My question: Is there a nonparametric test to compare a one sample
mean to a known mean?

I did not find anything on that. My current goofy "solution": I
experimented with SPSS and used my one sample data and generated a
dummy variable which I set at "3" for all respondents and then ran the
Mann-Whitney test to compare means. Of course, the second sample has a
mean of 3 with a SD of 0. The Mann-Whitney significance here is the
same (very close) to when I run a one sample t-test with the data, so
I guess the result is "correct".

I wouldn't accept it as a work-around. I don't know whether it may
happen to result in exactly the same test-value as doing a one-sample
t-test on rank-transformed data, but it is inferior (and probably has
less power) if it comes out different.


I would highly appreciate any help or advice on this issue. Many thanks in advance,

--
Rich Ulrich

.

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