I do not see how (probabilistic) inference is appropriate here at all.
I assume that _all_ employees are rated. There is no sampling, random
or otherwise.
Jon Cryer
At 11:14 AM 8/15/01 -0300, you wrote:
>
>
>"Silvert, Henry" wrote:
>>
>> I would like to add that with this kind of data [three-level ordinal]
>> we use the median instead of the average.
>
> Might I suggest that *neither* is appropriate for most purposes? In
>many ways, three-level ordinal data is like dichotomous data - though
>there are a couple critical differences.
>
> Nobody would use the median (which essentially coincides with the
>mode) for dichotomous data unless thay had a very specific reason for
>wanting that specific bit of information (and I use the word "bit" in
>its technical sense.) By contrast, the mean (=proportion) is a lossless
>summary of the data up to permutation (and hence a sufficient statistic
>for any inference that assumes an IID model) - about as good as you can
>get.
>
> With three levels, the mean is of course hopelessly uninterpretable
>without some way to establish the relative distances between the levels.
>However, the median is still almost information-free (total calorie
>content per 100-gram serving <= log_2(3) < 2 bits). I would suggest
>that unless there is an extremely good reason to summarize the data as
>ONE number, three-level ordinal data should be presented as a frequency
>table. Technically one row could be omitted but there is no strong
>reason to do so.
>
> "What about inference?" Well, one could create various nice
>modifications on a confidence interval; most informative might be a
>confidence (or likelihood) region within a homogeneous triangle plot,
>but a double confidence interval for the two cutoff points would be
>easier. As for testing - first decide what your question is. If it *is*
>really "are the employees in state X better than those in state Y?" you
>must then decide what you mean by "better". *Do* you give any weight to
>the number of "exceeded expectations" responses? Do you find 30-40-30
>to be better than 20-60-20, equal, or worse? What about 20-50-30? If
>you can answer all questions of this type, by the way, you may be ready
>to establish a scale to convert your data to ratio. If you can't, you
>will have to forego your hopes of One Big Hypothesis Test.
>
> I do realize that we have a cultural belief in total ordering and
>single parameters, and we tend to take things like stock-market and
>cost-of-living indices, championships and MVP awards, and quality- of-
>living indices, more seriously than we should. We tend to prefer events
>not to end in draws; sports that can end in a draw tend to have
>(sometimes rather silly) tiebreaking mechanisms added to them. Even in
>sports (chess, boxing) in which the outcomes of (one-on-one) events are
>known to be sometimes intransitive, we insist on "finding a champion".
>But perhaps the statistical community ought to take the lead in opposing
>this bad habit!
>
> To say that "75% of all respondents ranked Ohio employees as having
>'Met Expectations' or 'Exceeded Expectations.' ", as a single measure,
>is not a great deal better than taking the mean in terms of information
>content *or* arbitrariness. Pooling two levels and taking the
>proportion is just taking the mean with a 0-1-1 coding. It says, in
>effect, that we will consider
>
> (Exceed - Meet)/(Meet - Fail) = 0
>
>while taking the mean with a 0-1-2 coding says that we will consider
>
> (Exceed - Meet)/(Meet - Fail) = 1.
>
>One is no less arbitrary than the other. (An amusing analogy can be
>drawn with regression, when users of OLS regression, implicitly assuming
>all the variation to be in the dependent variable, sometimes criticise
>the users of neutral regression for being "arbitrary" in assuming the
>variance to be equally divided.)
>
> -Robert Dawson
>
>
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___________
----------------------------------------------- | \
Jon Cryer, Professor Emeritus ( )
Dept. of Statistics www.stat.uiowa.edu/~jcryer \ \_University
and Actuarial Science office 319-335-0819 \ * \of Iowa
The University of Iowa home 319-351-4639 \ /Hawkeyes
Iowa City, IA 52242 FAX 319-335-3017 |__________ )
----------------------------------------------- V
"It ain't so much the things we don't know that get us into trouble.
It's the things we do know that just ain't so." --Artemus Ward
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