NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/sci/math/stat/1787

Text File | 1992-09-02 | 1.8 KB | 43 lines

Newsgroups: sci.math.stat
Path: sparky!uunet!munnari.oz.au!uniwa!newsman!newsman!winzar
From: winzar@newsman (Hume Winzar)
Subject: Re: unweighted mean of means
Message-ID: <winzar.73.0@newsman>
Sender: [e-mail] (News Man)
Organization: Commerce, Murdoch University
References: <[e-mail]>
Date: Thu, 3 Sep 92 09:06:05 GMT
Lines: 31


>I have some questionnaire data from which I wish to derive a "knowledge
>index"   by taking the mean response to several of the questions.
>However, these are true-false questions and more of the questions are
>true than false.  Moreover, many people are clearly disposed to choose
>True as a response rather than False.  Of course, to the degree that
>they have this bias their knowledge index is inflated.

>I have solved this problem by taking the (unweighted) mean of the mean
>answer to false questions plus the mean answer to true questions.

An alternative is an approach often used for rescaling multiple choice
exams:
In this case there is a 50% probability of guessing a correct answer.
So all of the wrong answers must be about half of the guesses - the other
half of the guesses were correct by pure chance.  After calculating the
probable number of guesses you can subtract this number from the total
number of questions.  In this case it reduces to, for each person:
                 SCORE = N(correct) - N(wrong)

Of course this does not get you arround the systematic bias created by the
propensity to answer TRUE more often.
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 |      _--_|\     |   Hume Winzar
 |     /      \    |   Commerce School,
 |     *_.--._/    |   Murdoch University,
 |           v     |   Perth, Western Australia
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