I want to develop a questionnaire. Because the target population are children, I used 3-point likert-type scale (0 1 2) for my items. Now I want to remove invariant items (i.e. the items not having enough variance). Are there any standards for determining minimum variance value according to different likert-type scales? The issue could also be viewed from a frequency point of view. Is there any specific portion of people (e.g. 80% of them) that if they respond to an item identically (e.g. all responded 0) the item should be regarded as invariant?

  • $\begingroup$ Despite that this question is interesting from statistical point of view, I would say that it is tied more with psychometric issues, that is, the question about what shape is the distribution of the undelying continuous trait being measured, or, to put differently, what shape should that distribution be in order for you to say that it is psychometrically "good". And this is partly both subjective and pragmatic theme. $\endgroup$
    – ttnphns
    Dec 20 '13 at 10:31
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    $\begingroup$ It will also partly depend on the nature of the questionnaire and what you are trying to do and on the distributions of the other questions. Is this an ability test? Attitude? Are you interested in people who are at the extremes? $\endgroup$
    – Peter Flom
    Dec 20 '13 at 11:20
  • $\begingroup$ @PeterFlom great question. The questionnaire consists of different types of fears that children experience, so it is an attitude test and we may be interested in people who are at the extremes, i.e. children who fear a lot about animals, medical items, social situations and lots of other items. But the reason I want to remove invariant items is because I want to do factor analysis on the questionnaire items. $\endgroup$
    – Ehsan88
    Dec 20 '13 at 11:43
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    $\begingroup$ Let's take a step back then. Can you edit your question to give us a better idea of your overall aims? My blog post how to ask a statistics question may help $\endgroup$
    – Peter Flom
    Dec 20 '13 at 11:51

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