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Thread: Applying parametric tests on non-parametric data

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    Applying parametric tests on non-parametric data




    Hi all,

    I'm doing a research and I have some concerns, and I'd appreciate your kind assistance on them.

    Basically, I'm designing an instrument to measure something (a single dependent variable), and I'm going to conduct many statistical analyses, such as multiple regression, factor analysis, etc. As part of such analyses, I'll also be looking at basic statistics, such as correlations and statistical significance.

    The problem is that all my independent variables are categorical, mostly ordinal (5-points likert scale), with some nominal variables, too. My concern is that I've been asked to strictly make use of parametric tests on my data, although they are clearly non-parametric. For example, testing for statistical significance by applying t-test on a question with 5-likert scale responses, which I personally think does not make any sense.

    Furthermore, I tried to look for alternative non-parametric tests, but they can be very challenging, let alone their interpretations (especially to someone who is only uses SPSS). Given these circumstances: If I must use parametric tests to analyze non-parametric data, any tips on the possibility of maybe reducing the unreliability of results? (perhaps increasing likert scale points from 5 to 7, for example?)


    Thank you very much,
    Tx

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    Re: Applying parametric tests on non-parametric data


    The distribution of the independent variable in regression does not matter. Although this point is probably in dispute my understanding of Factor Analysis (as compared to SEM) is that distribution is not emphasized even if formally you assume normality. You can always use Spearman or Polychoric correlations if that is an issue (depending on data type).

    For t test there is a huge dispute about ordinal data. Formally you can only use t test if you can assume the distance between the levels is the same (which may or may not be reasonable - I don't think there is any agreement on this topic). As the number of levels and sample size increase normality is less of an issue generally.

    One thing you can do is run the parametric and non-parametric results and see if they are in the right direction (both are significant or not significant, sign in the same direction). A more advanced approach is to run simulations from your data to see if releasing the assumptions of normality influences the results.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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