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I am looking to study a particular type of error on a cognitive test to evaluate for potential clinical implications. As there is no existing research on this variable, I would like to run a pilot evaluation on a relatively large pool of subject data from our clinic (feasibly this would be about 200 subjects) to see if there are any trends to guide hypothesis testing in future studies (e.g., are patients from a particular clinical population more likely to make this type of error than those from another population). The data is such that a patient could potentially make 0-15 of these errors, although it's likely that there will be a strong tendency toward the 0-5 range.

Essentially, I am looking to identify subjects from within this pool who are making a relatively higher rate of these errors. Is there a recognized format for doing this type of pilot work? Barring that, what would your recommendations be?

This is obviously very exploratory, so I feel like I would have some latitude in defining what constitutes an 'outlier' for the purposes of this study, but any references or suggestions would be much appreciated.

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I'd encourage you not to think primarily in binary terms (outliers vs. non-outliers) but rather to look more comprehensively for predictors that are associated with this variable. It's an interval-level variable, which means you might be able to test associations using ANOVA or regression. Chances are you'll want to transform the scores first, since they are so skewed; taking the square root might help.

If you conduct an ANOVA or regression and find promising predictors, you can at that point return if you want to the narrower task of identifying or predicting outliers: you'll have a basis for saying what sort of person is likely to have the highest number of errors.

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  • $\begingroup$ I definitely appreciate the thought rolando, but it's worth adding that I'm likely going to be dealing with fairly messy archival data (in terms of predictor variables) that will be hard to structure for use in a regression. Hoping this pilot project will not only guide specific hypotheses, but also help give a sense of how to operationalize some of the potential predictors (or convince me that I'll need to work prospectively on this in the future). $\endgroup$ – Patrick Jul 7 '11 at 4:35
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From my understanding of your problem, the data seems skewed and univariate and the aim explanatory. The first step is plot skewness adjusted box-plots. I know of a $\verb+R+$ implementation in package $\verb+robustbase+$ (look for a function called $\verb+adjbox()+$. The associated white paper is very readable too.

Source: M. Hubert& E. Vandervieren An adjusted boxplot for skewed distributions, Computational Statistics & Data Analysis Volume 52, Issue 12, 15 August 2008, Pages 5186-5201. Ungated version: ftp://ftp.win.ua.ac.be/pub/preprints/04/AdjBox04.pdf

EDIT In principle, these adjusted boxplots assume that the data is continuous. If that's not the case, then this particular algorithm will spot too many outliers. But this problem is an algorithmic, not a statistical one: you can solve it by simply jittering your data a bit to remove ties (i.e. adding noise with small variance to every observations).

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