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I developed a re-coloring algorithm to make maps more accessible to the color vision impaired. In order to test this algorithm, I created a questionnaire in which participants answered questions about maps with confusing colors (red and green) and re-colored maps. This questionnaire format was based on the work of Cynthia Brewer. Map order was random.

There were two groups of participants: 41 subjects with normal color vision (passed D15 panel arrangement test) and 41 subject with a color vision impairment (failed D15 test). Each participant has three variables: questionnaire score using original maps (0 - 100), questionnaire score using re-colored maps (0 - 100) and color vision classification (0,1).

I have read about using gain scores with ANCOVA for this type of data. I thought I could treat the original map scores as a pre-test and the re-colored map scores as a post test. Unfortunately, these scores are not normally distributed. Also, a participant can only improve a finite amount. For example, if the participant scored 90% on the original map questionnaire, they can only improve at most 10% using the re-colored maps. Is it valid to also use the pre-test score as a covariate?

I am using R to run this analysis.

gung - Reinstate Monica
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  • Avoid change scores if possible. The difference between two ordinal variables is no longer ordinal. Consider ordinal regression on an absolute score as the dependent variable, e.g., proportional odds model. – Frank Harrell Sep 22 '15 at 19:57
  • Thank you for your feedback, Frank. I apologize for my ignorance but I thought my questionnaire data are bounded continuous (moderator changed the title of my posting). Questionnaire performance is measured from 0% to 100%... or should I just use the count of correctly answered questions as the score, instead? The questionnaire score distributions are severely skewed to the left (most normal vision participants scored 100% on both questionnaires) but change scores and potential change (100%- original map questionnaire score) can be normal with log transformation. – gmculp Sep 23 '15 at 16:55
  • If the underlying values are skewed or you have any floor or ceiling effects, change scores can have a bizarre distribution. That's why analyzing raw scores as ordinal is beneficial - this will handle any distribution plus floor and ceiling effects. – Frank Harrell Sep 23 '15 at 20:40
  • Thank you, Frank... I think I understand, now. So the dependent variable would be the re-colored map questionnaire score (post-test), the factor would be color vision status and the covariate would be the original map questionnaire score (pre-test). Which R package would you recommend? I see there are several in the [R example repository](http://www.uni-kiel.de/psychologie/rexrepos/posts/regressionOrdinal.html) – gmculp Sep 23 '15 at 20:56
  • Hi, @FrankHarrell. I found an example you provided in a [past post](http://stats.stackexchange.com/questions/65548/which-model-should-i-use-to-fit-my-data-ordinal-and-non-ordinal-not-normal-an) using the orm function from the rms package. I will use this example as a learning tool. Thanks! – gmculp Sep 23 '15 at 21:36

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