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I have collected psycophysiological data measuring the subjects (two groups) ability to perceive vibration. A vibrating probe moves against the skin at smaller and smaller displacements, and the subject indicates when they feel the vibration. Unfortunately, at high frequencies, the probe can only move a short distance, and sometimes the largest distance that the probe can move is still not large enough for the subjects to perceive. Thus, I have accurate threshold values for some subjects, but for some who never felt the vibration, I simply have a value that I know their threshold is greater than. Is there any way for me to still include this data? And what is the best way to analyze it?

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These are called censored observations. How to include it depends on the kind of statistical analysis you are conducting. – user10525 Jun 14 '12 at 21:12
I agree with Procrastinator except that I would use the term truncated. The approach to a simlar problem called right censoring occurs in survival analysis there you keep the truncated value but have an indicator variable to tell you whether the value is a complete value or a censored one. In survival analysis there is a simple way to deal with this but that is because you are estimating a survival curve. Here you may be wanting to calculate averages. If you ignore the trucation you underestimate the average. If you throw out the truncated points you underestimate the average. – Michael Chernick Jun 14 '12 at 21:37
To properly incorporate the truncated values you would need to have a probability model for the probe distance given that it is greater than the threshold. You could then take the mean of that distribution and compute a weighted average using the average for the values that were not trncated with the average for the truncated distribution where the weighting is according to the proportion of cases truncated. – Michael Chernick Jun 14 '12 at 21:37
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Truncation is what would happen if you threw away the unquantified data. You don't want to do that! You are correct, Cale, that there is information in these censored values and in suspecting that there are some standard ways to analyze them (and pitfalls for the unwary). But to provide a good answer we would need to know what kind of analysis you seek. In particular, the treatment of these data is fundamentally different depending on whether they appear as dependent or independent variables in a regression. Perhaps you could elaborate on this? – whuber♦ Jun 27 '12 at 3:11
Tobit? or not tobit? – rosser Jul 12 '12 at 11:54
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1 Answer

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Clustering the results and defining a scale might be a solution.

Make a category variable like so (or differently):

  1. High sensitivity
  2. Normal sensitivity
  3. Low sensitivity
  4. Insensitive (the ones that are off the scale in your case)

You could use this variable to do the analysis, but whether the results are meaningful depends on how well you define the categories.

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