**P.Mean: Interval scale for count data? (created 2008-08-07)**.

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Some of my colleagues insist that the variable: number of---,(say, quality distractors of an item) is not an interval scale measure but I feel to the contrary. What do you say and why?Will you get in trouble if you tell these colleagues that they are full of beans?

There certainly is a lot of controversy over the appropriate scale for many variables. This one, though, is pretty hard to argue for anything other than an interval/ratio scale.

Differences on this scale are clearly meaningful--the concept of two more or three fewer is pretty well established for count data. Ratios are also meaningful, as you can clearly define a three fold increase or one-tenth the size in a count variable.

There may be some marginal cases, and perhaps quality distractors is one example, perhaps. I know very little about quality distractors, to be honest. But almost every count variable that I have encountered can be easily analyzed on an interval or ratio scale.

One indirect litmus test is to ask whether an average is readily interpretable. That would indicate at least an interval level of scale. As far as I know, no one has objected to summarizing count variables using a mean.

For what it's worth, there are some subtle issues associated with counts, and you do need to be cautious. Often these variables need special models, such as Poisson regression.

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