I have an independent variable (distance between two stimuli) with 6 levels, but the levels are not equally spaced (e.g. 10, 15, 25, 35, 45, 60 pixels). The distance between two stimuli is important for me (I want to compare the performance in 10 pixels to performance in 60 pixels).

I am confused because I know that ordinal variables are typically non-numeric, and that the differences between points in the scale are not meaningful. But I also know that interval scale is where the differences between points on the scale are measurable and exactly equal.

If the differences between the points were equal, I would think that the variable is on an interval scale, but now I am not sure.

Would this variable be ordinal in this case?

  • 2
    $\begingroup$ It might depend on your problem, but that distance is a numerical variable, not a categorical one. When dealing with a numerical distance you are taking in account both order and distance between values. "Ordinal variables" are just categorical variables where there is an order between levels, but not a meaningful distance between levels. However, to take profit of the advantages of numerical variables, you need to analize your data using tools suited for numerical variables. $\endgroup$ – Pere Jun 4 '19 at 12:03

Welcome to the site, @greenscientist.

As I understand it, pixels can only take whole number values, so in that sense they are a discrete, numerical variable.

However, the distance between your two stimuli could, theoretically, take any positive value - i.e. it is a continuous variable in the range of values greater than or equal to 0. The pixels are just a structure that you've imposed, in the values of distance that you've been able to set up your experiment to measure. So I think you can analyse this as you would a continuous variable.

You could turn your measured pixel values into an ordinal variable if you wanted to, but the pixel values themselves are not ordinal, and you'd be throwing away information about the distance between the points.

  • $\begingroup$ Thanks a lot. Then, (a more general question) it is not critical to have equal differences between levels of a variable (e.g., level2-level1 = level3-level2 = level4-level3 etc.) for that variable to be a continuous (and interval) variable. Is this interpretation correct? Thanks again! $\endgroup$ – greenscientist Jun 4 '19 at 12:39
  • $\begingroup$ No, the underlying variable 'distance' will always be continuous and your choice of which values to measure it at does not change that. Having said that, you could have chosen to measure this continuous variable on a categorical/ordinal scale and therefore ended up with a categorical variable, if you had not retained information about distance. But to do so would probably have been a poor choice when you had an option to use a numerical variable (as, in fact, you did, since you used pixels). $\endgroup$ – Izy Jun 4 '19 at 13:08
  • $\begingroup$ The spacing of your measurements that is best for your experiment will depend on the specific circumstances of your experiment and dependent variable, and can be informed by prior knowledge of these (e.g. from previous experiments or theory). If you don't know anything of what the relationship might look like, relatively even spacing of your measurements is probably a good starting point, but for example if you wanted a higher level of certainty over a certain pixel range, you might choose to focus more measurements in that range. $\endgroup$ – Izy Jun 4 '19 at 13:10
  • $\begingroup$ See here for more discussion on spacing of your explanatory variables. $\endgroup$ – Izy Jun 4 '19 at 13:18

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