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Say I have some data with no labels. Each column is a separate numerical measurement, with each entry in the column being a single measurement of that type. I do not know anything else beyond that, however; what is being measured, or how it was measured, just that it was.

Is there any method to computationally determine the measurement level (nominal, ordinal, interval, ratio) of each column? Are there any methods that would work that would not depend on looking at the data in other columns?

How about if I have categorical strings instead of numerical measurements? Is there a way to determine nominal versus ordinal?

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  • $\begingroup$ are these numeric measurements made at fixed intervals over time or space ? $\endgroup$
    – IrishStat
    Commented Nov 3, 2017 at 14:08
  • $\begingroup$ Possibly, but not necessarily. It could be a simple likert scale. It could be measured once every year. It could be measured once a randomly occurring event happens. It could be a set of measurements that occur at some point within a certain time frame at different locations. But, we don't have access to any of this information. $\endgroup$
    – rbx
    Commented Nov 3, 2017 at 14:21
  • $\begingroup$ Measurement level tells us about the nature of the measurement process. It can also be considered a modeling decision. It is not, however, an inherent property of a set of numbers. $\endgroup$
    – whuber ♦
    Commented Nov 3, 2017 at 16:28

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In the absence of a known fixed interval between the observations in a particular column one could summarize the data and compute measures of central tendency and variation. One could examine the distribution/histogram and perhaps characterize it. Have you done this ,as it might disclose some reasonable reflections.

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