Cluster analysis variable types

[laurenhosking]

I have a variable which is exam results as a percentage is this variable Ratio, interval, Ordinal or Nominal and why please? I assumed the variable didn’t follow a normal distribution also by applying a distribution analysis 

[FreelanceReinh · Accepted solution]

Hi @laurenhosking,

The exam result may not follow a normal distribution (e.g., because it's restricted to the interval from 0% to 100%, unlike any normal distribution), but it's still measured on a ratio scale: There is a natural zero point (0%) on this scale and a student who reached, say, 60% has achieved twice as much (e.g., got twice as many points) as one who scored 30%, i.e., ratios of two (non-zero) values are meaningful. Of course, the exam result also satisfies the requirements of the lower level scales. For example, the difference between, say, 43% and 44% is the same as that between 70% and 71%, etc. (which is required for the interval scale).

[laurenhosking]

Fabulous thank you so much for your help . Just to clarify my measurement level of this variable would be ratio not interval in this case?

[PaigeMiller]

Maybe this helps?

https://www.formpl.us/blog/nominal-ordinal-interval-ratio-variable-example

[laurenhosking]

Thank you this does help a lot. I’m torn between interval and ratio now as I’ve seen online that percentages are always ratio but I’m not sure as normal scores would be interval.

[PGStats]

@FreelanceReinh provided you with a clear and detailed explanation why exam evaluations expressed as percentages are RATIO variables. If your data are normal scores, possibly taking negative values, then consider them as INTERVAL. But note that normal scores are, by definition, distributed normally.

[FreelanceReinh]

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@laurenhosking wrote:
Fabulous thank you so much for your help . Just to clarify my measurement level of this variable would be ratio not interval in this case?

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Sorry for the confusion and for the delay (I was offline for a while -- thanks to @PaigeMiller and @PGStats for stepping in). In general, the highest measurement scale is relevant, in your case ratio. But this doesn't mean that the weaker criteria of the lower levels in the hierarchy of scales are violated. Statistical methods for those could be applied to a ratio variable, too, but they would tend to be less powerful (than methods for ratio variables) because not all information would be used.

As mentioned, the exam result also shares the characteristics of an interval scale variable and you could even go a step further "down:" classify the percentages into ranges, e.g., 80-100%, 70-<80%, etc., denote these ranges as A, B, etc. and thus create an ordinal variable, albeit losing information (such as the difference between 85% and 90% or the ratio of 84% vs. 72%). Edit (addendum): Similarly, the ranges could be chosen narrow enough so that each distinct value had its own interval. This amounts to assigning ranks to the original values and thus using the exam results as an ordinal variable.