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I am designing a health science experiment for uni and am focussing the study on measuring range of motion in a person's knee before and after they wear a copper bracelet. To measure the ROM, we are using a goniometer, which is a giant protractor with 2 arms that align with the angle of the joint to provide the degree of movement in that joint. This might sound basic, but I'm having a fight with myself as to whether this data is ordinal or ratio. I think it might be ratio because measurements are taken when the person is lying down (ie flat at 0 degrees), and you cant have a -ve degree, but it could be considered ordinal if you use the baseline measurement as an arbitrary '0 degree' point and then have + or - results from that point. Which way is the 'normal' way of using this data, because ultimately I just want to have 'before' and 'after' data to compare - please help!

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    $\begingroup$ An aside: I would urge you to please be extremely careful with your study design. Involve a qualified statistician in the design before you collect any data. In goniometer studies in which I've been involved in the past (and only after data were collected), the single largest source of variation is the person taking the measurements and this variation appears to swamp all others in many cases. Cheers. $\endgroup$
    – cardinal
    Commented Oct 6, 2011 at 12:57

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"Ordinal" versus "interval" versus "ratio" (versus "nominal") is a statistical straitjacket. This classification can be useful for suggesting appropriate analyses, but in no circumstances should it be used to constrain your options. At this stage, it's almost a meaningless question.

In fact, angular measurements arguably fit none of the classical characterizations of data. But this doesn't matter. One thing you should be thinking about at this stage (in addition to experimental design) is the nature of the measuring process: how accurate is it? How precise? How repeatable? What are the identifiable sources of variation (due, perhaps, to differences in measuring instrument, skill of the measurer, physical characteristics of the person being measured, and so on) and how might each source be contributing to overall measurement variation? If you haven't identified these sources, do so before designing the experiment, because one of the experiment's secondary objectives will be to quantify the important sources of variation.

If you have databases of previous measurements, or can take preliminary measurements, then you can go further to characterize the likely (univariate) distribution of the measurement errors and to explore how that distribution might vary with other factors. In standard ways this characterization can suggest appropriate ways to re-express the angles, if necessary, so that the comparisons are performed in meaningful and powerful ways. However, it's likely that such a detailed study would not be necessary, provided reasonable care is taken to establish a reproducible, accurate measurement protocol and that measurements are recorded with full precision.

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In addition to the other comments/answers, in any study like this you need to be very aware of both order effects and placebo effects, see this video for an example of what people can be convinced of. Without double blinding and randomization of the order your study will have no more validity than what is shown in the video.

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