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Distance

  • Has natural zero point (no distance no travel).
  • You cannot travel a negative distance.
  • 2m to 4m is twice the distance.

Hence, distance is a ratio data.

Displacement

  • Has a zero point (stayed or ended up in the same place).
  • Can be negative (back 2m).
  • Can we talk about 'twice the displacement'?

So it seems that displacement is interval data.

Is that right?

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    $\begingroup$ No, it's not right. Why do you think you can't say "twice the displacement"? $\endgroup$
    – jbowman
    Jun 14 '19 at 1:55
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First, I'd not rely too completely on the whole Stevens' schema. It is meant to be a guide, not a prison. I wrote an article about this on Medium.

Second, why do you think ratio scales can't be negative? The key thing about a ratio scale is that ratios make sense. But I see no reason you cannot have a ratio with a negative number. For interval level data, ratios make no sense. E.g. temperature in Celsius or Fahrenheit is interval because e.g. 100 degrees (on either scale) is not twice as hot as 50 degrees (on the same scale). This can be seen by comparing C and F. 100 C = 212 F, but 50 C = 122 F (not 106). But a displacement of -1 meter is -1 the displacement of +1 meter.

Third, Stevens originally talked about permissible transformations. For interval data, we can transform in any way that preserves the relative size of the intervals. For ratio data, we may only multiply. See my article for more explanation and examples.

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Displacement is a vector. Not all variables fit nicely into the Stevens typology, and positions, distances and displacements is among them. See her a similar question about time (the 1-dim analogy) What type of data are dates?.

The mathematical/geometrical structure used to represent positions, displacements, (and distances) is Affine space. But for you it will better to just think about displacements as vectors, and forget about forcing them into the Stevens typology where they do not belong. See also Are the variable types here considered correct?.

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