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In one post it was written that:

You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales.

What does scale refer to here?

Does it refer to the units (e.g. physical) that the variable have or merely the numeric value?

Are variables with different empirical meanings in binary matrices on the same scale or not? They only get values 0/1, but the "physical meaning" of 0/1 might differ between variables.

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    $\begingroup$ It refers to both units and numeric values. If a subtraction makes sense, measurements are on the same scale. If I have 0 children and someone else has 7, they have 7 more than me. No units (unless #children is a unit), but the subtraction makes sense. If I am 1.8 m tall and someone else is 1.6 m, I am 0.2 m taller. 3 kg $-$ 2 m is meaningless, in contrast. But the advice isn't always true. If I have measurements on people's heights and the lengths of their index fingers, I am likely to want to work with the correlation matrix. $\endgroup$ – Nick Cox Apr 17 '18 at 14:35
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Partially answered in comments:

It refers to both units and numeric values. If a subtraction makes sense, measurements are on the same scale. If I have 0 children and someone else has 7, they have 7 more than me. No units (unless #children is a unit), but the subtraction makes sense. If I am 1.8 m tall and someone else is 1.6 m, I am 0.2 m taller. $3 \text{kg} − 2 \text{m}$ is meaningless, in contrast. But the advice isn't always true. If I have measurements on people's heights and the lengths of their index fingers, I am likely to want to work with the correlation matrix. – Nick Cox

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