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I am analyzing two datasets form Diggle's paper 1983:

Cells

Cells

Pine (actually Numata 1961)

Pine

The cells are coordinates between 0 and 1 and the pine are coordinates between 0 and 5.7 (both are square as you can see). The Pine is random and the Cells are not. I want to show differences in measurements between the two (for example the mean).

My question is- is it OK to scale one of the datasets to have the same coordinate range like the other? For example, I can divide Pine in 5.7 each coordinate and then present it as a different series in Excel scatter plot. Will I be losing ratio? Has anyone compared dataset in this way previously?

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  • $\begingroup$ Mean of what? You can define e.g. mean centre as means of each coordinate. This is common in e.g. demography. I can't tell how much sense it would make here. Descriptively, clustering in part of a map might be shown by the mean centre of a pattern not being the centre of the map itself. $\endgroup$ – Nick Cox Apr 11 '16 at 11:08
  • $\begingroup$ Thanks Nick. Yes, Mean center. Both mean centers are at the middle of the map in this case so it's a bit decisive. $\endgroup$ – John E. Mitchel Apr 11 '16 at 11:41
  • $\begingroup$ I don't find it difficult to imagine different distributions with the same mean centre, but so long as you think about the patterns, this is always something you can do. $\endgroup$ – Nick Cox Apr 11 '16 at 11:45
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You can define the mean centre as given by the means for each of two coordinates, Cartesian or (with more care) latitude and longitude. That is an easy calculation.

Such centres are especially commonly used in demography. There is some information, and even some entertainment, in calculating the mean centre of a country's population (which usually turns out to be somewhere which otherwise is of interest only to people who live nearby) and in tracking changes in that centre over time.

I can't tell how much sense it would make here.

Descriptively, and more generally, clustering in part of a map might be shown by the mean centre of a pattern not being the centre of the map itself. Even if this is quantifying the obvious, it may still be useful.

Mean centres have the limitations of any mean. For example, it is easy to imagine different distributions with the same mean centre or distributions for which the mean centre is an awkward or inadequate summary. But so long as you think about the patterns by looking at maps or plots, this is always something you can do. As always, the mean, median and mode do not in general coincide, so watch out if you really want something else.

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