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August 22

Correlation for unordered sets

When I read the definition of correlation, it boils down to "as one attribute rises, the other rises. As one attribute falls, the other falls." That makes sense for two ordered sets of values. What if you have unordered sets. For example, I have 5 people and I want to know if weight is correlated to nostril radius. So, I have five weights like [ 150, 127, 210, 108, 250 ] and five nostril radii [ 2.4, 2.2, 3.0, 1.9, 2.7 ]. I can arrange those attribute pairs however I like. So, it isn't that one is rising or falling. They are independent values. If I say they are "correlated", what do I really mean? Is it called something other than "correlated" because they are not ordered? Is the basic calculation, which I often see named "Person's Correlation" the same? I hope that it is clear that I am asking for a layman's term for correlation to use when data is not rising or falling, assuming that correlation is a proper measure to use for this data. 75.136.148.8 (talk) 12:22, 22 August 2024 (UTC)[reply]

For correlation, you need to know which values in each set belong together - ie there are five individuals with the weights and nostril radii given, so each weight is linked to a specific nostril radius. Then you can put the weights in rising order, and if the corresponding nostril radii in that order also rise, then you have a correlation. If the radii in that order actually fall, then you have an inverse correlation. If the radii show no pattern, there is no correlation. -- Verbarson ^talk_edits 12:54, 22 August 2024 (UTC)[reply]

Alternatively, plot weight as x-value and radius as y-value on a graph, giving five points. If they look like a diagonal line, there is a correlation of some sort. (Vertical or horizontal lines would only occur if all the values in one set were roughly identical, so no correlation.) -- Verbarson ^talk_edits 12:58, 22 August 2024 (UTC)[reply]

So, what you are saying, is that it doesn't matter what the order of the values in the sets are, the correlation will be the same, correct? If that is true, I am having trouble with the definition "as one rises, the other rises" because I can rearrange them however I like to disrupt rising and falling data points. 75.136.148.8 (talk) 10:30, 23 August 2024 (UTC)[reply]

You have five people. Each person has a weight and a nostril radius. If you want, you can order the people from smallest to largest weight (which induces a particular order on the nostril radii). If you want, you can order the people from largest to smallest nostril radius (which induces an order on the weights). But no matter what, each weight always corresponds to the same nostril radius (unless you're doing some pretty serious surgical intervention), so what you really have is a list of five ordered pairs (weight, nostril radius). Correlation does not care about which of these points you label first, second, third, fourth, fifth; but it would care a lot if you changed the correspondence between the two coordinates of the pair. 100.36.106.199 (talk) 10:37, 23 August 2024 (UTC)[reply]