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I am trying to discourage people from using radar chart diagrams (e.g. this one) where this is not appropriate.

I have already made the point that the optical effect will be distorted because variance in high values result in much larger changes of area covered.

I have also made the point that the optical impression of spikyness versus compactness (are the attributes balanced or not?) depends on the order of the items.

There is one question that remains open to me. Does the size of the area covered inside the line (the blue vs. red area in the chart) depend on the ordering of the items or not?

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Yes.

Suppose there are four attributes, and their values are $A = 1$, $B = 1$, $C = 0$, and $D = 0$.

In the order $ABCD$, the chart looks like a right triangle whose area is $\frac12$.

In the order $ACBD$, the chart looks like a straight line whose area is zero.

In theory, you can avoid this problem by connecting the points with segments of Archimedean spirals instead of straight lines. But nobody does that because it's more trouble than it's worth.

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