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I simulated an agent based modeling that individuals can end up with a different range of attitudes.

Individuals in Model 1 end up with the attitude range -3 +3

Individuals Model 2 end up with the attitude range -25 (min) + 25 (max)

In Model 1, individuals CAN reach attitude -25 or 25, but they didn't. I think it is similar to the situation where the samples with extreme attributes are not available in the sampling process.

What I'd like to measure is attitude polarization.

So I use excess kurtosis and standard deviation as dependent variables.

Is it statistically appropriate to compare Model 1 and Model 2 by kurtosis?

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  • $\begingroup$ Could you clarify what you mean by "statistically appropriate"? $\endgroup$
    – whuber
    Mar 15, 2021 at 14:33
  • $\begingroup$ If kurtosis of Model 1 is 0.20 and kurtosis of Model 2 is - 1.2, is it okay to interpret the results as Model 2 is more polarized than Model 1 without any correction of each kurtosis? $\endgroup$ Mar 15, 2021 at 22:26

1 Answer 1

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Excess kurtosis obtains the minimum, -2, with the equiprobable two-point distribution. I would guess this would be what you would like to call "polarized," e.g., half of the people in model 2 said "-25" and the other half said "25".

But in model 2, if half of the people said "-11" and the other half said "-10", then you would also have the minimum kurtosis, and I don't think you would call that a "polarized" result. So kurtosis has some problems when measuring polarization.

Another possibility is to rescale both so that the range is -1 to 1 (divide by 3 and 25, respectively), then find the sdevs of the resulting transformed data. I think higher sdev means greater polarization by this method, but lacking details of the experiment, I might be wrong.

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  • $\begingroup$ Thanks! It helps me to clarify the results. Sorry that I forgot to mention that it was the excess kurtosis. $\endgroup$ Mar 16, 2021 at 0:07
  • $\begingroup$ Thanks, edited. $\endgroup$ Mar 16, 2021 at 12:15

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