My question is very basic:

I understand linear regression and how to use it. I would like to know what to use in statistics when I don’t have a dependent and independent variable. For example, I understand how we could use height to predictic weight but I only have one variable. Take for instance if I have four people dividing up money. I want to show how closely the numbers are together. Each person is going to submit their opinion of how the money should be divided. I want to show how one person is way off from the others using descriptive statistics. These are percentages of the total.

1 20%, 30%, 30%, 20%

2 25%, 25%, 25%, 25%

3 20%, 20%, 30%, 30%

4 90%, 2.5%, 2.5%, 2.5%

I skewed the data to make it obvious but I want statistical numbers to show that #1-#3 All agree for the most part and #4 is way off. Am I missing something that blantantly obvious of how you would use regression?

  • $\begingroup$ Try calculating the intra class correlation coefficient, or if that is too heavy handed, try the mean and variance of Z-scores. $\endgroup$ – Jay Schyler Raadt Dec 23 '17 at 1:17
  • $\begingroup$ Who gets the remaining 2.5%? $\endgroup$ – whuber Oct 17 '19 at 11:25

For this specific type of problem, you might look into the Aitchison Distance, which is used in compositional data analysis, the method used to analyze data that sum up to a whole (in this case 100%). The Aitchison Distance is a measure of how different two unis with compositional data are from each other. Clearly, the outlying unit will have a large Aitchison Distance from the other units, while the others will have small Aitchison Distances from each other.


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