I have a series of well known data showing, for example, the average weight by age in Europe.

Let's say yesterday I called a lot of people and I asked for their age and weight. The data coming from these observations roughly follows the same trend (i.e. average distance between observation and ideal values is very close to zero).

One year later I do the same, but for some reason the weight increases among older people (i.e. average distance between observation and ideal values increases).

How do I verify this kind phenomena? How do I compare that the observations I did in the past are "better" (i.e. more close to the ideal) than the one I did today?

I did this by calculating the average distance between observation and ideal value, but it's a formula I made up. Is there something well known for doing this?

Thank you!

  • $\begingroup$ I see no reason why the average error wouldn't be a good indicator. You can also use the correlation coefficient, i.e. the ratio of the explained variance over the total variance. $\endgroup$ – Yves Daoust Mar 5 at 23:28

A common method to investigate such problems is to use profile analysis. Your independent variable is age. The dependent variable is the average weight. And you have multiple groups (time of measurement). For each analysis, you simply take one group and compare it to the ideal profile.

Profile analysis provides you information if both profiles are parallel, if they are equivalent (this is what you are looking for, but checking this requires the profiles to be parallel) or if the profiles are flat (no change even if age is changing).

There is an excellent chapter of this topic in the book Applied Multivariate Statistics by Johnson & Wichern. After using google I also found this free resource, but I didn't check its quality.

  • $\begingroup$ The thing is that I would avoid aggregations such as average weight to loose important details. For example what if the variance is extreme (uniform 50-150) in one dataset and in another is just a series of values very close to 100? They would be parallel but not really the same thing. $\endgroup$ – mir88 Mar 7 at 6:24
  • $\begingroup$ What you are stating is a very unlikely event. Does your data indicate such problems? $\endgroup$ – MachineLearner Mar 7 at 12:19
  • $\begingroup$ Not sure about unlikely, but it is happening and that's why I am searching a metric that can measure that $\endgroup$ – mir88 Mar 10 at 5:44

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