So I have 4 columns of data, shown below. The first column is the independent variable and the next 3 columns are the values of dependent variables.

1    223064 222724  222672
2    220066 219400  219298
3    217105 216128  215978
4    214105 212906  212709
5    211295 209732  209492

I would like to calculate the relative difference among the 3 dependent variables with respect to the variation in the independent variable, and the output should be a single value for each row. To clarify, the 3 (dependent variable) columns are values for the same event but for different times (independent variable) and they are diverging as we go downwards. Basically, I am trying to show the divergence of the data.

One way I can think of it is to calculate the difference among the columns themselves, ABS(1-2), ABS(2-3), ABS(3-1). Then Calculate the Mean and Standard Deviation of the 3 differences.

Is this a good way to do it? or, is there any other method to show the relative differences among the columns beside the above one suggested?


1 Answer 1


In general, standardized measure of difference can be called "effect size". Here is a nice post discussing some different effect sizes for 3 different groups (columns) of data. I would consider the general class of answers to your question "effect sizes for one-way ANOVA".

A common one (described in the link) is $\eta^2$. Mentally, you can consider this as finding out what fraction of variation of all of your data is due to group differences.

  • $\begingroup$ I did one-way ANOVA by following this tutorial, and it gave me F<Fcrit. $\endgroup$ Commented Jun 14, 2017 at 7:33
  • $\begingroup$ Sure. The F value of a one way ANOVA could itself be useful. If you are familiar with the ANOVA process, $\eta^2$ is just the SSR (or SSB) divided by the SST. I should add that $F<F_{crit}$ gets into hypothesis testing, which moves a bit away from your original question. Measures of effect size, in general, will be more true to what you have asked. $\endgroup$
    – mflo-ByeSE
    Commented Jun 14, 2017 at 13:38
  • $\begingroup$ I might add that these data are corresponding to 1 independent variable (1 additional column left of the 3 columns of data above). How do I show the effect of the change in the independent variable on the dependent variables? Apologies, as I am new to statistics. I have updated the OP above. $\endgroup$ Commented Jun 17, 2017 at 16:37
  • $\begingroup$ In this case (with three outcomes for different categories of an IV) you may change to a "MANOVA" approach (specifying the multiple dependent variables). Again, just check out some stuff for "MANOVA effect sizes"! $\endgroup$
    – mflo-ByeSE
    Commented Jun 17, 2017 at 16:41

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