I'm having trouble creating a composite measure. I have 5 different non-normal variables (all different scales). I'd like to create one score that takes into account these 5 variables. I can manually weight the variables. How do i do this? I have JMP, so I have been trying to use that, but am not sure where to begin. All the of the variables have different scales and units.


In general, a simple weighted linear composite can be formed as follows:

newvar = w1 * x1 + w2 * x2 + ... + w5 *x5

where w1 to w5 are your five weights and x1 to x5 are your five variables.

The question is what weights should you use?

A common approach in my field (psychology) would be convert each variable to a z-score and then unit-weight the variables (i.e., take a simple sum of z-scores). This in some sense represents an equal weighting that controls for the fact that the variables are on different metrics.

Even if you want to weight some variables conceptually more (e.g., variable 1 is more important), it can still be useful to first convert the variables to z-scores and then apply differential weights based on your conceptual weighting.

In other cases, the variables are on roughly the same scale (i.e., very similar standard deviations). In which case, you can often skip the z-score step. You see this a lot with multi-item self-report scales (e.g., life satisfaction, personality, etc.).

Also, sometimes you have items that are negatively related to the construct and you need to reverse certain items. So in that cause, you could use a weight of -1 instead of 1 after z-score transformation.

I've received a few questions about this over the while (see here).

I've never used JMP. But most general purpose statistics sofwtare have tools to create new composites: A quick google suggested this might be useful:http://www.jmp.com/support/help/Formula_Editor.shtml

  • $\begingroup$ Thank you. Do the datasets have the be normally distributed to do a z-score? For example, one variable is web page Alexa Ranking, which is the rank of websites by traffic (1 is highest ranked website, and so on). Another variable is the dollar amount per month that a company spends on advertising. Another variable is the % of website traffic they get from certain channels. Would it make sense to do the z-score approach with these variables? $\endgroup$ – Brandon Sep 21 '16 at 5:01
  • $\begingroup$ no they don't need to be normally distributed. As with any variable you want to think about what is a meaningful metric. Ranks make sense. Sometimes if you have a highly skewed variable, you may want to transform, but that's a separate issue to that of z-scores and so on. $\endgroup$ – Jeromy Anglim Sep 21 '16 at 5:14
  • $\begingroup$ Regarding your specific variables, you generally only create a composite where the resulting composite has substantive meaning. For instance, it seems strange to create a composite based on amount spent and amount of traffic. At the very least, amount spent is not a performance metric. But then again, that's more a theoretical issue, and presumably you have your reasons for wanting to create the composite. $\endgroup$ – Jeromy Anglim Sep 21 '16 at 5:15
  • $\begingroup$ Got it thanks. The dollar spend is a cost per click measurement. So if you have a lower spend it means that you're a better advertiser! So the methodology would be to take the 5 variables I have (one's a %, ones a $ figure, one's a rank, one's a #, etc.) and create a z-score for each of these variables. Then weight the z-scores however we'd like, and sum those weighted z-scores for each variable? What will that sum represent? $\endgroup$ – Brandon Sep 21 '16 at 5:23
  • $\begingroup$ If I want to end up with score between 1-100 to show your overall strength, what do i do to get that? $\endgroup$ – Brandon Sep 21 '16 at 5:25

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