I need some basic conceptual help.

When using models to check for association with psychometric scales such as the Lubben's social network scale or similar, would it ease interpretation if the dependent variable - the score on the scales - is coded as a standardized variable, that is in terms of a z-score?

Most of my independent variables are categorical. So for example, compared to a reference group of those currently married, I find that those who are separated/divorced have larger social networks (measured on a scale of 0-60) - going by the positive beta coefficient. But the reason I am thinking of using the social network scale as z-score values is so that I can say something a bit more meaningful - such as a larger social network which is larger by half a standard deviation. Or, for those with higher education, the social networks are larger - again would it benefit to know by how much in terms of SD rather than a number in the scale's range - which would not make much sense in and of itself.

What is recommended?

  • $\begingroup$ If the range of your scale is not interpretable, how do you expect a standard deviation in this scale to be? Scaling your outcome variable will not change the interpretation of your model if your error function is of the location-scale family, e.g. Gaussian. $\endgroup$ – Knarpie Oct 9 '17 at 9:24

This is a question on which different qualified people disagree.

My view is that if the dependent variable is well-known in your field, standardizing it loses interpretability. For example, if your dependent variable was weight of adult humans (in pounds or kilograms, depending on location) then readers would have a good intuitive understanding of its meaning. Similarly for IQ - people know that 100 is typical, 150 is very high and so on.

"Half a standard deviation" is not inherently more meaningful than "7 IQ points". Which is more interpretable depends on context.

Is the Lubben scale well known in your field? Do people have an intuition about it?

NOTE: There are other issues about standardizing variables that I have not touched on. I am just answering the specific question about interpretability.

  • $\begingroup$ It is ironic that your example, IQ, is nowadays a standardized scale, and 7 points difference on the IQ scale is defined as a synonym to half the population devitation. Only in the research of the old days did it have it's quotient meaning. ------ But then again, you did not argue against normalized scales, and instead against messing with conventional scales (for no good reason, since a degree of a difference can be expressed in addition to the scales, and in addition the term 'a standard deviation' is also very confusing: deviation of what? is it a t-test? etc?). $\endgroup$ – Sextus Empiricus Oct 24 '17 at 10:15
  • $\begingroup$ In the case of IQ scales (the standardized ones and not the old quotient calculated ones) "Half a standard deviation" is actually more meaningful than "7 IQ points". There has been use of many different definitions for the IQ scale and there is some ambiguity (standardization to $N(100,\sigma)$ with various different $\sigma$ ) . So in that case there is a good reason to express differences with the term SD, in addition the term SD (SD of the entire population) will also be less confusing. $\endgroup$ – Sextus Empiricus Oct 24 '17 at 10:24

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