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I have a problem with calculating and interpreting ratios.

My team is suffering from huge data gaps and, therefore, we have no choice but to use all resources we have.

I want to calculate how many new buildings were built (per 100 buildings between 2001 - 2011) per population growth (% between 2001 and 2011). If I divide the first (proportion of new buildings) by the latter (population growth), what does this really mean?!

For example, one of the cities had a ratio of -1008. I know that this means that there was much more construction than population growth, but how can I interpret the number exactly? What does 1008 really mean?

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    $\begingroup$ Why calculate a ratio that you can't interpret? (Sorry, but on the face of it that has to be a question.) $\endgroup$
    – Nick Cox
    Commented Apr 23, 2018 at 11:01
  • $\begingroup$ Of course, understandable. We only have this data, we really need to calculate "sustainable city urbanization"; we are a group of psychologists trying to make sense of our data - this is all that we have. As the time span coincides, we are trying to figure out how to use this. $\endgroup$
    – Marta Rodrigues Neves
    Commented Apr 23, 2018 at 11:04
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    $\begingroup$ Start plotting them, not dividing them $\endgroup$
    – kjetil b halvorsen ♦
    Commented Apr 23, 2018 at 12:45

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In a comment you say that you want to calculate "sustainable city urbanization" but that this is all the data you have.

Sorry, but first you'd have to precisely define SCU, then you figure out how to measure it and get the data. If the data you have doesn't measure it, then you need new data. In some ways, a bad estimate is worse than no estimate at all because you wind up thinking you know something that you don't.

As for what your ratio means, it means that the proportion of new buildings built was 1008 times the % of growth rate. I'm not sure there's any sensible interpretation beyond that - but that's more for you to tell us than for us to tell you. The problem isn't that there are different units - we take ratios of different units all the time - miles per gallon, yield per acre, etc. - it's that your particular two units don't really go together. Unless you can come up with one.

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  • $\begingroup$ Perfect, this kind of points us in the right direction. That was exactly what we were trying to measure. We defined the ideal ratio as being 1, this is the rate of urbanization (new buildings this is) is perfectly accompanying the population growth. Thus, there is no unjustified urban sprawl, but also no more population density. This is a particularly problem in Portugal, in which the study is being developed, and the optimal ratio had already been defined between our team and the city councils - I was just trying to interpret what the results meant, which you explained to me perfectly $\endgroup$
    – Marta Rodrigues Neves
    Commented Apr 23, 2018 at 11:20

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