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How do I normalize a set of data? Let's say we are looking at measurements of diameter of the heart in women and men. Men will have bigger hearts, so error in measuring by the observers will always be bigger. Is there a way to normalize heart size so that I will be able to compare inter-observer variability in measuring this size?

I have, lets say, 5 hearts of different size and 75 observers. Each 15 observer measure the length by ultrasound of one heart and I want to compare their performance. Which observer is best (against gold standard—i.e., the one that has the smallest error), but the one with the smallest heart, can have smaller error against the one who had the biggest heart to measure - but even if the error was let's say bigger by 4mm, the heart was 1.5 times bigger, so he performed better.

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    $\begingroup$ The traditional way to "standardize" observations are subtract the mean and divide by the standard deviation inside each group. $\endgroup$
    – Greenparker
    Commented Mar 7, 2016 at 12:17
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    $\begingroup$ Bigger error for bigger hearts sounds plausible but is nevertheless something to be checked for, not assumed. In the first instance given observers and measurements of male and female hearts I would want to keep the original measurements and decide on the analysis only after a first look at the data. For example, if error is really multiplicative, standardisation is not necessarily going to help, as comparisons arguably should use a logarithmic scale. $\endgroup$
    – Nick Cox
    Commented Mar 7, 2016 at 12:22
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    $\begingroup$ What data have you got? Since you want to look at inter-observer variability, I'm guessing you have multiple observations of the size of each heart. Is that right? Also, the error won't always be bigger but it might be bigger on average. $\endgroup$
    – Peter Flom
    Commented Mar 7, 2016 at 12:28
  • $\begingroup$ Hi, I have lets say 5 hearts of different size and 75 observers. Each 15 observer measure let's say length by ultrasound of the 1 heart and I want to compare their performance. (problem is, that everybody has different heart to measure and I can expect different errors). Which observer is best (against gold standard) (has the smallest error), but the one with the smallest heart, can have smaller error against the one who had the biggest heart to measure - but even if the error was let's say bigger by 4mm, the heart was 1,5 times bigger, so he performed better. $\endgroup$
    – Mitch
    Commented Mar 7, 2016 at 12:49
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    $\begingroup$ It sounds like the hearts are perfectly confounded with the observers. That's going to be a problem. $\endgroup$
    – gung - Reinstate Monica
    Commented Mar 7, 2016 at 12:55

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You can normalize in different fashions, for instance (as said by Greenparker), by subtracting the mean, or also by dividing by the mean. This will translate, respectively, in an absolute or relative normalization. I would beforehand though think twice about normalizing using gender specific means. Why do this? If you want to compare genders there are better ways (eg statistical tests of hypothesis).

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