I have a relatively simple problem that I can't seem to find a satisfactory solution to. If I have three scales for three different sets of data. One varies from [-5,5] the other from [1,10], and the last from [-10,10] what would an appropriate way to make a single scale for data from all three sets of data?
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2$\begingroup$ It depends on the purpose: why do you need a single scale? $\endgroup$– whuber ♦Commented Nov 6, 2013 at 21:23
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$\begingroup$ @whuber Sorry, the idea is to use the scale to actually compare values in each set of data. I want to know why one set of data has the letter A as a 5 for example while another has it at a 4. Right now the fact that one set gives it a 5 and the other a 4 can be chalked up to the fact that they are on different scales. $\endgroup$– asdfCommented Nov 7, 2013 at 17:13
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1$\begingroup$ Your comment is mystifying because it assumes we know what your data are about, but you haven't stated that. Thus your references to "letters" and your use of "has" are incomprehensible. Could you edit this question to provide enough information to understand what you're trying to do? $\endgroup$– whuber ♦Commented Nov 7, 2013 at 17:20
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Assuming you have enough data points, I don't see why you couldn't just normalize everything into units of standard deviations. For each group, calculate the group's average value, and the group's standard deviation. Then for each data point in each group, subtract the corresponding group average, and then divide that result by the group's standard deviation.
For example, let's say that your first group (with the scale from -5 to 5) has a mean of 1.7, and a standard deviation of 2.3. For each observation in the group, subtract 1.7 from the observation, and then divide the result by 2.3. The result is the number of standard deviations above (if the result is positive) or below (if the result is negative) the observation is from the mean of the group.
All of your observations from each of the three groups will now be on a common scale, whose mean is zero, standard deviation is one, and the units of this new scale is standard deviations.
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$\begingroup$ This is probably what I would do. It may run into problems if the means are close to either bounds and it can be more difficult to interpret. @asdf needs to consider why these should be on the same scale (do they measure the same thing)? $\endgroup$ Commented Jan 6, 2014 at 16:31