I have a simple question. Can one look for correlations between percentage and average ? For example, percentage of unemployment and average salary. Or shoul I use total numbers instead ? If I look for a relation between percentages and average I get significant correlation, but between totals data is not significant.
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$\begingroup$ Usually, when looking for correlations, it is an attempt to define cause and effect relationships. I can find correlations between the date of the year and my check number, but the fact both increase sequentially is rather expected. There is also a significant correlation between pirates and global warming, but there is (to my knowledge) no cause and effect relationship between the data. $\endgroup$– TavrockMar 6, 2017 at 8:14
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$\begingroup$ @subhashc.davar My variables are percentages of unemployed people in state every month and average salary of employed people in state every month. So I have unemployment data from bureau of statistics USA and average salary is calculated from randomly selected 10K people in that state. $\endgroup$– ExtriaMar 6, 2017 at 9:24
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$\begingroup$ @subhashc.davar Correct $\endgroup$– ExtriaMar 6, 2017 at 9:44
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2 Answers
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The biggest risk of looking at statistics of the aggregates is ecological fallacy (example here). Group-level aggregates do not necessarily are suitable for inferring individual-level characteristics. The most vivid example is the Simpson's paradox, which shows how you can get completely different results when looking at group-level vs individual-level data. If you only have the aggregated data, your results do not necessarily translate to the individuals.
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I'd be really uncomfortable with a correlation between a(n average of) continuous variable and a percentage, because the percentage is bounded by $[0,100]$. So if the percentage is near these boundaries, the relation (i.e. correlation) between the two is bound to be non-linear. A more suitable way of associating one continuous and a categorical variable is, for example, through regression.
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$\begingroup$ Thank you for your answer. I didn't thought that percentages are categorical variable so I used Pearson method to calculate correlation. But I do not understand why percentages are categorical variable ? $\endgroup$– ExtriaMar 6, 2017 at 8:58
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$\begingroup$ Most often a percentage is calculated by grouping in some way (e.g. the proportion of men out of the total sample). I assumed this is what you meant. But I must admit, sometimes a percentage is used to show change from a certain baseline point (e.g. my income has changed by 150%). This second case is slightly different because in this case the percentage is bounded only on the lower side ([$0,∞]$), but still the problem of non-linearity remains, especially if you include '100%' as the neutral (no-change) point. $\endgroup$– IWSMar 6, 2017 at 9:05
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$\begingroup$ Now I understand why my data is categorical, that you for explanation. $\endgroup$– ExtriaMar 6, 2017 at 9:17