I have collected vertical air pollutant samples at three different heights close to the road.
Meanwhile I observed meteorological data at one particular point i.e. above the building roof during sampling.
Since the air pollutants are collected spatially in height while the met. data is collected at a fixed point.
So here the pollutant data cannot be directly correlated with met. data.
So, I first correlated the pollutant concentration with height and estimated the "r" value.
Since "r" values are both in positive and negative, I normalized them by squaring say "r^2" (correlation to regression).
Now I correlated the "r^2"value with meteorological data.
Is this a meaningful statistical analysis?
Need expert suggestion?
Thanks and regards in advance
Ezhil
I'm glad that you are asking yourself these questions about the meteorological data. Variations in meteorological parameters spatially (both vertically and horizontally) at various scales (e.g. feet, tens of feet, hundreds of feet, miles, etc.) is an area that was historically neglected and still is understudied. Ideally, you would have collected at least a few meteorological parameters at each of your pollutant sampling locations. But often the ideal is not possible or practical.
If I am understanding you correctly, you calculated a correlation coefficient for height and concentration data. When you refer to "values" in the plural, are you saying that you calculated a correlation coefficient for a number of different locations? I'm wondering because at the beginning is sounded like you were dealing with a single location. Do you have data at multiple locations? If not, what is the source of more than a single correlation coefficient?
I don't understand why you want to eliminate the sign from your r values. That sign has meaning that I would think you would want to preserve. You shouldn't be thinking of correlation coefficients as being anything like the residuals in regression analysis, if I am understanding you correctly.
Did you find a strong correlation (or positive or negative) between pollutant concentration and height? Was it consistent from site to site (if you had multiple sites)?
If you do have a data from a significant number of different sites, then it would be meaningful to generate a correlation coefficient between you first set of correlation coefficients and a meteorological parameter. I don't see why you would square your initial correlation coefficients and I can see why you shouldn't.
That said, I think that instead of your second correlation analysis, you should instead be considering regression analysis and include your correlation coefficients as an independent variable to try. Since the correlation coefficients are derived from the pollutant concentrations and heights, be careful in how you interpret any results where you include the correlation coefficients with either of the other two (or both) in your regression analysis.
I will close with the caveat that while correlation coefficients can be useful, it can be tempting to try and do too much with them. My impression, from what you've shared, is that you are falling into that trap.
I look forward to hearing the advice that others post for you.
Dr.Matthew
I am glad and thankful for spending your time in giving me descriptive suggestion towards my question.
Yes off-course, I have measured pollutants vertically in three streets at three heights above ground.
Even, after reading several articles and your suggestions, understood that correlation values has to be used as it is because, they mean a lot between the two compared parameters.
However, still I am lit bit confused whether I can relate the "r" value (irrespective of sign) with a meteorological parameters. Because, most of the research papers similar to my study has reported varying correlation methods and their methods are not identical to each other. So, I don't find even a single reference for my method of correlation.
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