# Which variables have too much variation?

So I have 1000 variables (different lakes), each with 12 observations (each lake was tested once a year for 12 years). Some of the lakes are really small, so we think they have way too much variation. My task is to determine exactly what is too much variation, trying to figure out which lakes we should eliminate. I was thinking about running var.test between each lake to determine what lakes are significantly different from eachother, but I don't know if that will give me the results that I want. In addition to that, I have 1000 lakes, so I can't perform the test THAT many times.

Ideas?

revised description: we're observing the changing of the lakes over a 12 year span. each year, we observed the lakes 3 separate times. then we averaged those three to get one data point each year for each lake. problem is, we have A LOT of lakes, so we feel like including the significantly smaller ones, which freeze, melt, evaporate, etc. much quicker, will effect our study. we used remote sensory to gather the data so it grabbed EVERY lake of every size. what i need to figure out is what lakes should we use in our study, which lakes are large enough to be worth our time. And I'm not sure how to go about that.

• Hi @Lynn, welcome. First, what do you mean by "too much" variance? If you can assume that the measurements were correct, then that's simply the natural variation in those lakes. I would strongly advise against the use of pairwise var.test! Why should the lakes have equal variances is not clear to me and to perform almost a half a million tests is definitely not advisable. – COOLSerdash May 21 '13 at 19:17
• Why are you eliminating lakes? What are you trying to learn about the lakes? What is the problem, exactly, with a lot of variation in the observations? BTW, the usual terminology is to refer to the lakes as "subjects," "records," "cases," or "tuples" (depending on your background). The observations are your "variables." – whuber May 21 '13 at 19:17
• Sounds like you have ONE variable measured 12 times in each of a thousand lakes. A lake is not a variable – Peter Flom May 21 '13 at 19:17
• @Lynn What lakes you want to exclude (if any at all) should be based on a-priori scientific reasons. It is bad practice to exclude data just to get "the results that you want". – COOLSerdash May 21 '13 at 20:06
• @COOLSerdash You're absolutely right. But I think there is a more benign interpretation possible: the professor recognizes that high variability might be a marker for lakes that do not belong in the study in the first place. The crux of the matter, then, is to establish objective criteria to identify what the study population is and then compare the observations against those criteria. – whuber May 21 '13 at 22:39

I like to try to "let the data do the talking" instead of "coming to it and telling it what to say".

I encourage you to perform Exploratory Data Analysis before culling any data.

If this were my data then I would consider making a bubble plot where the mean (or median) lake size is along the x-axis, the variation in lake size is along the y-axis, and the bubbles are colored by kurtosis (or its multiplicative inverse if too much data occlusion occurs). It is particular and possibly goofy sounding but will give a distribution of central tendencies, the relation to distribution of variation tendencies, and the relation of that to variation in variation tendencies.

This will allow your high-performing human brain to look for patterns, clusters, or characteristic phenomena.

You might also make a graph of lake size, variation and kurtosis, and look there too.

EDIT: Before you average them for a year (and thus throw away data) why not put all the data into the analysis. I know it multiplies your sample size by 3x, but I think your sample size isn't too big. If you are under a million samples, you might have enough data, maybe.

I think a 3d scatterplot of mean size by variance of size, by kurtosis of size is going to give clear indication of clustering or divergence of the data. If there is a place to draw a line and cull data, a graph like that would inform it.

questions:

• what format is your data in?
• what software package are you using to process it?
• what graphing and analysis options are available with it?
• +1 Some interesting ideas. An example of a spatial nature (which might therefore have some application here) that takes a few steps in this direction recently appeared at gis.stackexchange.com/questions/52502/…. – whuber May 21 '13 at 22:41
• there is another quite well known example of a data plot for an analysis of star types that showed two quite distinct populations of, I think it was, normal sequence and blue giants, I believe it was shown in stack exchange a month or two ago, but can't trace it at present. – Robert Jones May 22 '13 at 11:20
• the Hertzsprung–Russell diagram on Wikipedia is such an example – Robert Jones May 22 '13 at 11:35
• @Robert Jones, did you mean this: en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram – EngrStudent May 22 '13 at 13:14
• Yes that was what I found in Wikipedia, though the example I was thinking of was much more schematic and of a different form, but either shows the point about different populations. Sorry about the delay in responding, but once questions are older than a day or two on the list, I tend not to find them when browsing. I'm afraid that I am somewhat of a novice still. – Robert Jones May 26 '13 at 10:51