I am an archaeologist studying bedrock mortars (the holes in boulders and rock outcrops that Native Americans would use to grind foodstuffs) in a large study area. I’m exploring whether the depth of an individual bedrock mortar is an indicator of a specific kind of food that was meant to be ground in it. More specifically, whether a bounded range of depths is correlated with a specific type of food (e.g. mortars between 0.25 – 5.5 cm deep were mostly used to grind acorn). Unfortunately, I did not have the ability to test for the presence of food residues in the mortars, so I only have a single variable- depth- to work with. Instead of performing regressions or similar multivariate tests to correlate specific foods with specific depth ranges, I am looking for patterns in the depth variable that suggest preferred ranges. I assume these ranges will be evident as modes in the distribution curve, and potentially as mixed distributions.
I measured the depth (continuous interval) of 699 bedrock mortars from my study area, and can assume that is essentially the entire population. When I plot the values, the resultant distribution curve is highly non-normal (right skewed, leptokurtic?, a long tail and lots of outliers on the right, p-value of
First, there might be value in plotting kernel density estimates rather than histograms. Second kernel density estimation would seem to lend itself to formal testing more than histograms. A quick search suggests that Silverman produced a mode estimation test - though there is also more recent work on this. The attached link looks like a good place to start. It also mentions more recent approaches.
http://adereth.github.io/blog/2014/10/12/silvermans-mode-detection-method-explained/
Thom's suggestion of kernel density estimate is good (it should be your first 'look'). If you know how to use Quantile-Quantile plots (comparison of empirical distribution vs. named distributions) you can interpret multimodal signatures from them. Also, the estimate of the CDF can highlight multimodality (the eCDF will be constant, or at least less steep, at the region of the valley between two distributions). Last, there are some dedicated hypothesis tests to consider, such as http://www.sciencedirect.com/science/article/pii/0167947394900809.
before doing ambitious computations, you should have a careful look at your data. There are features to be addressed : for instance the strong rounding effect, specially for small values - attached you will find a barplot of the table (R function) displaying the evidence that "round" values as , 0.5, 1, 2, 2.5, 3, 3.5 etc , are heavily over represented.
This does not imply that your questioning is invalid, but you must be aware of the limitations of your data. The depth patterns are in my opinion polluted by this rounding error, an effect which has nothing to do with the grinding itself. You should find out a way to circumvent that.
From a more technical point de vue, a fit of a mixture of normal laws (not a proposal, a mere example) on your data could be highly unstable because of this rounding pattern (increasing risk of obtaining null variances in the computations)
Thanks folks! The KDE has definitely been a good option, and thank you Thom and Stephen for those links, they have been very helpful. The Silverman's mode explanation actually had a link to another paper (Minnotte 1997) that would be very helpful. Alas, as you folks can probably tell, I am a relative layman and am limited largely to tests that are alrady programmed in different software packages (even R is a little rough for me at this point).
Jean, I am all too aware of the rounding bias, in the data. There was little I could do to avoid it (I wasn't the only one collecting the observations), and archaeologists tend to just measure to the whole centimeter. My fix so far has been to bin the data to various ranges and compare the resulting cubic b-spline interpolation lines of the counts, both with each other and now with the KDE curve. I was hoping that something like an adaptive KDE run through enough iterations (correct term?) would give me a more reliable result. At this point, I think measuring to the whole centimeter is accurate enough for my goals.
The KDE curve produced by by my "easier than R" software matches very well with the spline of the data binned at 1 cm, and doesn't change based on binning, but i can't selct bandwidths or anything. Since I'm not really trying to infer anything about hypothetical populations at this point, would it be worth me figuring out how to run a more complex KDE method in R?
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