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I'm an environmental scientist looking into dynamics of bacteria growth in river bed sediments. I collected lots of data, and used regression for most of the comparisons, but one (the most important) is giving me fits: I'm trying to figure out if bacteria have a habitat preference as it relates to sediment particle size (e.g., do bacteria like to live on fine clay particles, or do they prefer sand or gravel?)

Sediment samples were collected in 1000g glass "peanut butter" jars. Among other tests, the sediment was sampled for fecal bacteria and then run for grain size analysis. Here are the data types:

  • Bacteria counts - reported as the number of colony-forming units per 100g of sediment (cfu/100g)
  • Sediment grain size partition - grain size reported as a percentage of the whole sample, with 5 partitions (e.g., 10% gravel, 30% coarse sand, 25% med sand, 25% fine sand, 10% clay = 100% of sample)

What I really want to know is if bacteria counts can be explained by the prevalence of a certain grain size, or perhaps some "MiracleGro"-esque mix of the right proportions of all or some of the grain size classes. The latter of those two cases made simple regression messy, and probably isn't a valid test of the data. ANOVA may work, considering that "grain size partition" could be considered quasi-categorical. I just don't know if ANOVA is relevant, again considering that sediment grain size is several fractions of a whole that really have to be considered together.

Signed up for reddit just to ask this question, so that alone should describe my frustration/desperation. What statistical test is best suited for the situation?

i_brake_for_ducks
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    Welcome to Cross Validated! Can you explain the relevance of growth mixture models? (Or remove the tag if it was added in error?) – Scortchi - Reinstate Monica Dec 31 '18 at 18:34
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    You don't want a test, because you have no definite hypothesis to assess: you are *exploring.* This calls for graphical display of relationships among bacterial counts and the potential explanatory variables. It's likely you will need to [re-express the grain size fractions,](https://stats.stackexchange.com/questions/259208) because basic science suggests many possible meaningful properties including surface area and mass. This will require some creativity and as much information as possible. Let's hope you have a lot of jars! – whuber Dec 31 '18 at 18:35
  • As the tag "growth-mixture-model" appears to have two subscribers and also a less-than monthly posting rate - and some possible relevance here - I suggest keeping it for now. – James Phillips Dec 31 '18 at 19:11
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    @whuber's comment is a good start. After that, you might explore using a decision tree, like rpart or C5 in R. This might provide some hints about the important relationships. Start with a small tree, almost a stump. Also, since you're going to be doing exploratory analysis for a while, you should probably keep some portion of the data separated as a holdout sample. – zbicyclist Jan 01 '19 at 18:24
  • In response to comments regarding a definite hypothesis: H0: Sediment composition has no effect on bacteria growth in creek beds within the study area. H1: Bacteria growth is affected when one or more grain size partitions is dominant in creek beds within the study area. H2: Bacteria growth is positively influenced when a specific mixture of sediment particle sizes is present in creek beds within the study area. Hope this helps to clarify. – i_brake_for_ducks Jan 02 '19 at 05:03
  • @i_brake_for_ducks Unfortunately, those are not precise enough hypotheses to test. – mkt Jan 16 '19 at 10:53

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You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory variables. It's likely you will need to re-express the grain size fractions, because basic science suggests many possible meaningful properties including surface area and mass. This will require some creativity and as much information as possible. Let's hope you have a lot of jars!

mkt
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  • I've copied this comment by @whuber as a community wiki answer because the comment is, more or less, an answer to this question. We have a dramatic gap between answers and questions. At least part of the problem is that some questions are answered in comments: if comments which answered the question were answers instead, we would have fewer unanswered questions. – mkt Jan 16 '19 at 10:54