I graphed a variable and it looked kind of bimodal but I'm not sure. Is there a more quantitative method of establishing this? Once again, I'm using Minitab.
To think about ways to infer whether your data is bimodal or unimodal you need to hypothesize on whether there is a good fundamental underlying reason that the thing creating your data is bimodal or not.
If we change your question slightly to say "given a measurement of nitrogen oxide emission, what is the probability the emission came from a petrol or diesel vehicle?". From this we can begin to estimate what the distribution of diesel emission looks like vs distribution of petrol and can do tests to see if these two distributions are statistically different.
Using standard Bayesian Inference and a Mixture Model, you can calculate these distributions and probabilities. Until you clarify your answer further, I will point you to this:
- General Wikipedia reference: http://en.wikipedia.org/wiki/Mixture_model
- python-based (and better theoretical explination) http://scikit-learn.org/stable/modules/mixture.html
If you can separate out the two types sources of diesel emission you can just run a the following tests to see if they are equal:
- Eyeball test (simple sanity check, not rigorous)
- Two-sample Kolmogorov–Smirnov http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
(1) get more data to make sure it doesnt smooth out
(2) look for humps
(3) google "mixture distribution"
(4) Use log normal plot of cumulative weight vs size in phi units.
Unimodal give one straight line plot, bimodal two different straight line plots and the inflection point is the change of modal distributions.
It's not uncommon for mixing of traction and saltation loads or traction and suspension loads mixing as velocity of transport decreases