Hello, when I plot an histogram with my data, I see that instead of a normal distribution, the measurements form two peaks, instead of one. How is it possible to prove that my sample consists of two different subpopulations, while another sample with different measurements does not?
Thank you for your time
Well, a sample can only have two sub-samples and not poplulation. To statistically prove that, you need to do run various statistics, t-test (basically paired-samples), correlation to see if they covariate and a Stochastic process using a Monte Carlo Simulation to see how each distribution goes running a Bootstrap.
@Busari Yusuf: Thanks for the answer. Actually this is the approach we are trying, Monte Carlo simulation. However we cannot find a proper available algorithm that statistically proves that our sample is better explained as two subpopulations instead of one population or vice versa. In case you are familiar with something relevant I would be grateful if you could let us know!
Ioannis Tsirkas , I believe a simple algorithm can be developed to test if the data represent two subpopulations:
1) You create an index variable for each data point x_i, let's say a binary variable y_i equal to 1 for some data points and 0 for the rest (i = 1,2,..., n data points)
2) You calculate separately the empirical distribution of the data points for y_i = 1 and for y_i = 0: d(x | y_i = 1) and d(x | y_i = 0)
3) You test the equality of distribution between d(x | y_i = 1) and d(x | y_i = 0), i.e. the null H0: d(x | y_i = 1) = d(x | y_i = 0)
In step (3) the null should be rejected if the data comes from two different sub-populations/samples. I would suggest using non-parametric tests as e.g. Mann-Whitney or Kruskal-Wallis in (3).
The definition of (1) should be based on your theoretical information about the phenomenon at hand, i.e. basically you are testing your theory about the existence of two sub-populations. A different data-driven approach is to randomly create (1) and repeat the steps (1) to (3) until the null in (3) is rejected - this is equivalent to seeing (1) to (3) as an optimization problem for the optimal separation between sub-distributions in your data set.
@Rolando Gonzales Thank you very much for your answer amd time, we will try to apply your suggestions!
You can compare your supposed model with the competing hypothesized models using the criteria like goodness of fit, AIC,... . In addition, there are some bimodal distributions in the statistical literature. It is an obligation to have a look at them.
Weighted distribution is a statistical concept near what you are seeking.
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics
- Solid State Physics
- PEAKS