I have several datasets for which each sample is associated with 2 values for 2 totally independent variables. I can represent them graphically with variable 1 along the x axis and variable 2 along the y axis.
Each datasets thus looks like a cluster of points on this 2 scatterplot representation. There is quite some variability within each dataset resulting in some overlap between each cluster. What test should I use to check if the difference between 2 (or more) of these dataset is statistically significant. I can calculate the centroid of each cluster and the variability along both axis and use that I suppose but what test would be the most appropriate?
Maybe I'm blanking out because I am tired but, since I never asked a question on researchgate before, I thought I'd give it a shot.
- If your data is approximately normally distributed and you have reasonably large sample sizes for both clusters, the t-test might be appropriate.
- If your data is not normally distributed or you have concerns about the assumptions of the t-test, the Mann-Whitney U test is a non-parametric alternative.
A t-test is one-dimensional, and you have two-dimensional data. Not my area, but it seems that Syrjala's test for the difference between the spatial distributions of two populations is what you need. According to the documentation for the R package " It is designed to be sensitive to differences in the way the populations are distributed across the study area but insensitive to differences in abundance between the two populations."
Read more here https://search.r-project.org/CRAN/refmans/ecespa/html/syrjala.html
Another possibility would be to use a test to compare the mean x values for each cluster and then the mean y value. If either of the differences is not significant then the difference between the clusters would not be significant. The test to use is covered by Satish's answer.
Greg Williams – separate tests of the x and y axes don't catch the situation where the clusters differ on a dimension that is a function of both, such as
x – 2y = 0
The dimensions need to be considered simultaneously to test for any separation on the xy plane.
I don't understand. I was thinking of the clusters as spots on a plane. If they overlap on x or y then they overlap, if they don't they don't. Your equation, x = 2y would create clusters on a diagonal but if they touched you woulkd still catch it.
Didnt Hotteling develop the t2 test for rather simple multidimensional questions? https://en.wikipedia.org/wiki/Hotelling%27s_T-squared_distribution
Depending on the context, ie what you actually measured and what you are actually testing, a repeated measures ANOVA might be an option, where x and y are your independent variables.