I have one dataset of two variables (x,y). When the data is plotted in a 2D diagram, I see some data points create a good cluster, while the other data points are scattered randomly.
Here is an example:
(These data points were collected through an experiment. The weight is equal among all points. After plotting the data points, I found that some points can create a cluster. Then, I changed the color of these points to green color to show those better.)
Based on the plot, I have two clusters: (1) Green points (2) Red Points. Each data point in both clusters has two variables: X, Y.
My question is that:
How can I conduct a statistical test to (statistically) show that the Green cluster has lower entropy than the red cluster?
H0: No differences
Ha: Green cluster is statistically better (Less Entropy) than the red cluster.
I actually want to show that among all data points (Red + Green), the green data points create a good cluster.