# Which statistical test should I use for testing dependent variables across 5 datasets?

5 pupils are given the task of hand drawing a hundred trapezoids with a given perimeter. The vertices are marked A,B,C,D counter-clockwise starting with the longer parallel edge (A and B). The lengths for the 6 pairwise distances between the 4 vertices are recorded. These six distances are dependent variables as the lengths and angles of edges influence each other.

Assumptions: 1) None of the trapezoids drawn are truly identical. 2) The pupils do not get better or worse in the task over time, they draw the shapes with more or less the same error rate, i.e. the hundred states (i, i+1) are independently drawn.

My hypothesis is that all pupils draw trapezoids with essentially the same AB,AC,AD...CD vertex-vertex distance distributions.

The question: How can I rigorously test which vertex-vertex distances are drawn significantly longer or shorter by any two of the pupils? Please advise which statistical test to use.

First, let's assume normal distribution for the measured distance distributions, but I'm also interested how to proceed if the distances are not normally distributed.

• Might I suggest an alternative approach? Rather than seeking a formal test, first explore the data: do they even look like what you are hypothesizing? Simply drawing all the trapezoids in a normalized fashion (with a common center, say, and oriented with their major axes horizontal) on a single plot would likely answer most questions you might be asking, as well as suggest new ones.
– whuber
Commented Sep 3, 2019 at 12:46