Finding heterogeneity in simple data set (which day is the most different?)

valkener

New Member
I have a data set with an amount of tests that were done by a group of people for each day over two weeks (no weekends). Basically, I need to know which day differs the most from others. Here is the data set:

M T W TR F
48 43 42 40 50
47 49 42 46 51
38 44 47 53 52
41 46 47 40 44
49 47 55 45 49
39 44 36 54 57
42 46 51 49 60
41 37 49 53 54
34 52 49 56 48
45 43 43 57 58
39 51 42 48 45
43 37 48 45 45
43 35 46 39 46
40 34 40 36 40
36 40 34 37 41
39 36 43 40 38
42 50 34 40 48
36 30 36 35 46
37 51 38 33 44
44 48 40 42 46
43 44 45 44 48
41 41 45 39 55
43 40 47 40 54
45 43 48 40 54
40 41 46 43 51
43 42 44 43 43

What I have done is a pairwise test comparing each day to the others. For examples for Mondays vs. Tuesdays, for the first value I calculated 48 - 43, for the second value I calculated 47 - 49 and so on. Then I took the average of all of those values, which resulted in this:

Mon vs Tue -2.8
Mon vs Wed -3.2
Mon vs Thurs -3.5
Mon vs Fri -8.1
Tues Vs Mon 2.8
Tue Vs Wed -0.4
Tue Vs Thur -0.6
Tue Vs Fri -5.3
Wed Vs Mon 3.2
Wed Vs Tue 0.4
Wed Vs Thur -0.2
Wed Vs Fri -4.9
Thur Vs Mon 3.5
Thurs Vs Tue 0.6
Thur Vs Wed 0.2
Thur Vs Fri -4.6
Fri Vs Mon 8.1
Fri Vs Tue 5.3
Fri Vs Wed 4.9
Fri Vs Thurs 4.6

I created a graph showing the results:

From the graph, it looks like Fridays is an 'off day' here. But my analysis does not account for variance or standard deviation. I am not very confident in finding the day with the most heterogeneity.

I have created a box plot of the distributions, however, I am not sure what conclusions should be drawn in regards to which days are the most different?

The objective was to find out which day(s) are the most different. My initial reaction is that Fridays and Mondays seem the most different. When looking at just the shape of the boxes, however, it seems like Mondays and Tuesdays are smaller (square) compared to W-F. So I am not sure how I can best state which distribution(s) seem(s) the most different. The total mean is 49.

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