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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 days differ 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: Pairwise Analysis for Heterogeinity

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.

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1 Answer 1

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I think you should run Anova test on this data. I ran the test and I got a p value equal to 0.00008 , less than 0.05 , thus disapproving null hypothesis that means of all days are equal.So according to test result , the means of all days are significantly differently.

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  • $\begingroup$ Which day is the most different? $\endgroup$
    – Carlo
    Sep 16, 2015 at 19:23

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