In the training of machinists, 16 apprentices were tested on four tasks, which require machine skills. The different skills were tested on different days.

A 4×4 Latin square design replicated four times was employed for this study.

The Latin letters represent the tests; the rows, the subjects; while the columns represent the days. Their scores in the tests are presented as follows:  Analyze the responses and check the usual assumptions. Are there any significant differences between the mean performances of apprentices?

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Days Apprentices I II III IV 123456789 5178 A 30 C 49 D 56 B 49 2 C 44 D 57 B 46 A 45 D 55 B 50 A 49 C 62 B 51 A 52 C 61 D 68 B 41 A 42 C 55 D 62 6 D 48 C 53 A 42 B 49 C 46 B 47 D 64 A 47 A 41 D 66 B 55 C 62 9 B 40 A 45 D 60 C 52 10 A 30 B 47 C 50 D 61 11 D 46 C 47 A 36 B 43 12 C 48 D 61 B 50 A 45 13 A 39 B 48 C 41 D 59 14 B 55 C 58 D 52 A 34 15 C 49 D 66 A 44 B 41 16 D 64 A 33 B 59 C 42