I analyzed the data you provided using R. The figure in attachment displays the interaction of the medians of the counts by Time and Side. The parametric Anova reveals main effect, neither interaction:

Analysis of Variance Table

Df Sum Sq Mean Sq F value

Time 5 1.368 0.2736 0.1601

Side 3 37.442 12.4808 7.3047

Time:Side 15 25.604 1.7069 0.9990

The nonparametric test with the nparLD R package by Brunner yiels a significant main effect of Side:

ex.f2$ANOVA.test

          Statistic       df     p-value

Time      0.2748661 2.840040 0.832967591

Side      6.0784027 1.753738 0.003552651

Time:Side 0.7536513 3.251970 0.529904565

But since this test gives Warning(s):

The covariance matrix is singular. I would not rely too much upon it.

I summed the counts for each Side over the 6 Times. Now the Friedman aligned ranks test is quite significant.

Summed data:

tot_s1 tot_s2 tot_s3 tot_s4

[1,] 24 8 11 15

[2,] 11 12 16 13

[3,] 21 10 8 11

[4,] 14 7 19 14

[5,] 20 11 9 14

[6,] 21 6 12 16

Now the Friedman's Aligned Rank Test for Multiple Comparisons is quite significant:

T = 9.5555, df = 3, p-value = 0.02275

Post hoc:

friedmanAlignedRanksPost(y)

tot_s1 tot_s2 tot_s3 tot_s4

tot_s1 NA 0.0008771597 0.0392407 0.28848746

tot_s2 0.0008771597 NA 0.2056672 0.02346498

tot_s3 0.0392407017 0.2056671796 NA 0.31720971

tot_s4 0.2884874633 0.0234649783 0.3172097 NA

Side1 is different from Side2 and Side3

Side 2 is different from Side4.

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