I have released 10 insects for 4 arm olfactometer and their movement counted at 5min intervals for 30 min. There were 6 replicates for each. When analyzing the data there are various methods and I'm confused what to choose and what is the correct method.
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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