# Correction needed for an non-parametric Anova?

I'm trying to analyze the behavioral data of my research experiment and I'm a bit lost... o_O

Briefly, subjects undergo 4 different conditions (of increasing complexity 1<2<3<4).

At the end of each conditions, they perform a little test.

These are the results :

  Subject Cond 1 Cond 2 Cond 3 Cond 4
01     96    100     88     80
02    100    100     92     72
03    100    100     80     72
04    100    100     92     76
05     96    100     80     68
06    100     96     92     76
07    100    100     96     92
08    100     96    100     72
09    100     96     92     84
10    100     88     88     72
11    100     92    100     84
12    100     96     92     76
13    100    100     88     80
14    100     96     88     80
15    100     96     88     76


I want use a statistical test to affirm when the difficulty increases, scores decrease.

I think I should use a non-parametrical ANOVA (Friedman).

But, the results of condition 1 and 2 caps at 95-100.

Do I need to perform any correction before applying the Friedman ANOVA? Someone told me about an ArcSine correction but I don't know if it's valid or not...

• It seems the test at Cond 1 is not providing useful information about differences among subjects. I don't see how a transformation will cure this. Massive ties may interfere with the power of the Friedman test. // Is it useful just to compare Conditions 2 and 3 with each other? Tests for those conditions seem to have useful information. Wilcoxon signed-rank test gives P-val 0.001 with CI $(10,16)$ for shift. // Also Cond 3 has median signif below 100 (P-val 0.002). – BruceET Sep 27 '18 at 17:27