Which statistical test do I use? I am running a study but am unsure which analysis to run. My study involves changing attitudes where participants will be given a questionnaire (on a scale of 1= strongly disagree, 5= strongly agree, etc.), then put in one of 4 conditions (each person in 1 condition only) then given the questionnaire again to see if attitudes are more likely to be changed by a certain condition. Which test is appropriate for this? Please help!
 A: One possibility is to find After$-$Before differences d1, ..., d4 for the four
groups. Then do a Kruskal-Wallis nonparamatric test do see whether locations of
the differences are greater in some groups than in others.
For example, suppose counts of differences in Likert scores for the four groups (100 in each group) are as below. [Computations use R.]
table(d1)
d1
-2 -1  0  1  2 
 8 20 48 15  9 
table(d2)
d2
-2 -1  0  1  2 
14 15 15 24 32 
table(d3)
d3
-2 -1  0  1  2 
 8 11 22 29 30 
table(d4)
d4
-2 -1  0  1  2 
 4 10  2 41 43

Then a Kruskal-Wallis test gives a highly significant result, with a P-value very nearly $0.$
d = c(d1,d2,d3,d4); g=rep(1:4, each=100)
kruskal.test(d~g)

        Kruskal-Wallis rank sum test

data:  d by g
Kruskal-Wallis chi-squared = 47.327, df = 3, p-value = 2.961e-10

Then, in order to see the pattern of differences among the groups, you
could do two-sample Wilcoxon (rank sum) tests on pairs of groups ad hoc. Using
the Bonferroni method for avoiding false discovery, you might consider
differences as significant if P-values are below 1%.
For example Groups 1 and 2, and Groups 3 and 4, differ significantly, but
Groups 2 and 3 do not.
wilcox.test(d1,d2)$p.val
[1] 0.003413176
wilcox.test(d2,d3)$p.val
[1] 0.5473373
wilcox.test(d3,d4)$p.val
[1] 0.003390662

Notes: (1) Suppose you believe it makes sense to interpret your Likert scores as
interval-numerical (and moreover to assume differences are roughly normal), instead of ordinal categories. Then you might use oneway.test in R (which assumes normal data, but does not assume group variances to be equal),
and, subsequently, use Welch two-sample t tests _ad hoc. [Conclusions about significant
differences for my fake data are about the same.] Both methods work for unequal numbers of subjects in the four groups.
The time to decide on the method of analysis is before you get data. It is
bad practice to do both nonparametric and nonparametric analyses and report
the one with the smaller P-value.
(2) In case you want them, here is the R code by which I simulated group differences
for my example above.
set.seed(810);  n = 100
d1 = sample(-2:2, n, rep=T, p=c(1,2,5,2,1))
d2 = sample(-2:2, n, rep=T, p=1:5)
d3 = sample(-2:2, n, rep=T, p=c(1,1,2,2,2))
d4 = sample(-2:2, n, rep=T, p=c(1,1,1,5,6))

I have programmed some fairly large differences among the groups.
With multiple runs (no set.seed) $n=100$ and $n=50$ subjects
per group almost always lead to rejection of the K-W null hypothesis.
Not quite so frequently with $n = 25.$
