Here are simulated data that may be sufficiently similar to yours to
illustrate my Comments. Likert scores are simulated in R, using various
vectors of preference for the four modes of transportation. If you use
the same seed I used, you will get the same hypothetical data. [R converts
these vectors to probabilities before use in sample
.]
set.seed(2020)
plane = sample(1:6, 272, rep=T, p = c(1,2,2,3,3,3))
auto = sample(1:6, 68, rep=T, p = c(1,2,3,3,2,1))
coach = sample(1:6, 9, rep=T, p = c(1,2,3,3,2,1))
train = sample(1:6, 140, rep=T, p = c(1,2,3,2,2,1))
all = c(plane,auto,coach,train)
gp = rep(1:4, c(272,68,9,140))
In the boxplot below, widths of boxes indicate varying sample sizes, and notches
in the sides of the boxes are approximate nonparametric confidence intervals for
group medians (calibrated so that two nonoverlapping intervals suggest a significant
difference in location). [The sample size for Coach
is too small for a meaningful
CI.]
boxplot(all ~ gp, varwidth=T, col="skyblue2", notch=T,
names=c("Plane","Auto","Coach","Train"))

A Kruskal-Wallis test finds significant differences among the centers of the populations at the 5% level.
kruskal.test(all ~ gp)
Kruskal-Wallis rank sum test
data: all by gp
Kruskal-Wallis chi-squared = 8.6787, df = 3, p-value = 0.03388
However, a nonparametric Mann-Whitney-Wilcoxon (rank sum test) between
Plane
and Train
give P-value about $0.012,$ but one version of
the ad hoc Bonferroni P-value is about $0.07$ (not significant at 5%).
wilcox.test(plane, train)
Wilcoxon rank sum test with continuity correction
data: plane and train
W = 21863, p-value = 0.01212
alternative hypothesis: true location shift is not equal to 0
Moreover, MWW comparisons of Coach
with other groups shows no significant
difference (even without a Bonferroni adjustment), on account of the small
sample size for Coach
.
wilcox.test(plane, coach)
Wilcoxon rank sum test with continuity correction
data: plane and coach
W = 1318, p-value = 0.6913
alternative hypothesis: true location shift is not equal to 0
Note: In these circumstances, my personal opinion is that it it's OK
to declare a significant difference between Plane
and Train
because
the K-W test finds 'difference(s)', of which at least this difference must be one.
But I would not feel comfortable finding differences involving Auto
and Coach
without Bonferroni (or some other) protection against 'false discovery'.