What is the drawback of using a non-parametric test when parametric alternative could have been used? I want to analyze the difference between two paired samples. My initial plan was to compare them using the Wilcoxon test because I didn't want to bother checking whether the data is properly distributed for (e.g) paired t-test, and selecting a non-parametric test sounds like a safer mode of action. What is the drawback of my laziness? What am I risking?
 A: The first difficulty with your question is the implication that it is
always appropriate to use the nonparametric test without checking anything, while it takes considerable effort to discover whether it is OK to use a t test. It is true that
a nonparametric test does not require normal data, but nonparametric
tests have their own requirements. For example, a Wilcoxon signed
rank test works best when data are symmetrical, and does not work well
if there are ties--especially in small samples.
Whether you use a Wilcoxon signed rank test or a t test, a paired test is essentially a one sample test on differences, so it is easy to compare
the power of the two tests in case data are normal. It is a good idea to look at a stripchart, boxplot, and normal probability plot of the data before deciding which test to use.
The issue of power has been discussed briefly in comments. If data
are normal and not rounded to give ties, both tests may OK, but the t test will have the better power.
Suppose you have a sample of size $n = 12$ pairs with differences
distributed $\mathsf{Norm}(\mu=2,\sigma= 2)$ then what is the probability I will detect that the mean is not $0,$ using a t test with significance level $\alpha = 0.05 = 5\%?$ The answer by simulation is about $0.88 = 88\%.$
set.seed(422)
pv = replicate(10^5, t.test(rnorm(12,2,2))$p.value)
mean(pv <= .05)
[1] 0.88211

If the normal data are rounded to integers, then the t test gives almost
the same power, about $87.5\%.$
set.seed(422)
pv = replicate(10^5, t.test(round(rnorm(12,2,2)))$p.value)
mean(pv <= .05)
[1] 0.8745

If I use a Wilcoxon signed-rank test on the same data, what is the probability I will detect that the data are not centered at $0?$
With the nonparametric Wilcoxon test the power is only about $0.78 = 78\%.$
set.seed(422)
pv = replicate(10^5, wilcox.test(rnorm(10,2,2))$p.value)
mean(pv <= .05)
[1] 0.78466

In this case, if the data are rounded to integers, than there will be
warnings about the ties induced by rounding, P-values may not be accurate
and the power will be below $75\%.$
set.seed(422)
pv = replicate(10^5, wilcox.test(round(rnorm(10,2,2)))$p.value)
mean(pv <= .05)
[1] 0.74398

On average, there are more than four ties out of 12 differences distributed
$\mathsf{Norm}(2,2).$
set.seed(422)
nr.tie = replicate(10^5, 10-lengh(unique(round(rnorm(10,2,2)))) )
mean(nr.tie)
[1] 4.23821

