Nonparametric tests
are also referred to as **distribution-free** tests. These tests have the
obvious advantage of not requiring the assumption of ** normality** or the
assumption of

Parametric tests are
preferred because, in general, they have more power.

If the two samples
are **not paired**, **Non-paired Mann-Whitney U Test** can be applied.

If the two samples
are **paired**, **paired Wilcoxon Signed Rank Test** can be
applied. In Empower, the paired data
should be organized by two variables (eg x1 x2), each
observation represents one pair. If data for each pair was represented by one variable
in two observation, and a pair ID variables was used
for identifying the pairs, we can use Empower “*Transpose multiple observations to multiple variables*” function to restructure the data.

**Two sides or
one side:**

The *p*-level reported with a *t*-test
represents the probability of error associated with rejecting the hypothesis of
no difference between the two group when, in fact, the hypothesis is true.

Some researchers suggest that if the
difference is in the predicted direction, you can consider only one half (one
"tail") of the probability distribution and thus divide the standard *p*-level
reported with a *t*-test (a "two-tailed" probability) by two.
Others, however, suggest that you should always report the standard, two-tailed
t-test probability.

Below is the **sample
input window**

Below is the **sample
output **of the above:

Nonparametric
two sample U test

Wilcoxon rank
sum test with continuity correction

data: OZONE by MONTH.NEW

W
= 127.5, p-value = 0.0001208

alternative
hypothesis: true location shift is not equal to 0

**Empower also
output following box plot to show the distribution for each group.**