Database Reference
In-Depth Information
difference in location
-3.417658
The
wilcox.test()
function ranks the observations, determines the respective
rank-sums corresponding to each population's sample, and then determines the
probability of such rank-sums of such magnitude being observed assuming that
the population distributions are identical. In this example, the probability is given
by the
p
-value of 0.04903. Thus, the null hypothesis would be rejected at a 0.05
significance level. The reader is cautioned against interpreting that one hypothesis
test is clearly better than another test based solely on the examples given in this
section.
Because the Wilcoxon test does not assume anything about the population
distribution, it is generally considered more robust than the
t
-test. In other words,
there are fewer assumptions to violate. However, when it is reasonable to assume
that the data is normally distributed, Student's or Welch's
t
-test is an appropriate
hypothesis test to consider.
3.3.4 Type I and Type II Errors
A hypothesis test may result in two types of errors, depending on whether the test
accepts or rejects the null hypothesis. These two errors are known as type I and
type II errors.
• A
type I error
is the rejection of the null hypothesis when the null
hypothesis is TRUE. The probability of the type I error is denoted by the
Greek letter .
• A
type II error
is the acceptance of a null hypothesis when the null
hypothesis is
FALSE
. The probability of the type II error is denoted by the
Greek letter .
Table 3.6
lists the four possible states of a hypothesis test, including the two types
of errors.
Table 3.6
Type I and Type II Error
H
0
is true H
0
is false
H
0
is accepted Correct outcome
Type II Error
H
0
is rejected
Type I error
Correct outcome
