Early is the only way to avoid big errors!
The most costly types of errors (and we will save you the
effort of reading the sadistics from the statistics books
although we have included it below in case you are so motivated)
indicate that Type 1 and Type 2 errors are the most costly.
Type 1 and Type 2 errors relate to accepting the wrong hypothesis.
Something was missed or misunderstood. A miss or misunderstanding
could be a missed requirement, a missed design constraint,
a missed opportunity to reuse components or modules that already
exist, and other missed design and development parameters
or it could be accepting the wrong requirement, the wrong
design constraint, or reusing components or modules that should
not be reused. Missing or misunderstanding the critical product
parameters early into definition and design generally results
in the most expensive errors, and often in the failure of
the product to be a commercial success.
The below excerpt is taken from "Fundamental Statistics
for Business and Economics," written by Thomas R. Dyckman
and L. Joseph Thomas, Prentice Hall, Englewood Cliffs, New
Jersey, 1977, Chapter 12, Pages 370-371.
12-2 Selecting the Null Hypothesis
The choice of a null hypothesis is based on the relative
seriousness of the different errors that we can make. Errors
mean incorrect decisions. There are two kinds of incorrect
decisions that we can make in hypothesis testing. We can incorrectly
choose H1. That is, we can accept H1
when H0 is true. Alternatively, we can accept
H0 when H1 is true. Some books
refer to this latter error as "not accepting H1
when it is true," arguing that although the data are
not what we would expect under H0, they are
not sufficiently contradictory to allow us to reject H0.
Although it is true that the data often do not strongly support
H0, this is merely a semantic difference; we will use "accept
H0" as the phrase of choice. The important
question in both situations is what real decisions are to
be made based on the data. Figure 12-1 summarizes the correct
and incorrect decisions that can be made.
Figure 12-1 Decisions in Hypothesis
Testing
The two correct decisions are accepting H0
when it is true and accepting H1 when it is
true. The two incorrect decisions are accepting H1
when H0 is the true hypothesis, and accepting
H0 when H1 is the true hypotheis.
These errors are called "incorrect decision of the first
kind" and "incorrect decision of the second kind,"
respectively. Since these phrases are rather lengthy, the
shorter phrase Type I error and Type II error are typically
used.
A Type I error in hypothesis testing is the error
of accepting H1 when H0 is
true (incorrectly rejecting H0).
A Type II error in hypothesis testing is the error
of accepting H0 when H1 is
true (incorrectly accepting H0).
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