eldo_user

Monte Carlo Analysis
Additional Uncertainty Analyses (the .mcm File)
quantifies this uncertainty in the sample estimate by computing lower and upper values of an
interval which will contain the population parameter (with a given level of confidence.)
Hypothesis Tests
Hypothesis tests also address the uncertainty of the sample estimate. However, instead of
providing an interval, a hypothesis test attempts to refute a specific claim about a population
parameter based on the sample data.
To reject a hypothesis is to conclude that it is false. However, to accept a hypothesis does not
mean that it is true, only that we do not have evidence to believe otherwise. Thus hypothesis
tests are usually stated in terms of both a condition that is doubted (null hypothesis) and a
condition that is believed (alternative hypothesis).
A common format for a hypothesis test is:
• H0 — A statement of the null hypothesis, for example, a population is normal.
• Ha — A statement of the alternative hypothesis, for example, a population is not
normal.
• Test Statistic — The test statistic is based on the specific hypothesis test.
• Significance Level — The significance level, alpha, defines the sensitivity of the test. A
value of α = 0.05 means that we inadvertently reject the null hypothesis 5% of the time
when it is in fact true. This is also called the type I error. The choice of α is somewhat
arbitrary. In practice values of 0.1, 0.05, and 0.01 are commonly used.
Note
There is an important distinction between statistical significance and practical significance.
Statistical significance simply means that we reject the null hypothesis. The ability of the
test to detect differences that lead to rejection of the null hypothesis depends on the sample size.
For example, for a particularly large sample, the test may reject the null hypothesis that a output
measure is normal. However, in practice the non-normality may be relatively small and has no
real engineering significance. Moreover, if the sample size is small, a difference that is large in
engineering terms may not lead to rejection of the null hypothesis. The designer should not trust
blindly the results of a test, but should combine engineering judgment with statistical analysis
(this is why graphical analysis is important).
Robust Measures of Location
A basic task is to estimate a location or central value that best describes the data. There are
various alternatives to the mean for measuring location. These alternatives were developed to
address non-normal data since the mean is an optimal estimator if the data are normal. The
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Eldo® User's Manual, 15.3