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Randomized target design
10.4.3 Non-parametric tests
and rerandomization
Because the distribution of natural events is often far from Gaussian and
may not be known well, tests that do not rely on the nature of the probability
distribution are needed to assess significance levels in many experiments
using meteorological data. If it is found, for example, that rainfall in
seeded cases averages 1.2 times as much as in unseeded cases, the significance
level of this result can be assessed by considering a large set of simulated
experiments for which the rainfall amounts are retained but the seeding
decision is reassigned randomly. If there were no real seeding effect,
then the fraction of these simulated experiments producing apparent seeding
increases by factors of 1.2 or more can be used to determine the confidence
limit to be associated with the result. The same approach can be used with
other characteristics of the results. A common statistic used in this way
is the sum of the ranks associated with seeded storms, for which the test
is evaluated using a Wilcoxon test.
"Rerandomization" can be used even when there is no real randomization.
For example, one way to test for the significance of an apparent correlation
(e.g., between lifetime of cumulus clouds and dewpoint depression in the
environmental air) is to rerandomize the values of one of the variables
and recalculate the correlation coefficient with the rerandomized variables,
thus determining the probability that the measured correlation coefficient
would arise by chance. This avoids the assumption of Gaussian distributions
inherent in standard estimates of the errors in correlation coefficients.
This can be a valuable technique when it is suspected that the distributions
are not Gaussian.
A danger still present with rerandomization is that presented by correlated
sequences in the data. If correlated sequences are rerandomized, too great
a significance level may be attached to the result.
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Some dangers in Up: 10.4
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Randomized target design
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