Statistics for Environmental Engineers

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Resample 4



Resample 5







Resample у data

Original/ * data

—I-1-1 1 1 1


0    20    40    60    80    100

Intercept (b0)

FIGURE 50.3 Emerging joint confidence region based the original data plus five new sets generated by resampling, with replacement.

normally distributed data, 6.0% for a rectangular parent distribution, and 5.9% for a skewed parent distribution. The effect of modest serial correlation in the data was much greater than these differences due to nonnormality. A positive autocorrelation of r = 0.4 inflated the percentage of tests found significant from the correct level of 5% to 10.5% for the normal distribution, 12.5% for a rectangular distribution, and 11.4% for a skewed distribution. They also showed that randomization would negate the autocorrelation and give percentages of significant results at the expected level of about 5%. Normality, which often causes concern, turns out to be relatively unimportant while serial correlation, which is too seldom considered, can be ruinous.

The bootstrap method is a special form of simulation that is based on resampling with replacement. It can be used to investigate the properties of any statistic that may have unusual properties or one for which a convenient analytical solution does not exist.

Simulation is familiar to most engineers as a design tool. Use it to explore and discover unknown properties of unfamiliar statistics and to check the performance of statistical methods that might be applied to data with nonideal properties. Sometimes we find that our worries are misplaced or unfounded.

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