Abstract
Empirical estimates of power and Type I error can be misleading if a statistical test does not perform at the stated rejection level under the null hypothesis. We employed the permutation test to control the empirical type I errors for zero-inflated exponential distributions. The simulation results indicated that the permutation test can be used effectively to control the type I errors near the nominal level even the sample sizes are small based on four statistical tests. Our results attest to the permutation test being a valuable adjunct to the current statistical methods for comparing distributions with underlying zero-inflated data structures.
Highlights
Statistical analysts sometimes encounter data that have an excessive number of zeros and these data often present analytical difficulties because traditional methods rely on assumptions that may be unrealistic and plausible transformations may not be found
These figures clearly demonstrate that both empirical Type I errors and testing powers became reasonably stable after the sample size surpassed 100 permutations
The empirical Type I errors of the four tests with and without permutation tests are summarized in Table 1 for the case of a zero-inflated exponential distribution
Summary
Statistical analysts sometimes encounter data that have an excessive number of zeros and these data often present analytical difficulties because traditional methods rely on assumptions that may be unrealistic and plausible transformations may not be found. Some zero inflated data may be viewed as having a mixed distribution where zeros have a point distribution and the distribution of non-zero observations is positive and continuous. This distribution has not been investigated adequately and statistical methods with favorable Type I and Type II errors for comparing these non-traditional distributions are desired. Monte Carlo simulations were employed to compare several approaches including the LR, Wald, central limit theorem (CLT), modified central limit theorem (MCLT) tests with respect to their empirical Type I errors and testing powers for three zero-inflated continuous distributions [7]. The LR, Wald, and MCLT tests were found to be preferable to the tests based on central limit theory
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