New two-sample tests for skewed populations and their connection to theoretical power of Bootstrap-t test
WANG, Haiyan - Personal Name
Various tests are available to compare the means of two populations. Tests
for skewed data, however, are not well studied even though they are often needed in
pharmaceutical study and agricultural economics. In particular, there is no available
result to give power and sample size calculation for a two-sample Bootstrap-t test in
skewed populations. In this paper, we propose easy-to-compute new tests and study
their theoretical properties. The proposed work starts with derivation of a second-order
Edgeworth expansion for the pooled two-sample t-statistic. Then new test rejection
regions are formed based on Cornish–Fisher expansion of quantiles. The new tests
account for first-order and second-order population skewnesses that were ignored in
two-sample t test. We report the theoretical type I error accuracy and power of the
newly proposed tests and the large sample t test. We also provide the detailed conditions
under which the proposed tests give better power than the two-sample large sample
test. Our new tests, TCF 1 and TCF, are asymptotically equivalent to Bootstrap-t test up
to O(N −1 ) and O(N −3/2 ), respectively. Compared with commonly used two-sample
parametric and nonparametric tests, the new tests are computationally efficient, give
for skewed data, however, are not well studied even though they are often needed in
pharmaceutical study and agricultural economics. In particular, there is no available
result to give power and sample size calculation for a two-sample Bootstrap-t test in
skewed populations. In this paper, we propose easy-to-compute new tests and study
their theoretical properties. The proposed work starts with derivation of a second-order
Edgeworth expansion for the pooled two-sample t-statistic. Then new test rejection
regions are formed based on Cornish–Fisher expansion of quantiles. The new tests
account for first-order and second-order population skewnesses that were ignored in
two-sample t test. We report the theoretical type I error accuracy and power of the
newly proposed tests and the large sample t test. We also provide the detailed conditions
under which the proposed tests give better power than the two-sample large sample
test. Our new tests, TCF 1 and TCF, are asymptotically equivalent to Bootstrap-t test up
to O(N −1 ) and O(N −3/2 ), respectively. Compared with commonly used two-sample
parametric and nonparametric tests, the new tests are computationally efficient, give
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Statement of Responsibility
Haiyan Wang 1...[et al]
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