| Summary: | 碩士 === 淡江大學 === 數學學系 === 86 === Runs test can be applied to one-sample and two-sample
problems. In the two-sample, runs tests can be used to test
whether the two samples come from the same distribution, and on
the subject of one-sample problem, it is used to detect
randomness of sample when alternative hypothesis is a trend.
Quite a few authors presented different test statistics, among
which are Mann ( 1945 ), Daniels ( 1950 ), Cox and Stuart ( 1955
), and linear rank statistics. The purpose of the thesis is the
modification of David's ( 1947 ) runs above and below median to
improve power.
In this paper, we propose a modification of the runs statistic
by omitting some sample points around the median. Then, we show
the probability density function of our modified test statistic
under hypothesis of randomness.In the simulation ,we fixed
significance level, and use runs and modified runs test
statistics to find the critical region. During the simulation
process, we also use randomized test to get the power.
And by simulation, we find that the power of our modified test
statistic is better than that of the runs test.
Finally, we suggest the range of omitable number of sample
points to get the better power.
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