Modified Runs Test

• Main Authors: Lin, Yeong-chung, 林永忠
• Other Authors: Wei-hou Cheng
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/50890385952214130732

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.