臺灣博碩士論文加值系統

無母數統計方法中，連串檢定 ( runs test ) 是經常被用到的一種
。對於兩個樣本，連串檢定可用於檢定兩組獨立的連續型隨機樣本是否來
自相同的分布，如 Wald - Wolfwitz 連串檢定。而對於一個樣本，當對
立假設為趨勢假設的情況下，連串檢定也可應用於檢定一組樣本是否具有
隨機性。有不少學者對此提出相關的檢定統計量，如 Mann ( 1945 )、
Daniels ( 1950 )、Cox and Stuart ( 1955 ) 及線性秩統計量 (
linear rank statistics )。本篇論文主要目的在修正 David ( 1947 )
的中位數上下連串檢定 ( runs above and below median )，來進一步探
討檢力的變化。 我們提出藉由略去中
位數 M 附近的樣本值來作為修正方法，並推導出在樣本值為隨機的假設
下，修正統計量的機率密度函數。在模擬研究中，我們固定顯著水準，利
用連串與修正式連串檢定統計量在原始假設之下之機率密度函數尋求棄卻
域 ( critical region)，並使用隨機化檢定 (randomized test) 求得較
客觀之檢力。 根據我們的模擬試驗，我們可
以比較連串與修正式連串統計量的檢力。從模擬結果可以明顯看出，修正
後的檢力都較高。從模擬結果看來，只要單邊略去的樣本個數介於總樣本
個數除於10與5之間，似都有不錯的結果。

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.