政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/60437

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/60437

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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/60437

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题名:	以無母數方法來檢測變異 A nonparametric test for detecting increasing variability
作者:	鄭雅文 Cheng, Ya Wen
贡献者:	黃子銘 Huang, Tzee Ming 鄭雅文 Cheng, Ya Wen
关键词:	無母數檢定變異 nonparametric test variability
日期:	2010
上传时间:	2013-09-05 15:11:55 (UTC+8)
摘要:	當我們探討的是兩組樣本的變異是否有所差異時，常見的方法有以ANOVA 為基礎的檢定與秩檢定，傳統的秩檢定需要假設兩母體具有相同的中位數或知道其差異。本研究採用Moses (1963) 提出的rank-like 檢定方法，此方法在處理兩組樣本的變異問題時，優點是不需要估計任何中心參數，也不需要假設母體中心參數相同，在資料偏態的情況下也表現得很穩健，我們試圖在樣本數極小的情況下對此方法作修正，將此檢定方法與以ANOVA 為基礎的檢定和秩檢定進行模擬比較，以能夠良好的控制型一誤差與檢定力作為評斷標準。由模擬的結果可得知，rank-like 檢定方法與修正後的方法在不同的分配下皆表現的穩健而修正後的方法特別適用於小樣本的情形。 We consider the problem of detecting variability change in the two-sample case.Several classical variability tests are investigated, including the ANOVA based tests and the rank tests. Traditional two-sample rank tests assume that the location parameters for both samples are identical or of known difference. In this thesis, a modified version of the distribution-free rank-like test proposed by Moses (1963) is proposed. Moses’s test has several advantages. It does not require location parameter estimation, is applicable without assuming that location parameter are identical, and is robust for skewed data. However, Moses’s test has no power when each of the two samples has size 5 or less. The modified version of Moses’s test proposed in this thesis has some power when the sample sizes are small. Comparative simulation results are presented. According to these results, both Moses’s test and the proposed test are robust under all conditions, and the proposed test works better when the sample sizes are small.
參考文獻:	[1] 洪志真. 監控製程變異之SPC 方法(II). 2003. [2] M.S. Bartlett. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 160(901):268, 1937. [3] R.C. Blair and G.L. Thompson. A distribution-free rank-like test for scale with unequal population locations. Communications in Statistics: Simulation and Computation, 21:353–371, 1992. [4] G.E.P. Box. Non-normality and tests on variances. Biometrika, 40(3/4):318– 335, 1953. [5] M.B. Brown and A.B. Forsythe. Robust tests for the equality of variances. Journal of the American Statistical Association, 69:364–367, 1974. [6] Y.L. Chen. A Test for Two-Sample Problem Based on Sample Spacings. Tamsui Oxford Journal of Mathematical Sciences, 20(2):267–278, 2004. [7] H.B. Mann and D.R. Whitney. On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1):50–60, 1947. [8] L.E. Moses. Rank tests of dispersion. The Annals of Mathematical Statistics, 34:973–983, 1963. [9] R.G. O’Brien. A general ANOVA method for robust tests of additive models for variances. Journal of the American Statistical Association, 74:877–880, 1979. [10] S.F. Olejnik and J. Algina. Type I error rates and power estimates of selected parametric and nonparametric tests of scale. Journal of Educational Statistics, 12:45–61, 1987. [11] P.H. Ramsey. Testing variances in psychological and educational research. Journal of Educational Statistics, 19:23–42, 1994. [12] P.H. Ramsey and P.P. Ramsey. Updated version of the critical values of the standardized fourth moment. Journal of statistical computation and simulation, 44(3):231–241, 1993. [13] P.H. Ramsey and P.P. Ramsey. Testing variability in the two-sample case. Communications in Statistics: Simulation and Computation, 36(2):233–248, 2007. [14] L.H. Shoemaker. Tests for differences in dispersion based on quantiles. The American Statistician, 49(2):179–182, 1995. [15] S. Siegel and J.W. Tukey. A nonparametric sum of ranks procedure for relative spread in unpaired samples. Journal of the American Statistical Association, pages 429–445, 1960. [16] P. Sprent and N. C. Smeeton. Applied nonparametric statistical methods. Chapman & Hall Ltd, fourth edition, 2007.
描述:	碩士國立政治大學統計研究所 98354001 99
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0098354001
数据类型:	thesis
显示于类别:	[統計學系] 學位論文

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