| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.advisor | Huang, Tzee Ming | en_US |
| dc.contributor.author (Authors) | 鄭雅文 | zh_TW |
| dc.contributor.author (Authors) | Cheng, Ya Wen | en_US |
| dc.creator (作者) | 鄭雅文 | zh_TW |
| dc.creator (作者) | Cheng, Ya Wen | en_US |
| dc.date (日期) | 2010 | en_US |
| dc.date.accessioned | 5-Sep-2013 15:11:55 (UTC+8) | - |
| dc.date.available | 5-Sep-2013 15:11:55 (UTC+8) | - |
| dc.date.issued (上傳時間) | 5-Sep-2013 15:11:55 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0098354001 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/60437 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計研究所 | zh_TW |
| dc.description (描述) | 98354001 | zh_TW |
| dc.description (描述) | 99 | zh_TW |
| dc.description.abstract (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。 | zh_TW |
| dc.description.abstract (摘要) | 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. Comparativesimulation results are presented. According to these results, both Moses’s test and the proposed test are robust under all conditions, and the proposed testworks better when the sample sizes are small. | en_US |
| dc.description.tableofcontents | 1 緒論 72 文獻回顧 93 研究方法 12 3.1 Moses rank-like 檢定............................. 13 3.2 Moses rank-like 檢定小樣本的改進.................. 14 3.3 Savage 檢定...................................... 15 3.4 Siegel-Tukey 檢定................................ 16 3.5 Conover Squared Rank 檢定........................ 17 3.6 以ANOVA 為基礎的檢定.............................. 17 3.6.1 Brown-Forsythe 檢定........................ 17 3.6.2 O’Brien 檢定.............................. 18 3.6.3 結合Brown-Forsythe 檢定與O’Brien 檢定...... 194 模擬分析與討論 20 4.1 模擬設定......................................... 20 4.2 模擬結果與分析.................................... 225 結論與建議 37 | zh_TW |
| dc.format.extent | 345946 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0098354001 | en_US |
| dc.subject (關鍵詞) | 無母數檢定 | zh_TW |
| dc.subject (關鍵詞) | 變異 | zh_TW |
| dc.subject (關鍵詞) | nonparametric test | en_US |
| dc.subject (關鍵詞) | variability | en_US |
| dc.title (題名) | 以無母數方法來檢測變異 | zh_TW |
| dc.title (題名) | A nonparametric test for detecting increasing variability | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (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 ofthe 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 scalewith unequal population locations. Communications in Statistics: Simulationand 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 randomvariables is stochastically larger than the other. The Annals of MathematicalStatistics, 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 modelsfor 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 selectedparametric and nonparametric tests of scale. Journal of EducationalStatistics, 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 thestandardized 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. TheAmerican Statistician, 49(2):179–182, 1995.[15] S. Siegel and J.W. Tukey. A nonparametric sum of ranks procedure for relativespread 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. | zh_TW |
