本文利用軟體R程式與內建的介面套件Tcl/Tk，製作成檢定母體變異數同質性與平均數相等性的使用者工具(TEM)。使用者無須撰寫任何程式碼，只要利用滑鼠游標點擊，便可完成數據資料的讀取及得到檢定結果的輸出。TEM同時搭配了編輯資料與繪製分群分布圖的簡易功能，使用者可與檢定結果做比較與參考。TEM利用視窗化的介面與自動化的檢定流程，大幅縮減使用者在檢定時所需的時間。TEM包含有三種變異數同質性的檢定法，及六種平均數相等性的檢定法。其中，在一階段與二階段抽樣程序中，提供全距分布與二次項分布的顯著機率值查詢。在二階段抽樣程序檢定法中，亦可查詢全距檢定與變異數分析檢定計算樣本所需的z值。

The TEM, constructed by using the statistical software R and interface package Tcl/Tk, is a user tool for testing the homogeneity of variances and the equality of means. There is no need to write any code, TEM is easy-to-use. It can retrieve the data file from a directory and output testing results by clicking mouse. TEM also provides the utility of editing data and plotting density functions. It significantly saves users time by using window interface and automated testing procedures. TEM includes three methods for testing the homogeneity of variances and six methods for the equality of means. Furthermore, TEM offers p-value for the range test and ANOVA test of the One-stage and Two-stage sampling procedures. It also gives z-value for computing final sample size in the Two-stage sampling procedure.

1 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 檢定方法 . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 變異數同質性檢定 . . . . . . . . . . . . . . . . . . . 3
2.1.1 Bartlett’s test . . . . . . . . . . . . . . . . . 3
2.1.2 Fligner-Killeen test . . . . . . . . . . . . . . 4
2.1.3 Levene’s test . . . . . . . . . . . . . . . . . . 5
2.2 平均數相等性檢定 . . . . . . . . . . . . . . . . . . . 6
2.2.1 單因子變異數分析檢定法(One-way ANOVA)  . . . . . . . 7
2.2.2 改良型F 檢定 . . . . . . . . . . . . . . . . . . . 7
2.2.3 Welch方法. . . . . . . . . . . . . . . . . . . . . 8
2.2.4 James方法. . . . . . . . . . . . . . . . . . . . . 9
2.2.5 一階段抽樣程序檢定(One-stage sampling procedure) . . 9
2.2.6 二階段抽樣程序檢定(Two-stage sampling procedure) . .11
3 多筆獨立且同分布t 的R 分布與Q 分布. . . . . . . . . . . . 14
3.1 全距檢定法的全距R 分布. . . . . . . . . . . . . . . . . 14
3.2 變異數檢定法的二次項式Q 分布. . . . . . . . . . . . . . 16
4 TEM使用者工具 . . . . . . . . . . . . . . . . . . . . . 18
4.1 簡介與安裝. . . . . . . . . . . . . . . . . . . . . . 18
4.2 使用者的資料檔案型態與讀取資料. . . . . . . . . . . . . . 20
4.3 檢定操作流程. . . . . . . . . . . . . . . . . . . . . 24
4.3.1 變異數同質性檢定與平均數相等性檢定. . . . . . . . . . . 26
4.3.2 二階段抽樣程序檢定(Two-stage sampling procedure). . . 31
4.3.3 顯著機率值與二階段程序的z 值. . . . . . . . . . . . . 46
5 結論與討論. . . . . . . . . . . . . . . . . . . . . . . 49
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . 51
附錄(程式碼). . . . . . . . . . . . . . . . . . . . . . . 53

[1] Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 160(901):268–282.
[2] Bishop, T. A. and Dudewicz, E. J. (1978). Exact analysis of variance with unequal variances: Test procedures and tables. Technometrics, 20(4):pp. 419–430.
[3] Bishop, T. A., Dudewicz, E. J., Juritz, J. M., and Stephens, M. A. (1978). Percentage points of a quadratic form in student t variates. Biometrika, 65(2):pp. 435–439.
[4] Brown, M. B. and Forsythe, A. B. (1974a). Robust tests for the equality of variances. Journal of the American Statistical Association, 69(346):pp. 364–367.
[5] Brown, M. B. and Forsythe, A. B. (1974b). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16(1):pp. 129–132.
[6] Chen, S. Y. (2001). One-stage and two-stage statistical inference under heteroscedasticity. Communications in Statistics - Simulation and Computation, 30(4):991–1009.
[7] Chen, S. Y. and Chen, H. J. (1998). Single-stage analysis of variance under heteroscedasticity. Communications in Statistics - Simulation and Computation, 27(3):641–666.
[8] Chen, S. Y. and Chen, H. J. (1999). A range test for the equivalency of means under unequal variances. Technometrics, 41(3):pp. 250–260.
[9] Chen, S. Y. and Chen, H. J. (2000). A range test for the equality of means when variances are unequal. Am. J. Math. Manage. Sci., 20(1&2):145–170.
[10] Conover, W. J., Johnson, M. E., and Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23(4):pp. 351–361.
[11] Hsu, Y. P. (2012). Initial sample size selection for the two-stage sampling procedure. Master’s thesis, Tamkang University.
[12] James, G. S. (1954). Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika, 41(1/2):pp. 19–43.
[13] Olkin, I. (1960). Contributions to probability and statistics : Essays in honor of Harold Hotelling.
[14] Welch, B. L. (1947). The generalization of ‘student’s’ problem when several different population variances are involved. Biometrika, 34(1/2):pp. 28–35.
[15] Wilcox, R. R. (1983). A table of percentage points of the range of independent t variables. Technometrics, 25(2):pp. 201–204.