臺灣博碩士論文加值系統

分層隨機抽樣法在抽樣調查實務應用上很普遍，但對該調查資料母體平均數做進一步相關之估計或檢定，則甚少見到較嚴謹的作法。究其原因，分層抽樣母體平均數可視為單變量變異數分析線性比較（linear contrast）之特例，雖可採用正確 t（exact t）檢定法 （以texact 表之），惟該法須滿足各層變異數一致的要求，此一條件十分嚴苛，導致實務應用相當受限。Satterthwaite 雖已提出一近似 t （approximate t）檢定法 （以tappr 表之），但公式較繁複，故實證上較少採用。實務上，或有為求操作便利，勉強採用簡單隨機抽樣所對應的 t 檢定法為之，惟此係錯誤之作法。
為使分層抽樣的統計推論更為簡化，更利於應用，本研究透過模擬研究，探討在分層隨機抽樣架構下，是否可放寬各層變異數一致之限制，以及放寬此一限制後仍可採用 texact 的條件。所採方法係以蒙地卡羅模擬法，就各種不同的分層數、各層所占母體比例、樣本數以及層內變異數之設計組合，每一組合均進行 1000 次之模擬後，再計算並比較 texact 與 tappr 之模擬檢定力大小。模擬結果顯示放寬上述限制條件確屬可行；亦即以 texact 檢定法進行統計推論時，各分層之層內變異數均相等的假設並非必要。經歸納研究結果，texact 與 tappr 二者適用之條件如下：(1) 在分層抽樣設計下，當各層所占母體比例相等時，可直接用 texact 進行推論。(2) 當樣本數大於50時，可直接使用 texact 進行推論。(3) 樣本數小於50，則使用 tappr 進行推論。
欲以 texact 進行統計推論，必須先滿足各分層均符合常態性且所占母體比例已知之條件。在實證方面，本研究分別以2001年 5 月香港來台旅客及2001年第 1、2季來台觀光旅客消費調查之樣本資料進行實例分析。本研究所提出之 texact 檢定建議，可適用於任何期間、任何型態的觀光、休閒消費支出之統計推論。此一成果，亦可再擴大其應用層面，提供旅遊者、觀光政策的主管當局以及旅遊產業經營者的參考資訊，協助制定有效之經營管理策略。

It is of interest to make inference about the mean for a population consisting of different strata. Assuming that prior probabilities of strata and normality of the measure are given, traditional methods require that the equality of within-stratum variances be first examined. If the variances are equal, then use the exact t statistic; otherwise use the approximate t statistic. In this study, we have investigated the necessity of the equal-variance assumption for the exact t statistic by comparing the power of the two t tests. Based on extensive Monte Carlo simulation, it has been found that the equal-variance assumption can be ignored if prior probabilities are equal. In addition, the sample size of 50 is large enough to make the exact t test effective for the problem of inference about the population mean, regardless of the equality of within-stratum variances. A simple procedure has been recommended to facilitate statistical inference. The procedure, illustrated with Taiwan’s inbound tourism expenditure data, is particularly useful for the studies where stratified random sampling is conducted and inference for the mean daily expenditure is desirable. The procedure applies for any type of tourism expenditure during any time period. The resulting information is useful for tourism policy makers, the tourism industry, and tourists.

中文摘要………………………………………………………………i
英文摘要………………………………………………………………iii
誌謝……………………………………………………………………iv
目錄……………………………………………………………………v
表目錄…………………………………………………………………vii
圖目錄…………………………………………………………………ix

第一章　緒論…………………………………………………………1
1.1 研究動機…………………………………………………………1
1.2 研究目的…………………………………………………………4
第二章　文獻回顧與探討……………………………………………5
2.1 兩母體平均數相等之檢定………………………………………5
2.2 分層抽樣架構下母體平均數之推論……………………………8
第三章　研究方法與步驟……………………………………………13
3.1 蒙地卡羅模擬設計………………………………………………13
3.2 模擬步驟…………………………………………………………16
第四章　結果與討論…………………………………………………22
4.1 名目水準�唌�0.05 模擬結果比較…………………………… 22
4.1.1 模擬顯著水準比較 ………………………………………… 22
4.1.2 模擬檢定力比較 …………………………………………… 23
4.2 名目水準�唌�0.01 模擬結果比較…………………………… 33
4.2.1 模擬顯著水準比較 ………………………………………… 33
4.2.2 模擬檢定力比較 …………………………………………… 34
4.3 彙整與結論………………………………………………………35
第五章　實例分析－以來台觀光客平均每人每日消費金額為例…75
5.1實例背景說明…………………………………………………… 75
5.2實例分析………………………………………………………… 77
5.2.1 實例1：依旅遊目的分層…………………………………… 78
5.2.2 實例2：依居住地分層……………………………………… 80
5.3小結……………………………………………………………… 84
第六章　結論與建議…………………………………………………86
6.1結論……………………………………………………………… 86
6.2建議……………………………………………………………… 87
6.2.1 管理上的建議 ……………………………………………… 87
6.2.2 後續研究建議 ……………………………………………… 88

參考文獻………………………………………………………………89
附錄：SAS 程式………………………………………………………92

參考文獻
Aguilo Perez, E., & Juaneda, S.C. (2000), Tourist Expenditure for Mass Tourism Markets, Annals of Tourism Research 27: 624-637.
Andrew, B.P. (1997), Tourist and the Economic Development of Cornwall, Annals of Tourism Research 24: 721-735.
Boneau, C.A. (1960), The Effects of Violations of Assumptions Underlying the t-Test, Psychological Bulletin 57, 49-64.
China National Tourism Administration (2006), http://www.cnta.com/32-lydy/2j/ 2001y.asp
Cochran, W.G. (1947), Some Consequences When the Assumptions for Analysis of Variance are not Satisfied, Biometrics 3, 22-38.
Cochran, W.G. (1951), Testing a Linear Relationship Among Variances, Biometrics 7, 17-32.
Cochran, W.G. (1977), Sampling Techniques (3rd ed.), New York: John Wiley & Sons.
Douglas, A., & Harpman, D. (1995), Estimating Recreation Employment Effects with IMPLAN for the Glen Canyon Dam Region, Journal of Environmental Management 44: 233-247.
Eadington, W.R., & Redman, M. (1991), Economics and tourism, Annals of Tourism Research 18, 41-56.
English, D.B.K. (2000), A simple procedure for generating confidence intervals in tourist spending profiles and resulting economic impacts, Journal of Regional Analysis & Policy 30, 59-74.
Gurland, J. & McCullough, R.S. (1973), Testing Equality of Means After a Preliminary Test of Equality of Variances, Biometrika 49, 3 and 4, 403-417.
Ingram, J.A., & Monks, J.G. (1989), Statistics for Business and Economics, San Diego: Harcourt, Brace & Jovanovich.
Johnson, N. & Kotz, S. (1970), Continuous Univariate Distributions (Vol. 2), New York: John Wiley & Sons.
Johnson, R. & Moore, E. (1993), Tourism Impact Estimation, Annals of Tourism Research 20: 279-288.
Lee, C.K., Var, T., & Blaine, T.W. (1996), Determinants of inbound tourist expenditures, Annals of Tourism Research 23: 527-542.
Markowski, C.A., & Markowski, E.P. (1990), Conditions for the effectiveness of a preliminary test of variance, The American Statistician 44, 322-326.
McCullough, R.S., Gurland, J., &Rosenberg, L (1960), Small Sample Behavior of Certain Tests of the Hypothesis of Equal Means under Variance Heterogeneity, Biometrika 47, 3 and 4, 345-353.
Moser, B.K., Stevens, G.R., & Watts, C.L. (1989), The two-sample t test versus Satterthwaite’s approximate F test, Communications in Statistics �{ Theory and Methods 18, 3963-3975.
Moser, B.K., & Stevens, G.R. (1992), Homogeneity of variance in the two-sample means test. The American Statistician 46(1): 19-21.
Newbold, P. (1988), Statistics for Business and Economics, Englewood Cliffs, NJ: Prentice-Hall.
Satterthwaite, F.E. (1946), An Approximate Distribution of Estimates of Variance Components, Biometrika Bulletin 2, 110-114.
Scheaffer, R.L., Mendenhall, W., & Ott, L. (1990), Elementary survey sampling (4th ed.), Boston: PWS-KENT.
Shapiro, S., & Wilk, M. (1965), An analysis of variance test for normality (complete samples), Biometrika 52, 591-611.
Snedecor, G.W., & Cochran, W.G. (1980), Statistics Methods (7th ed.), Ames, IA: Iowa State University Press.
Welch, B.L. (1937), The significance of the Difference Between Two Means When the Population Variances are Unequal, Biometrika 29, 350-362.
Taiwan Tourism Bureau (2002), 2001 Annual report on tourism. Taipei: Tourism Bureau. (http://202.39.225.136/ auser/B/Annual_2002)
Weaver, D., & Oppermann, M. (2000), Tourism management, New York: John Wiley & Sons.
交通部觀光局 (2002)，觀光政策白皮書，台北：交通部觀光局編印。
交通部觀光局 (2002)，九十年觀光年報，台北：交通部觀光局編印。
交通部觀光局 (2002)，九十年度來華旅客消費及動向調查報告，台北：交通部觀光局編印。