課程名稱︰心理及教育統計學下 課程性質︰必修 課程教師︰姚開屏 開課學院：理學院 開課系所︰心理系 考試日期（年月日）︰2009/3/27 考試時限（分鐘）：9:10~10:20 10:30~12:20 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Part.I : Close Book Time : 9:10~10~20 AM (Total = 50 points) 1.Compare the logic behind t-test and ANOVA. 【比較t檢定與ANOVA的邏輯】 2.Why not doing multiple t-test for comparing more than 2 group means? 【當比較超過兩個平均數時，為什麼不做多個兩兩平均數相比的t檢定？】 3.What is fixed treatment effect? What is random treatment effect? 【在ANOVA裡，甚麼是因素的固定效果及隨機效果？】 4.Discuss the assumptions of ANOVA and its robustness. 【討論ANOVA的假設及其強韌性】 5.What is the purpose of "magnitude of experimental effect"? (e.g. η^2 ω^2) 【ANOVA裡為何談到"magnitude of experimental effect" (目的)？】 6.What is the definition of "orthogonal contrast"? What is the property of orthogonal contrast in ANOVA? 【如何定義"orthogonal contrast"？在ANOVA，它有何特質？】 7.What's Bonferroni inequality? What's multiplicative inequality? 【甚麼是Bonferroni inequality? 甚麼是multiplicative inequality?】 8.What is the rationale behind Home test？ 【Holm檢定背後的邏輯】 9.Compare Tukey's HSD test and Scheffe test. 【比較Tukey's HSD test 及 Scheffe test】 10.Please list the priori and posteriort comparisons that use different criti- cal values for different comparisons. 【有哪些事前或事後檢定，他們所使用的臨界值隨著不同的比較而不同？】 ┌────────────────────────────────────┐ │BONUS: extra 5 points │ │Proof: For one-way ANOVA, the test statistic of F follows F distribuion │ │ with df=J-1,N-J (J=the number of groups , N=total sample size) │ │【加分題(5分)：證明單變項ANOCA，F檢驗值為自由度為J-1，N-J的F分配】 │ └────────────────────────────────────┘ Part.II : Open Book Time : 10:30~12~20 AM (Total = 50 points) The following data illustrate the ages of car buyers. (n=10 for each group) USA - Ford/Buick/GM/Chrysler European - BMW/Volve/Benz/Volkswagaen Asian - Toyota/Honda/Mazda/Mitsubishi/Nissan Domestic - YuLong/Formosa ┌────┬───────────────┬────────────┐ │USA │40 42 51 47 33 83 35 69 50 60 │ΣX=510 ; ΣX^2 = 28238 │ ├────┼───────────────┼────────────┤ │European│72 42 51 45 21 24 21 39 45 30 │ΣX=390 ; ΣX^2 = 17478 │ ├────┼───────────────┼────────────┤ │Asian │72 42 58 42 67 39 45 27 33 55 │ΣX=480 ; ΣX^2 = 24954 │ ├────┼───────────────┼────────────┤ │Domestic│75 65 59 62 55 70 65 67 78 54 │ΣX=650 ; ΣX^2 = 42814 │ └────┴───────────────┴────────────┘ Use α=0.05 to answer the following questions. Please remember to write out null / alternative hypotheses and the conclusion. Please approximate df of error to 35 when you try to find the critical values from the table of our textbook. 1.Conduct one-way ANOVA 【Let me tell you : MES=193.72222】 2.Compose SSB to "orthohonal contrasts" and conduct statistical test on the comntrasts. 3.Conduct mean comparisons on eacg pair of groups by using Bonferroni t-test, Newman-Keul tests, and Tukey HSD. 4.Do the following contrasts by using Holm's multistage procedure and Scheffe tests: a. USA v.s. European b. Asia v.s. Domestic c. West v.s. East d. Non-domestic v.s. Domestic 5.Treat Domestic as the control group, then conduct Dunnett's test. 6.Calculate η^2 and ω^2. 7.What is the power of this one-way ANOVA？ --

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