心統(下)段考Ⅰ 2000/4/13
一、是非題
1. ( )F分配的偏態係數(skewness)＞0
2. ( )假設一研究者想比較小學一到六年級每晚睡眠時間是否有差異，
則使用ANOVA犯第一類錯誤的機率，比用多個t-test犯第一類錯誤
的機率來得低。
3. ( )In one-way ANOVA, the expected values of MSb and MSw are both
Equal to σ^2.
4. ( )If the observed F-ratio is 1.00 or less, the null hypothesis in
ANOVA willbe rejected at α= .25
二、填充與選擇
1. 假設研究者甲想用多個t-test來比較小學一到六年級每晚睡眠時間是否有
差異，則共需要做多少個比較？Ans: _____個
2. 如果Ho為真，想在上一題的作法下(設每個t-test的α= .05)。拒絕至少
一個Ho的機率為(a)稍低於.05 (b).05 (c)稍高於.05 (d)遠大於.05。
Ans: _____
3. The means of 31 persons in the experimental group and 31 persons in the
control groups were compared using a t-test. The value of t was 2.5. If
ANOVA is performed on the same data, what will be the value of the F-ratio?
Ans: _____
4. The critical value for t in the Question 3 with α= .05 is 2.00; what
is the critical F value for the corresponding ANOVA with α= .05? Ans: _____
5. 請問變異數分析(ANOVA)的目的為何？Ans: _____
6. 請寫出two-way ANOVA的線性模式(linear model)。Ans: _____
7. 請問資料轉換(transformation)的目的為何？Ans: _____
8. 請問在ANOVA中採行未加權平均術法(unweighted-means solution)
的目的乃為處理什麼情況？Ans: _____
9. 請問事後比較(post hoc comparisons)的目的為何？Ans: _____
10. 請問進行兩兩平均數的事後比較時，Tukey HSD, Newman-Keuls,
Scheffe三者檢定力(power)由大到小的排列順序為何？Ans: _____
11. 重覆量數設計的優缺點為何？
優點：______________
缺點：______________
12. 請將受試者代號S1, S2, ……填入各細格(cell)，其中A為受試者內變項
，B為受試者間變項，每一細格有五個分數
B1 B2 B3
A1 ( ) ( ) ( )
A2 ( ) ( ) ( )
13. 請在等格受試者間設計固定效果模式下完成下列變異數分析總表。
______________________________________________________
Source SS df MS F Is ρ＜.05?
------------------------------------------------------
A ( ) ( ) ( ) 1.5 ( )
B ( ) ( ) ( ) ( ) ( )
AB ( ) 1 ( ) 3 No
Residual 240 40 ( )
Total 333
------------------------------------------------------
14. X、Y、Z三個依變項在各實驗情境的細格平均數(cell means)如下，
(a) 請問此研究為 ___ X ___ 的設計
(b) 並請完成該表格。(n = 10 for each cell)
A1B1 A1B2 A2B1 A2B2 A3B1 A3B2 AB顯? A著? B嗎?
X 10 20 20 30 30 40 __ __ __
Y 20 20 10 30 10 30 __ __ __
Z 30 30 30 10 30 10 __ __ __
^α1 ^α2 ^α3 ^β1 ^β2 αβ11 αβ12 αβ21 αβ22
X __ __ __ __ __ __ __ __ __
Y __ __ __ // // // // // //
Z // // // // // // // // //
αβ31 αβ32
X __ __
Y // //
Z // //
Note: O = significant; X = not significant
三、名詞解釋
(1) main effect:
(2) interaction:
(3) simple main effect:
(4) fixed-effects factor:
(5) between-subjects variables:
(6) experiment-wise error rate:
四、請證明1-way ANOVA中SSt = SSb + SSw，而且各SS的算式如下所示：
SSt = [X] － [T]
SSb = [A] － [T]
SSw = [X] － [A]
[T] = #@$%^$&
[X] =%$&^%($
[A] =*%)(#(!#@#
p.s.因為數學算式打不出來，所以請參照筆記……
五、計算
＊請就以下題目進行所需之統計分析
＊可參考筆記，課本等，可使用計算機，但不可看別人的材料、以及交談
＊請詳列計算過程，並算至少小數點以下兩位
Assume you have just accepted a position as chief scientist for a leading
agricultural company. Your first assignment is to make a recommendation
concerning the best type of grass to grow in the Pacific Northwest and the
best fertilizer for it. To provide the database for your recommendation,
having just graduated summa cum laude in statistics, you decide to conduct
an experiment involving a factorial independent groups design. Since there
are three types of grass and two fertilizers under active consideration,
the experiment you conduct is 2 X 3 factorial, where the A variable is
the type of fertilizer and the B variable is the type of grass. In your
field station, you duplicate the soil and the climate of the Pacific
Northwest. Next you divide the soil into 30 equal areas and randomly set
aside 5 for each combination of treatments. Next, you fertilize the areas
with the appropriate fertilizer and plant in each area the appropriate grass
seed. Thereafter, all areas are treated alike. When the grass has grown
sufficiently, you determine the number of grass blades per square inch
in each area. Your recommendation is based on this dependent variable.
The "denser" the grass is, the better. The following scores are obtained:
Number of Grass Blades per Square Inch
Red Kentucky Green
Fertilizer Fescue Blue Velver
-------------------------------------------------
Type 1 14 15 15 17 20 19
16 17 12 18 15 22
10 11 25
Type 2 11 7 10 6 15 11
11 8 8 13 18 10
14 12 19
-------------------------------------------------
a. What are the null and alternative hypotheses for this experiment?
b. Using α = 0.05, what are your conclusions?
Draw a graph of the cell means to aid in interpreting the result.
type by Kbilly
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