Statistics
Problems 1-4: Below is Yates algorithm applied to data from a full 23 factorial with factors A, B and C.
|
Treatment |
Means |
Cycle 1 |
Cycle 2 |
Cycle 3 |
Fitted Effect |
|
(1) |
6.23 |
14.11 |
40.82 |
127.82 |
15.98 |
|
a |
7.88 |
26.71 |
87.00 |
5.20 |
0.65 |
|
b |
12.98 |
38.20 |
2.39 |
23.20 |
2.90 |
|
ab |
13.73 |
48.80 |
2.81 |
|
? |
|
c |
18.28 |
1.64 |
12.61 |
46.18 |
5.77 |
|
ac |
19.92 |
0.75 |
10.60 |
0.41 |
0.05 |
|
bc |
|
1.64 |
-0.89 |
-2.01 |
-0.25 |
|
abc |
24.98 |
1.16 |
-0.48 |
0.41 |
? |
The model fitted here is 𝑋'!( = 𝜇 + 𝛼' + 𝛽! + 𝜒( + 𝛾01 + 𝛾02 + ⋯ + 𝜖'!( where i = main effect of A at level i,
'! '(
j = main effect of B at level j, k = main effect of C at level k, and ’s are interactions between factors.
1. Compute the value labeled . A. 23.34
B. 23.82
C. 26.14
D. 26.62
2. Compute the value labeled . A. −1.37
B. −0.48
C. 0.41
D. 1.37
3. ( 333 )What is an estimate of 𝛾012?
A. −0.41
B. −0.05
C. 0.05
D. 0.41
Normal Q-Q Plot
4. ( Theoretical Quantiles ) ( 0.5 ) ( 1.0 )A Normal probability plot of the fitted effects (excluding 15.98) is given on the right. Which effect (main effect or interaction) is most significant according to this plot?
A. ( -1.0 -0.5 0.0 )Main effect of A
B. Main effect of B
C. Main effect of C
D. Interaction between B and C
0 1 2 3 4 5 6
Fitted Effect
5. Which of the following is TRUE about a Latin Square design (for 3 factors)?
A. Factors A, B and C can have different number of levels.
B. We must assume that there are no 2 and 3-factor interactions.
C. A Latin Square design can be costly to implement because we have to run all factor combinations.
D. We cannot apply the T Method on data from a Latin Square design.
6. A primary interest of designing a randomized block experiment is:
A. to produce experimental units that are identical
B. to increase the between-treatments variation to more easily detect differences among the treatment means
C. to provide better comparisons of treatments by accounting for differences in experimental units
D. (A) and (C)
7. Which of the following statements are true?
A. Sums of squares of effects that are judged unimportant can combined to obtain a new error sum of squares that can be used to perform F test statistics.
B. It is possible that 𝑅$ of a smaller model is larger (better) than 𝑅$ for a bigger model.
adj adj
C. The coefficient of determination 𝑅$ for a bigger model is always at least as big as the 𝑅$ of a smaller model.
D. All of the above statements are true.
Source df SS MS
A=Size 2 ? ? B=Distance 1 ? 7.157
AB Interaction 2 0.224 0.112
Error 12 13.651 1.138
Total 17 28.624
8. ( B=Distance 1.0in 0.5in )A plot of means is given on the below. What conclusion(s) can you derive from this plot?
A. ( 54.5 55.0 55.5 56.0 56.5 57.0 )Increasing the hole size (A), reduces tensile strength.
B. Increasing the hole size (A), increases tensile strength.
C. ( Aver age Strength )Increasing the distance (B) of the hole from the edge, increases tensile strength.
D. Both (A) and (C).
0.149in 0.185in 0.221in
A=Size