Question

In: Statistics and Probability

Consider the isatin yield experiment below. Set up the 2^4 experiment in this problem in two...

Consider the isatin yield experiment below. Set up the 2^4 experiment in this problem in two blocks with ABCD confounded. Analyze the data from this design. Is the block effect large?. Show the steps to perform this in Minitab.

factor low high
A:acid strength (%) 87 93
B:Reaction time (min) 15 30
C:Amount of acid (ml) 35 45
D:reaction temperature (c) 60 70
A B C D yield

-1

 -1 -1 -1 6.08
1 -1 -1 -1 6.04
-1 1 -1 -1 6.53
1 1 -1 -1 6.43
-1 -1 1 -1 6.31
1 -1 1 -1 6.09
-1 1 1 -1 6.12
1 1 1 -1 6.36
-1 -1 -1 1 6.79
1 -1 -1 1 6.68
-1 1 -1 1 6.73
1 1 -1 1 6.08
-1 -1 1 1 6.77
1 -1 1 1 6.38
-1 1 1 1 6.49
1 1 1 1 6.23

Solutions

Expert Solution

Consider the 2^4 isatin yield experiment in two blocks with ABCD confounded.

factor low high
A:acid strength (%) 87 93
B:Reaction time (min) 15 30
C:Amount of acid (ml) 35 45
D:reaction temperature (c) 60 70

Using Minitab:

Full Factorial Design

Factors: 4 Base Design: 4, 16 Resolution with blocks: V
Runs: 16 Replicates: 1
Blocks: 2 Center pts (total): 0


Block Generators: ABCD


Alias Structure

I

Blk = ABCD

A
B
C
D
AB
AC
AD
BC
BD
CD
ABC
ABD
ACD
BCD

Factorial Regression: Yield versus Blocks, A, B, C, D

Analysis of Variance:

Source DF Adj SS Adj MS
Model 15 1.04484 0.069656   
Blocks 1 0.00141 0.001406   
Linear 4 0.47113 0.117781
A 1 0.14631 0.146306
B 1 0.00181 0.001806   
C 1 0.02326 0.023256   
D 1 0.29976 0.299756
2-Way Interactions 6 0.38139 0.063565   
A*B 1 0.00001 0.000006   
A*C 1 0.00456 0.004556   
A*D 1 0.10401 0.104006
B*C 1 0.01756 0.017556   
B*D 1 0.25251 0.252506   
C*D 1 0.00276 0.002756   
3-Way Interactions 4 0.19092 0.047731
A*B*C 1 0.08851 0.088506
A*B*D 1 0.04101 0.041006   
A*C*D 1 0.00016 0.000156
B*C*D 1 0.06126 0.061256   
Error 0 * *
Total 15 1.04484


Coded Coefficients:

SE
Term Effect Coef  
Constant 6.382
Blocks
1 -0.009375
A -0.19125 -0.09563
B -0.02125 -0.01062  
C -0.07625 -0.03813
D 0.2738 0.1369  
A*B -0.001250 -0.000625   
A*C 0.03375 0.01688   
A*D -0.16125 -0.08062
B*C -0.06625 -0.03312
B*D -0.2512 -0.1256   
C*D -0.02625 -0.01313   
A*B*C 0.14875 0.07438   
A*B*D -0.10125 -0.05062   
A*C*D -0.006250 -0.003125   
B*C*D 0.12375 0.06187


Regression Equation in Uncoded Units:

Yield = 6.382 - 0.09563 A - 0.01062 B - 0.03813 C + 0.1369 D - 0.000625 A*B + 0.01688 A*C
- 0.08062 A*D - 0.03312 B*C - 0.1256 B*D - 0.01313 C*D + 0.07438 A*B*C
- 0.05062 A*B*D - 0.003125 A*C*D + 0.06187 B*C*D

Equation averaged over blocks.


Effects Pareto for Yield:

## The block effect is not large.

orchestra answered 1 year ago
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