Chapter 3 Homework Steve Brainerd 2
Chapter 3 Problems: 3-6 EXCELDesign Expert Format EXCEL Format
Coating Type ConductivityCoating type
1Coating type 2
Coating type 3
Coating type 4
1.00 143.00 Conductivity 143.00 152.00 134.00 129.001.00 141.00 141.00 149.00 136.00 127.001.00 150.00 150.00 137.00 132.00 132.001.00 146.00 146.00 143.00 127.00 129.002.00 152.002.00 149.00 Anova: Single Factor2.00 137.002.00 143.00 SUMMARY3.00 134.00 Groups Count Sum Average Variance3.00 136.00 Coating type 1 4 580 145 15.333333.00 132.00 Coating type 2 4 581 145.25 44.253.00 127.00 Coating type 3 4 529 132.25 14.916674.00 129.00 Coating type 4 4 517 129.25 4.254.00 127.004.00 132.004.00 129.00 ANOVA
Source of Variation SS df MS F P-value F critBetween Groups 844.6875 3 281.5625 14.302 0.00029 3.4903Within Groups 236.25 12 19.6875
Total 1080.9375 15
Chapter 3 Homework Steve Brainerd 3
Chapter 3 Problems: 3-6 EXCELConductivity Problem 3-6
143.00141.00
150.00
146.00
152.00
149.00
137.00
143.00
134.00136.00
132.00
127.00129.00127.00
132.00
129.00y = -0.8125x2 - 1.9625x + 148.94R2 = 0.6814
125.00
130.00
135.00
140.00
145.00
150.00
155.00
0 1 2 3 4 5Coating Type
Con
duct
ivity
ConductivityPoly. (Conductivity)
Chapter 3 Homework Steve Brainerd 8
Chapter 3 Problems: 3-6• Design Expert Analysis and EXCEL Analysis 3-6c
Total N = 16a = # levels = 4 TINV(0.05,df) TINV(0.01,df)
0.05 0.01
Mean COATING 4 df =N-a ta/2,N-a ta/2.N-a MSe
n # Replicates
SE Standard Error:
sqrt(Mse/n)
129 12 2.178812792 3.05454 19.69 4 2.218670773
Confidence Interval low highmean-((tα/2,N-a)*sqrt(Mse/n))
mean-((tα/2,N-a)*sqrt(Mse/n))
95% 124 13499% 122 136
Chapter 3 Homework Steve Brainerd 9
Chapter 3 Problems: 3-6• Design Expert Analysis and EXCEL: 3-6c second part Mean
difference Coating 1 - 4
Total N = 16a = # factors = 4 TINV(0.05,df) TINV(0.01,df)
0.05 0.01
Mean Difference COATING 1 - 4 df =N-a ta/2,N-a ta/2.N-a MSe
n # Replicates
SE Standard Error:
sqrt(2Mse/n)
15.75 12 2.178812792 3.05454 19.69 4 3.137674298
Confidence Interval low highmean-((tα/2,N-a)*sqrt(Mse/n))
mean-((tα/2,N-a)*sqrt(Mse/n))
95% 9 2399% 6 25
Chapter 3 Homework Steve Brainerd 10
Chapter 3 Problems: 3-6• 3-6d Fishers LSD ( page 99)• Calculate the LSD term as:
• LSD = tα/2,n-a*Sqrt(2MSe/n)
• tα/2,n-a = t0.05,12 = 2.18• MSe = 19.69• n= 4• LSD = 2.18*3.14 = 6.66• So any absolute value mean difference > 6.66 = signifiance
Mse n sqrt(2Mse/n) t(0.05,12) t(0.01,15) LSD= t0.05,12 (sqrt(2Mse/n))
19.6875 4 3.14 2.18 3.05 6.66
Chapter 3 Homework Steve Brainerd 11
Chapter 3 Problems: 3-6• 3-6d Fishers LSD EXCEL If Absolute difference between
means > LSD = significance!
Mse n sqrt(2Mse/n) t(0.05,12) t(0.01,15) LSD= t0.05,12
(sqrt(2Mse/n))19.6875 4 3.14 2.18 3.05 6.66
Coating Coating Value A value BDifference A-
BLSD Significance at
α = 0.05
1 2 145 145.25 0.25 NO1 3 145 132.25 12.75 YES1 4 145 129.25 15.75 YES2 3 145.25 132.25 13 YES2 4 145.25 129.25 16 YES3 4 132.25 129.25 3 NO
Chapter 3 Homework Steve Brainerd 12
Chapter 3 Problems: 3-6• 3-6d Fishers LSD 1–3, 1-4, 2-3 ,and 2-4 are significantly
different from JUMP
Chapter 3 Homework Steve Brainerd 13
Chapter 3 Problems: 3-6• Graphical comparison of Means 3-6e : t df for error = 12
Graphical Comparison of Means Example 3-6e
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
50.00%
125 130 135 140 145 150 155
Mean +/- SE*t
P(X)
Stu
dent
t di
strib
utio
n
Student t P(X) (df = , 1 tail)
ACTUAL DATA TreatmentMeans
Chapter 3 Homework Steve Brainerd 23
Chapter 3 Problems: 3-6• JUMP JMP Analysis 3-6 JUMP Starter
Index LSD
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