Post on 05-Aug-2020
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 a: Do the four catalysts have the same effect on the
concentration?Catalyst Concentration Means Catalyst 1 Catalyst 2 Catalyst 3 Catalyst 41 58.2 58.2 56.3 50.1 52.91 57.2 57.2 54.5 54.2 49.91 58.4 58.4 57 55.4 501 55.8 55.8 55.3 51.7
1 54.9 56.90 54.92 56.32 54.5 Anova: Single Factor2 57
2 55.3 55.78 SUMMARY
3 50.1 Groups Count Sum Average Variance
3 54.2 Catalyst 1 5 284.5 56.9 2.31
3 55.4 53.23 Catalyst 2 4 223.1 55.775 1.209167
4 52.9 Catalyst 3 3 159.7 53.23333 7.723333
4 49.9 Catalyst 4 4 204.5 51.125 2.0825
4 50 Mean 54.264 51.7 51.13
ANOVA : Single FactorCount N 16 MEAN 54.26 Source of Variation SS df MS F P-value F crit
Between Groups 85.68 3.00 28.56 9.92 0.00 3.49Within Groups 34.56 12.00 2.88
Total 120.24 15.00
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 One-Way ANOVA example
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 b: Residuals
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 c: Confidence intervals. Overall
Mean Concentration
Overall df =N-a ta/2,N-a ta/2,N-a MSe
nh for unequal sample sizes
SE Standard Error:
sqrt(Mse/n)
54.26 12 2.178812792 3.054538 2.8801 3.87 0.8626a 4.00
Confidence Interval low high sum(1/ni) 1.03
Mean Concentration
mean-((tα/2,N-a)*sqrt(Mse/n))
mean-((tα/2,N-a)*sqrt(Mse/n)) nh = a/sum(1/ni)
95% 52.38 56.1499% 51.62 56.89
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 c: Confidence intervals. Catalyst 1
Total N = 16.00a = # levels = 4.00 TINV(0.05,df) TINV(0.01,df)
0.05 0.01
Mean Concentration
Catalyst 1 df ta/2,N-a ta/2,N-a MSe n catalyst 1
SE Standard Error: sqrt(Mse/n)
56.90 4 2.776450856 4.6041 2.8801 5.00 0.7590a
Confidence Interval low highMean
Concentration mean-((tα/2,N-a)*sqrt(Mse/n))
mean-((tα/2,N-a)*sqrt(Mse/n))
95% 54.79 59.0199% 53.41 60.39
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 Graphical Comparison Create table and plot Student t
P(X) vs mean +/- SE*t
t value (SD units SE * t T histogram
mean +/-t*sqrt(Mse/n)
Student t P(X) (df = , 1 tail) TDIST(T,df,1)
-3 -2.587725433 51.67 0.16%
-2.5 -2.156437861 52.10 0.69%-2 -1.725150289 52.53 2.39%
-1.5 -1.293862717 52.96 6.81%-1 -0.862575144 53.40 15.97%
-0.5 -0.431287572 53.83 30.90%-0.2 -0.172515029 54.09 42.09%
0 0 54.26 50.00%0.5 0.431287572 54.69 30.90%1 0.862575144 55.12 15.97%
1.5 1.293862717 55.55 6.81%
2 1.725150289 55.98 2.39%
2.5 2.156437861 56.41 0.69%
3 2.587725433 56.85 0.16%
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 Graphical Comparison
Graphical Comparison of Means Example 3-15
56.955.853.251.1
-5.00%
5.00%
15.00%
25.00%
35.00%
45.00%
50 51 52 53 54 55 56 57 58
Mean +/- SE*t
P(X)
Stu
dent
t di
strib
utio
n
Student t P(X) (df = , 1 tail)
ACTUAL DATA TreatmentMeans
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 DESIGN EXPERT Outputs
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 DESIGN EXPERT Outputs
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 DESIGN EXPERT Outputs
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP (Jump Starter menu) File screen
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP (New Data Table menu): Copy/Paste from EXCEL
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP (New Data Table menu): Copy/Paste from EXCEL
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP (New Data Table menu): Ensure data is correct
type. Right click on Heading (Concentration in this example)
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats menu): click ONE WAY
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Set Y response and X grouping data. Once set press OK.
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on RED down arrow for choices.
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Quantiles ,Means/ANOVA test and compare means
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Quantiles
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Means/ANOVA test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Means/ANOVA test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Normal Quantile Plots
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Normal Quantile Plots
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means 4 choices
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means Each Pair, Student t test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means All Pairs, Tukey HSD test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means With Best, HSU MCB test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means test With Control, Dunnett’s
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER
(Basic stats ONEWAY menu):
• Click on Un-equal variances
• Bartlett’s test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER
(Basic stats ONEWAY menu): Un-equal Variances
• Bartlett’s test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER Menu : Other tests• Click on Index : Find Bartlett’s test
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER Menu : Other tests• Click on Index : Find Bartlett’s test and Press Run Script
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER Menu : Bartlett’s tests • Setup Y response and X Grouping Press OK
Chapter 3 3-15 ANOVA Steve Brainerd
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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER
Menu : Levene and Bartlett’s tests for equal variances
• Setup Y response and X Grouping Press OK