chapter 3 3-15 anova examplemyplace.frontier.com/~stevebrainerd1/statistics/ece... · chapter 3...

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


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Chapter 3 3-15 One-Way ANOVA example


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Chapter 3 3-15 ANOVA example• 3-15 b: Residuals


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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


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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


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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%


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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


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Chapter 3 3-15 ANOVA example• 3-15 DESIGN EXPERT Outputs


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Chapter 3 3-15 ANOVA example• 3-15 JUMP (Jump Starter menu) File screen


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Chapter 3 3-15 ANOVA example• 3-15 JUMP (New Data Table menu): Copy/Paste from EXCEL


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Chapter 3 3-15 ANOVA example• 3-15 JUMP (New Data Table menu): Copy/Paste from EXCEL


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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)


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats menu): click ONE WAY


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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.


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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.


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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


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Quantiles


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Means/ANOVA test


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Means/ANOVA test


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on Normal Quantile Plots


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Normal Quantile Plots


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER (Basic stats ONEWAY menu):• Click on compare means 4 choices


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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


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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


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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


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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


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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


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(Basic stats ONEWAY menu): Un-equal Variances

• Bartlett’s test


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Chapter 3 3-15 ANOVA example• 3-15 JUMP STARTER Menu : Other tests• Click on Index : Find Bartlett’s test


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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


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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


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Menu : Levene and Bartlett’s tests for equal variances

• Setup Y response and X Grouping Press OK

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