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Multiple Parameter Testing
ANOVA
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Company ConfidentialCopyright NN, Inc. 2004
Multiple Parameter Testing: ANOVA
USEFULNESS AND GENERAL METHOD
It is often desirable to compare several means instead of two. For
example, we may want to compare the output of different machines or
The difference of several suppliers to a quality characteristic. The
method to use in such situations is ANalysis Of VAriance. The basic
idea of this procedure is to split the total variability of the response
variable ( the variability of all observations) in two: the variation
between processes and the variation within processes.
We will first view a One Way ANOVA, then progress to a Two Way
ANOVA example.
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Multiple Parameter Testing: One-Way ANOVA
EXAMPLE OF ONE-WAY ANALYSIS OF VAIANCE
A Level 3 master in Eltmann, Germany needed to compare the hardness results
from five (5) furnaces in the Heat Treat Department. The analysis will be
conducted using the previous months data collection.
The furnace numbers and the respective average hardness data are listed below:
Instructions:
Using the OneWay ANOVAanalytical method, verify whether there is a
statistical difference in the results between HT furnaces
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Multiple Parameter Testing: One-Way ANOVAOpen MinitabStat > ANOVA > One-Way
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Multiple Parameter Testing: One-Way ANOVA
Choose Mean Value as the Response and Furnace as FactorGo to Graphs and select Box Plot, and then select OK twice
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Multiple Parameter Testing: One-Way ANOVA
Furnace
Mean
Value
OFEN 24OFEN 23OFEN 21OFEN 15OFEN 14
64.4
64.2
64.0
63.8
63.6
63.4
63.2
63.0
Boxplot of Mean Value by Furnace
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Multiple Parameter Testing: One-Way ANOVA
Is there a statistical difference in the means of these 5 furnaces?
Is variation the same between these furnaces?
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Multiple Parameter Testing: One-Way ANOVA
Stats>ANOVA>Test for Equal Variances
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Multiple Parameter Testing: One-Way ANOVA
Choose Mean Value as Response and Furnace as Factor
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Furn
ace
95% Bonferroni Confidence Intervals for StDevs
OFEN 24
OFEN 23
OFEN 21
OFEN 15
OFEN 14
0.450.400.350.300.250.200.150.10
Bartlett's Test
0.075
Test Statistic 20.53
P-Value 0.000
Levene's Test
Test Statistic 2.16
P-Value
Test for Equal Variances for Mean Value
Multiple Parameter Testing: One-Way ANOVA
Is there a statistical difference in Variation between the furnaces?
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Multiple Parameter Testing: One-Way ANOVA
Conclusions:
A One-Way ANOVA is helpful in determining if there are differences between more
than two population means.
What i f I want to look at two var iables?
Two-way ANOVA tests the equivalency of population means when results are
classified by two variables with two or more categories each.
Two-way ANOVA determines if there are differences in means from either factor
(significant main effects) and also if the factors together influence the result
(significant interactions).
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Multiple Parameter Testing: ANOVA
EXAMPLE OF TWO-WAY ANALYSIS
OF VARIANCE
You are a biologist who is studying how zooplankton live in two lakes. You set up twelve
tanks in your laboratory, six with water from each lake. You add one of three
nutrient supplements to each tank and after 30 days you count the zooplankton in a
unit volume of water. You use two-way ANOVA to test if the population means are
equal, or equivalently, to test whether there is significant evidence of interactions and
main effects.
1Open the file EXH_AOV.MTW.
2Choose Stat ANOVA Two-way.
3In Response, enter Zooplankton.
4In Row factor, enter Supplement. Check Display means.
5In Column factor, enter Lake. Check Display means. Click OK.
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Multiple Parameter Testing: ANOVA
TWO-WAY ANALYSIS OF VARIANCE
Analysis of Variance for ZooplankSource DF SS MS F P
Suppleme 2 1919 959 9.25 0.015
Lake 1 21 21 0.21 0.666
Interaction 2 561 281 2.71 0.145
Error 6 622 104
Total 11 3123
Individual 95% CISuppleme Mean --+---------+---------+---------+---------
1 43.5 (-------*-------)
2 68.3 (--------*-------)
3 39.8 (--------*-------)
--+---------+---------+---------+---------
30.0 45.0 60.0 75.0
Individual 95% CI
Lake Mean ------+---------+---------+---------+-----Dennison 51.8 (----------------*----------------)
Rose 49.2 (----------------*----------------)
------+---------+---------+---------+-----
42.0 48.0 54.0 60.0
Session
window
output
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Multiple Parameter Testing: ANOVA
TWO-WAY ANALYSIS OF VARIANCE
(continued)
Interpreting the results
The default output for two-way ANOVA is the analysis of variance table. For the
zooplankton data, there is no significant evidence for a supplement*lake interaction
effect or a lake main effect if your acceptable a value is less than 0.145 (the p-value for
the interaction F-test). There is significant evidence for supplement main effects, as the
F-test p-value is 0.015.
As requested, the means are displayed with individual 95% confidence intervals.
Supplement 2 appears to have provided superior plankton growth in this experiment.
These are t-distribution confidence intervals calculated using the error degrees of
freedom and the pooled standard deviation.