3-08 ANOVA Revision

8/11/2019 3-08 ANOVA Revision

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Company ConfidentialCopyright NN, Inc. 2004

Multiple Parameter Testing

ANOVA


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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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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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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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Is there a statistical difference in the means of these 5 furnaces?

Is variation the same between these furnaces?


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Stats>ANOVA>Test for Equal Variances


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Choose Mean Value as Response and Furnace as Factor



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


Is there a statistical difference in Variation between the furnaces?




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).




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.
http://localhost/Programmi/MINITAB%2014/Data/Exh_aov.MTWhttp://localhost/Programmi/MINITAB%2014/Data/Exh_aov.MTW




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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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.

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3-08 ANOVA Revision