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Simultaneous Estimation100(1- )% confidence intervals for theestimation of r treatment averages are given

by the Bonferroni intervals:

n

MS t y Error a N r ii )(2

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Example:

For the RF power example, construct a 90%confidence interval for estimating the meanof treatments 3 and 4 simultaneously.

570.333

4.625 16,025.03 t

570.3330.707 16,025.04 t

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Example: Dot diagram of the RF power example:

500 550 600 650 700 750 y i

1 2 3 4

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By inspection of the diagram, we canconclude:

The four averages could not be

obtained from the same distribution. Treatment 4 yields the highest averageetch rate.

Treatment 1 yields the lowest averageetch rate.

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Comparing Pairs of means :

Fishers TestThe least significant differences (LSD) between pairs of treatment averages is given by:

cost.,2

)(2=

n for

nMSE

a N t

jn

in for

jn

in

MSE a N

t +

,)11()(2

Or,

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Example:

Fishers test for the RF power data, at =0.05:

49.245

)70.333(2

)16,025.0(== t LSD

See page 94 for calculated differences:

All pairs of averages are significantlydifferent.

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The LSD Plot:A plot of the treatment averages and their leastsignificant differences (LSD):

160 180 200 220

530

578.75

627.5

676.25

725

EtchRate

RF Power