STATISTICS 324        Assignment 13        Due  May 7, 2004

Exercises from the textbook, "Probability & Statistics for Engineering"
by J. Devore

Section 10.1:  3 (also prepare an ANOVA table and summarize its results),
6 (show sample means Ybar_{i.} and calculation of SSA, with SSE = 563.134,
display ANOVA table; provide estimate of variance sigma^2 of the errors
epsilon_{ij} )

Section 10.2:  11, 12, 13, 15(also obtain a 95% CI for
theta = (1/2)( mu_1 + mu_2 ) - (1/2)( mu_3 + mu_4 ),
a contrast between the averages of the "ate"'s and the "tite"'s)

Section 10.3:  22, 23

Section 11.1:  10 (Show sample means for "method" and "batch" factors,
Ybar_{i.} and Ybar_{.j}, and calculations of SSA (method) and
SSB (batch), with SSE = 24.04467; display ANOVA table and test of
hypothesis results; perform a multiple comparison analysis, using Tukey's
method, for treatment ("method") factor, if appropriate)

Additional:  To examine the importance of "blocking", reanalyze the
concrete strength data of Exercise 10 as a one-factor model with "method" as
the treatment factor, ignoring "batch" as a blocking factor; comment on
results, and any other interesting features between analysis and results
from Exer. 10 compared to this analysis)
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R-output (partial) for Exercises 6 and 15, Chap. 10 (provided for reference)
One-factor ANOVA Results for Y (Total Fe) on factor Iron-type (A)

> iron.df <- data.frame(irontype,fe)
> aov.iron <- aov( fe ~ irontype )
> summary(aov.iron)
          Df Sum of Sq  Mean Sq  F Value        Pr(F)
 irontype  3   509.122 169.7073 10.84904 3.199045e-05
Residuals 36   563.134  15.6426
    Total 39  1072.256

> model.tables(aov.iron, type="means", se=T)

Tables of means
Grand mean = 28.64

 irontype
     1      2      3      4
 26.08  24.69  29.95  33.84

Standard errors for differences of means
        irontype
          1.7688
replic.  10.0000
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R-output (partial) for Exercises 10 and Addn., Sec. 11.1
(provided for reference)
Two-way ANOVA Results for Y (Compressive Strength) on factor
Method (A) and blocking factor Batch (B)

> concrete.df <- data.frame(method,batch,strength)
> aov.concrete <- aov (strength ~ method + batch )
> summary(aov.concrete)
          Df Sum of Sq  Mean Sq  F Value       Pr(F)
   method  2  23.22867 11.61433 8.694568 0.002278362
    batch  9  86.79333  9.64370 7.219342 0.000202151
Residuals 18  24.04467  1.33581
    Total 29 134.0667

> model.tables(aov.concrete, type="means", se=T)

Tables of means
Grand mean = 30.733

 method
     1      2      3
 29.49  31.31  31.40

 batch
     1     2     3     4     5     6     7     8     9    10
 31.63 30.77 30.90 33.33 31.97 28.00 29.10 32.80 28.43 30.40

Standard errors for differences of means
          method    batch
         0.51688  0.94369
replic. 10.00000  3.00000