STATISTICS 224        Assignment 12        Due  May 7, 2004

Exercises from the textbook, "Probability & Statistics for Engineers"
by R. Johnson

Section 12.2:  12.6 (show sample means Ybar_{i.} and calculation of SSA,
with SSE = 276.8038, display ANOVA table; also, part (c) obtain
individual 95% CIs for the 3 pairs of differences of mean weight losses,
mu_1 - mu_2, mu_1 - mu_3, and mu_2 - mu_3);

12.10 (also, construct ANOVA table, and provide estimate of variance
sigma^2 of the errors epsilon_{ij} ),  12.16 (c)--read only

Section 12.4:  12.22 (Show sample means for "layout" and "crew" factors,
Ybar_{i.} and Ybar_{.j}, and calculations of SSA (layout) and SSB (crew),
with SSE = 20.3979; display ANOVA table and test of hypothesis results);

12.23 (modified, so you reanalyze the construction times data of
Exercise 12.22 as a one-factor model with "layouts" as the treatment factor,
ignoring "crews" as a blocking factor; comment on results, and any other
interesting features between analysis and results from Exer. 12.22 compared
to this analysis);
12.32 (except use Tukey's multiple comparisons method to obtain
simultaneous pairwise CIs, with critical value q_{.05; 3,21} = 3.57 )

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R-output (partial) for Exercise 12.6 (provided for reference)
One-way ANOVA Results for Y (Weight Loss) on factor Lubricant

> aov.loss <- aov( loss ~ lubtype )
> summary(aov.loss)
          Df Sum of Sq  Mean Sq  F Value       Pr(F)
  lubtype  2  230.5858 115.2929 8.746815 0.001724723
Residuals 21  276.8038  13.1811
    Total 23  507.3896

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

Tables of means
Grand mean = 12.496

 lubtype
      1        2        3
  9.350   11.425   16.713

Standard errors for differences of means
        lubtype
         1.8153
replic.  8.0000

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R-output (partial) for Exercises 12.22 and 12.23 (provided
for reference)
Two-way ANOVA Results for Y (Construction Times) on factor
Layout (A) and blocking factor Crew (B)

> times.df <- data.frame(layout,crew,times)
> aov.times <- aov( times ~ layout + crew )
> summary(aov.times)
          Df Sum of Sq  Mean Sq  F Value        Pr(F)
   layout  3  362.3646 120.7882 88.82392 8.900000e-10
     crew  5   89.9971  17.9994 13.23622 4.708187e-05
Residuals 15   20.3979   1.3599
    Total 23  472.7596

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

Tables of means
Grand mean = 53.154

 layout
      1       2       3       4
 49.417  53.733  50.200  59.267

  crew
      1       2       3       4       5       6
 52.775  53.125  54.950  51.050  50.825  56.200

 Standard errors for differences of means
          layout     crew
        0.67327  0.82458
replic. 6.00000  4.00000