Problem 3.26, when assumptions are violated
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Estimates of terms:
We can estimate the mean response for Failure Time
for problem 3.26 from the data by
i     i  Yi.
which is called the Predicted Value and
 ij  Yij  Yi.
which is called the Residual Value.
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OK, what about when things go wrong
Problem 3.26 data
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Plot that data
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Put in means and error bars
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Plot Residuals vs. Predicted
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A clear problem exists but run the test(s) for
equal variances
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What to do, what to do….. Use Box-Cox transformation
to transform the data!!!!!!!!!!!!!!
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Do the transformation and..
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Plot again
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Residuals vs. Predicted
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Testing equal variances
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Now Normality Plot of Residuals
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Test of Normality
Goodness-of-Fit Test
Shapiro-Wilk W Test
W
0.985985
Prob<W
0.9869
Note: Ho = The data is from the Normal
distribution. Small p-values reject Ho.
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Whew, now do ANOVA….
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Compare Trt. groups with Tukey
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Reporting results after the analysis of
transformed data
 The purpose of diagnostics is to make sure that the
assumptions are at least approximately correct, in
which case the p-values reported for significance tests
of means comparisons are valid.
 In reporting results, such as means of treatment
groups, generally use the untransformed or raw data.
 Transformations of the data are used to obtain valid pvalues, summaries of the original (untransformed or
raw) data are used to report results.
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