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One-Way ANOVAProblem 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

which is called the Predicted Value and

which is called the Residual Value.

.i i iY

.ij ij iY Y

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OK, what about when things go wrongProblem 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 Prob<W0.985985 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 dataThe 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 p-values, summaries of the original (untransformed or raw) data are used to report results.