# One-Way ANOVA

One-Way ANOVA Problem 3.26, when assumptions are violated 1 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. 2 OK, what about when things go wrong Problem 3.26 data

3 Plot that data 4

Put in means and error bars 5 Plot Residuals vs. Predicted

6 A clear problem exists but run the test(s) for equal variances

7 What to do, what to do.. Use Box-Cox transformation to transform the data!!!!!!!!!!!!!! 8

Do the transformation and.. 9 Plot again

10 Residuals vs. Predicted 11

Testing equal variances 12 Now Normality Plot of Residuals

13 Test of Normality Goodness-of-Fit Test Shapiro-Wilk W Test

W 0.985985 Prob

Note: Ho = The data is from the Normal distribution. Small p-values reject Ho. 14 Whew, now do ANOVA.

15 Compare Trt. groups with Tukey 16

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 pvalues 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 17 to report results.

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