=+e) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown here. For each pair of shelves, the difference is shown along with its standard error and significance level. What does it say about the questions in part d?

M20_SHAR8696_03_SE_C20.indd 767 14/07/14 7:37 AM 768 CHAPTER 20 Design and Analysis of Experiments and Observational Studies Dependent Variable: PROTEIN Bonferroni

(I)

SHELF

(J)

SHELF Mean Difference

(I-J)

Std.

Error Pvalue 95%

Confidence Interval Lower Upper Bound Bound 1 2 0.75 0.322 0.070 -0.04 1.53 3 -0.21 0.288 1.000 -0.92 0.49 2 1 -0.75 0.322 0.070 -1.53 0.04 3 -0.96 0.283 0.004 -1.65 -0.26 3 1 0.21 0.288 1.000 -0.49 0.92 2 0.96 0.283 0.004 0.26 1.65