The following data represent the complete set of measurements of the dry sheer strength (in pounds per square inch) of birch plywood, bonded with 5 different resin glues A, B, C, D, and E. Eight pieces (n = 8) of plywood were tested with each glue type. You may use R for all parts of this problem unless otherwise specified. The data are stored in the file =birch.txt=, which is posted to Canvas. 504 499 473 458 479 468 463 517 B 455 483 476 493 498 466 492 484 500 502 483 519 538 528 509 500 D 520 511 564 533 495 543 513 540 E 514 496 503 482 512 532 510 499 Recall from Birch plywood I the statistical model underlying an ANOVA analysis and the null hypothesis and alternative hypothesis appropriate to this problem. A) Create a graph with 5 side-by-side box plots. Comment briefly. Remark: A visual inspection of the data should be a routine part of an ANOVA. An examination of the side-by-side box plots can help give a feeling for differences among glue types, as well as aid in checking that the variances are roughly similar. B) Perform a test for the homogeneity of variances. Is the result of the test consistent with what you might conclude from the boxplots created in part (b)? C) Construct appropriate QQ plots to evaluate the assumption of normality made in part (a). D) Report the complete ANOVA table for these data, including all relevant sums of squares, mean squares, degrees of freedom, test statistic, and p-value. Make a conclusion in the context of the problem. E) Make pairwise mean comparisons via appropriate tests using (i) the Bonferroni method; (i) Fisher's protected LSD method; and (ii) Tukey's HSD method. Perform the tests using adjusted p-values when adjusted p-values are appropriate. Use an experiment-wise error rate of a = 0.05 to declare significance. Interpret your results. F) Compare the results of the Bonferroni method, Fisher's protected LSD method, and Tukey's HSD method. G) Create a compact letter display based on the results of Tukey's HSD. H) Compute the yardstick value of Ii - 7; that leads to a rejection of Ho : fi = Hj at an experiment-wise error rate of a = 0.05, for (i) Fisher's LSD, (ii) Tukey's HSD, and (ii) the Bonferroni method. You may use R to find the critical values, but otherwise do the computation by hand. 1) Perform the Kruskal-Wallis rank sum test and comment on the results. The following data represent the complete set of measurements of the dry sheer strength (in pounds per square inch) of birch plywood, bonded with 5 different resin glues A, B, C, D, and E. Eight pieces (n = 8) of plywood were tested with each glue type. You may use R for all parts of this problem unless otherwise specified. The data are stored in the file =birch.txt=, which is posted to Canvas. 504 499 473 458 479 468 463 517 B 455 483 476 493 498 466 492 484 500 502 483 519 538 528 509 500 D 520 511 564 533 495 543 513 540 E 514 496 503 482 512 532 510 499 Recall from Birch plywood I the statistical model underlying an ANOVA analysis and the null hypothesis and alternative hypothesis appropriate to this problem. A) Create a graph with 5 side-by-side box plots. Comment briefly. Remark: A visual inspection of the data should be a routine part of an ANOVA. An examination of the side-by-side box plots can help give a feeling for differences among glue types, as well as aid in checking that the variances are roughly similar. B) Perform a test for the homogeneity of variances. Is the result of the test consistent with what you might conclude from the boxplots created in part (b)? C) Construct appropriate QQ plots to evaluate the assumption of normality made in part (a). D) Report the complete ANOVA table for these data, including all relevant sums of squares, mean squares, degrees of freedom, test statistic, and p-value. Make a conclusion in the context of the problem. E) Make pairwise mean comparisons via appropriate tests using (i) the Bonferroni method; (i) Fisher's protected LSD method; and (ii) Tukey's HSD method. Perform the tests using adjusted p-values when adjusted p-values are appropriate. Use an experiment-wise error rate of a = 0.05 to declare significance. Interpret your results. F) Compare the results of the Bonferroni method, Fisher's protected LSD method, and Tukey's HSD method. G) Create a compact letter display based on the results of Tukey's HSD. H) Compute the yardstick value of Ii - 7; that leads to a rejection of Ho : fi = Hj at an experiment-wise error rate of a = 0.05, for (i) Fisher's LSD, (ii) Tukey's HSD, and (ii) the Bonferroni method. You may use R to find the critical values, but otherwise do the computation by hand. 1) Perform the Kruskal-Wallis rank sum test and comment on the results
