STAT 342
More Anova Practice Problems.
1. During each of four experiments on the use of carbon tetrachloride as a worm killer, ten rats were infested with larvae (Armitage 1983). Eight days later, five rats were treated with carbon tetrachloride; the other five were kept as controls. After two more days, all the rats were killed and the numbers of worms were counted.
In this analysis, we look at the counts of worms for the four control groups. Significant differences, although not anticipated, might be attributable to changes in experimental conditions. A finding of significant differences should result in more carefully controlled experimentation and thus greater precision in later work.
Based on the following R output (and attached plots), answer the above question.
Analysis of Variance Table
Response: rats$wcount
Df Sum Sq Mean Sq F value Pr(>F)
rats$group 3 27234 9078 2.2712 0.1195
Residuals 16 63954 3997
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = rats$wcount ~ rats$group)
$`rats$group`
diff lwr upr p adj
g2-g1 32.8 -81.5993 147.1993 0.8440446
g3-g1 -15.6 -129.9993 98.7993 0.9791349
g4-g1 80.8 -33.5993 195.1993 0.2215071
g3-g2 -48.4 -162.7993 65.9993 0.6293676
g4-g2 48.0 -66.3993 162.3993 0.6353260
g4-g3 96.4 -17.9993 210.7993 0.1149938
2. The data set gives measurements on cholorpheniramine maleate tablets from another manufacturer (we examined one manufacturer in class). Based on the analysis and plots, are there systematic difference between the labs? If so, which pairs differ significantly? Lastly, is there evidence that the assumptions of the model are met, and if not, how worrisome is this? Can you think of other plots that could help you answer the above question?
Analysis of Variance Table
Response: labs$chlor
Df Sum Sq Mean Sq F value Pr(>F)
labs$lab 6 0.154857 0.025810 11.991 6.195e-09 ***
Residuals 63 0.135600 0.002152
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = labs$chlor ~ labs$lab)
$`labs$lab`
diff lwr upr p adj
lab2-lab1 -0.041 -0.104189971 0.022189971 0.4397581
lab3-lab1 -0.004 -0.067189971 0.059189971 0.9999953
lab4-lab1 0.062 -0.001189971 0.125189971 0.0578620
lab5-lab1 0.111 0.047810029 0.174189971 0.0000262
lab6-lab1 0.056 -0.007189971 0.119189971 0.1154264
lab7-lab1 0.043 -0.020189971 0.106189971 0.3813731
lab3-lab2 0.037 -0.026189971 0.100189971 0.5640043
lab4-lab2 0.103 0.039810029 0.166189971 0.0001092
lab5-lab2 0.152 0.088810029 0.215189971 0.0000000
lab6-lab2 0.097 0.033810029 0.160189971 0.0003090
lab7-lab2 0.084 0.020810029 0.147189971 0.0026147
lab4-lab3 0.066 0.002810029 0.129189971 0.0350255
lab5-lab3 0.115 0.051810029 0.178189971 0.0000126
lab6-lab3 0.060 -0.003189971 0.123189971 0.0734741
lab7-lab3 0.047 -0.016189971 0.110189971 0.2770437
lab5-lab4 0.049 -0.014189971 0.112189971 0.2322194
lab6-lab4 -0.006 -0.069189971 0.057189971 0.9999484
lab7-lab4 -0.019 -0.082189971 0.044189971 0.9686906
lab6-lab5 -0.055 -0.118189971 0.008189971 0.1284911
lab7-lab5 -0.068 -0.131189971 -0.004810029 0.0269411
lab7-lab6 -0.013 -0.076189971 0.050189971 0.9956808
b. Find the significantly different labs based on the Bonferroni method as well.