Question 1. Eating paint It has been estimated that lead poisoning resulting from an unnatural craving (pica) for substances such as paint may aﬀect as many as a quarter of a million children each year, causing them severe, irreversible retardation. Explanations for why children voluntarily consume lead range from “improper parental supervision” to “a child’s need to mouth objects.” Some researchers, however, have been investigating whether the habit of eating such substances has a nutritional explanation. One such study involved a comparison of a regular diet and a calciumdeﬁcient diet on the ingestion of a lead acetate solution on rats. Each rat in a group of 20 was randomly assigned to either an experimental or a control group. Those in the control group received a normal diet, while those in the experimental group received a calcium deﬁcient diet. Each of the rats occupied a separate cage and was monitored to observe the amount of a 0.15% lead-acetate solution consumed during the study period (ml). Here is the data: Control: Exper : 5.4 6.8 6.2 7.5 3.1 8.6 3.8 7.6 6.5 5.5 5.8 4.9 6.4 5.4 4.5 4.5 4.9 8.5 4.0 6.3
1. Carefully describe how to randomize in this experiment and draw an possible experimental plan, i.e. show which rat is randomized to which trial, which rat is assigned to which cage, etc. You could present a table similar to: Cage: Rat : Treatment: 1 2 c 2 10 e 3 12 e 4 ..... 14 ..... e .....
2. Construct side-by-side dot and box plots. What do the graphs seem to indicate?
3. Find the simple summary statistics for each group. Find a standard error for each mean, and a conﬁdence interval for the mean of each group. Interpret the se’s and the conﬁdence intervals. 4. Estimate the diﬀerence in the means and obtain an estimated se for the diﬀerence and a conﬁdence interval for the diﬀerence. Interpret the se and the conﬁdence interval. 5. Deﬁne the parameters of this experiment, and give the null and alternate hypothesis in words and symbols. [You may use either a one or two sided test.] 6. What is the p-value. Interpret the p-value. 7. What do you conclude? 8. Suppose that a biologically signiﬁcant diﬀerence is about 1.5. What is the estimated power at the current sample size if you test at α = 0.05? [Yes, I know that this is a retrospective power analysis and is technically a “no-no”.] 9. What sample size would be needed to be 80% conﬁdent of detecting half the diﬀerence above (i.e. a diﬀerence of 0.75) at α = 0.05?
Question 2. The cigarette butt paper Review the paper where the eﬀect of cigarette butts on the parastitic load was examined at Suarez-Rodriguez, M., Lopez-Rull, I. and Garcia, C.M. (2013). Incorporation of cigarette butts into nests reduces nest ectoparasite load in urban birds: new ingredients for an old recipe? Biological Letters 9, 20120931. http://dx.doi.org/10.1098/rsbl.2012.0931 The authors have provided the raw data as an electronic supplement to this paper. Download the supplement. There are two tabs in the workbook corresponding to the results of Figure 1 and Figure 2. 1. Discuss the 3 R’s in relation to how the nests from the two species were chosen. 2. There are two factors in this ﬁrst study – host species and nest content. Create a suitable summary table and graph comparing the distribution of nest content across the two species. Are you concerned? Why? 3. Is the design balanced? Will this be of concern in later analyzes? 4. “Cellulose from cigarette butts was present in 89.29 per cent . . .”. Reproduce this result using your statistical package. Hint: create a derived variables as present/absent based on butt weight. Never report a naked estimate. Find a standard error for these statistics. What assumptions are you making about the sampling plan when you compute a standard error. What assumptions are you making about the other factor (nest content) when you ignore it during the analysis? 5. ”. ....