









Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Notes; Professor: Clark; Class: Statistical Methods I; Subject: Statistics; University: Hollins University; Term: Fall 2008;
Typology: Study notes
1 / 15
This page cannot be seen from the preview
Don't miss anything!
(11 pts) Biologists studied the relative brain sizes (measured as brain weight divided by body weight, times 1000) for 96 species of mammals. The species were also classified by whether their average litter size is less than 2 or not. Summary statistics are below: average litter Variable size N Mean StDev Q 1 Medi Q 3 relative brain 2 or more 45 10.97 9.84 3.32 7.97 18. size under 2 51 6.886 5.460 2.480 5.000 10. A simulation was used to produce 1000 repetitions where the 96 brain sizes were randomly assigned to the 2 litter size groups. a) (5 pts) Based on these simulation results, would you consider the increase in average brain sizes for the larger litters to be statistically significant? Explain by estimating and interpreting the p -value.
b) (3 pts) The previous study was operationally identical to that of another study and the results of the two studies were combined. The sample sizes were now roughly twice as large in each group, and the other summary statistics remained similar to the values listed above. Without calculating, would the p -value for this combined study be larger, smaller, or approximately the same as that in (a)? Explain your reasoning.
b) (3 pts) For games played away from Hollins, which player successfully makes a high proportion of free throws? Justify your answer with appropriate calculations.
c) (4 pts) Now combine games played at Hollins and away from Hollins. When these games are combined, which player successfully makes a higher proportion of her free throws? Justify your answer with appropriate calculations.
d) (4 pts) Explain why Simpson’s paradox occur’s here. (Be sure that you do more than describe the paradox; be sure to explain why it happens in this case.) Base your explanation on the data provided.
b) (3 pts) Now consider the general case that there are 4N subjects, of whom 2N are men and 2N are women. Derive an expression for the probability that N subjects of each gender are assigned to each group, as a function of N.
c) (3 pts) Produce and submit a graph of your function from b), for values of N ranging from 1 to 10. Does the function appear to be increasing or decreasing? Explain why this makes sense.
Note that the data appear in both “stacked” format (c1 and c2) and unstacked format (c4 and c5). a) (4 pts) Which group (intrinsic or extrinsic) tended to achieve higher creativity scores? Report the values of appropriate summary statistics (i.e., measures of center) to support your answer. (Do not bother to write a paragraph or even a sentence.)
b) (4 pts) Which group (intrinsic or extrinsic) tended to have higher variability in creativity scores? Report the values of appropriate summary statistics (i.e., measures of spread) to support your answer. (Do not bother to write a paragraph or even a sentence.)
c) (2 pts) Do any of the creativity scores in either group show up as outliers on boxplots? If so, identify the values of the outliers. (You do not need to conduct an
The values in c10 are differences in group means, obtained from simulating the random assignment process 10,000 times, assuming no difference between the intrinsic and extrinsic motivation groups. d) (6 pts) Use this column of simulation results to approximate the p -value of the randomization test. Describe how you do this, as well as reporting the approximate p -value.
e) (8 pts) Summarize the conclusion that you would draw from this study. Be sure to address the issue of cause-and-effect as well as the issue of statistical significance.
f) (3 pts) Suppose that you were asked to write a Minitab macro to conduct this simulation analysis. What would the first line of this macro be (i.e., the line that performs the random assignment of subjects to groups)?