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Agenda: STAT 401 Week 5 Lab 2
Prev HW comments/solutions
Example experiments worked through from design to result (with JMP)
Example problems from book.
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2.1
2.1.1
Examples
Example: Bone Density
Sample size
A client requests the following: “I want to do a randomized experiment to
compare two treatments for preventing bone loss in elderly women. I want to
use a .05 level t-test that has at least an 80% chance of detecting a difference of
at least 4 units betwen mean loss in bone density for the two treatments. How
many subjects do I need?” Further discussion clarifies that equal sample sizes
are desired.
Review of the literature suggests that we may expect the responses to be
approximately normally distributed and that σ 2 ≈ 25.
What sample size size is needed?
2.1.2
Analyze the data
Despite the recommendation above, we have an experiment with n = 10. The
data are in bone.csv. Do the two treatments have different means? Verify the
assumptions of common standard deviation and of normality.
2.2
2.2.1
Example: Transgenic Mice
Sample size
This problem is based on a study of genetic contributions to Downs syndrome.
A researcher wants to test whether the weight of transgenic mice with an extra
285E6 DNA fragment differs from non-transgenic mice.
The researcher wants to be able to detect a difference of 0.5 with a power
of 0.8 using a 0.05-level t-test. Equal sample sizes are desired. The variance is
estimated to be approximately 15. What sample size is needed?
2.2.2
Analyze the data
The data are in mousewt.txt. They are the weights, in grams, of two groups of
mice: 79 non-transgenic mice and 81 transgenic mice with an extra 285E6 DNA
fragment.
The sample sizes (N), means and variances of the two groups of mice are:
non-transgenic, N=79, mean = 27.62, variance = 14.60
transgenic, N = 81, mean = 28.09, variance = 9.49
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1. Create a normal probability plot for each group. Are the weights normally
distributed?
2. Calculate the standard deviation and coefficient of variation for both
groups of mice. Which group is more variable?
3. Calculate the standard error of the mean weight for each group of mice.
4. Test whether the two group variances are the same.
5. Calculate the pooled estimate of the standard deviation.
6. How many degrees of freedom are associated with the pooled estimate of
sd?
7. Calculate the se of the difference between the two means.
8. Do the two groups have different means?
2.3
Example: Schizophrenia Data
An experiment examined maternal twins where one twin has schizophrenia and
the other is unaffected. The data for the experiment are in schizophrenia.txt.
The response variable is the volume of the hippocampus. The researchers were
interested in whether the volume differed. Verify any assumptions needed to
answer the question.
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Book Problems
Ch 9: 10, 13, 41, 53, 71,
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References
• STAT 401 Page
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