PBHL-B302 Homework #1 Name: Jacob Letterman
Please note that many of these problems ask you to do two things - if you do only one, you can only be awarded half credit.
1.
(12 pts) Explain (1) what is wrong with each of the following randomization procedures and (2) describe how you would do the randomization correctly. You should use your notes and think about things like sampling bias, and proper randomization schemes we discussed in the notes and how to employ them.
(1)
Ten subjects are to be assigned to two treatments, 5 to each. For each subject, a coin is tossed. If the coin comes up heads, the subject is assigned to the first treatment; if the coin comes up tails, the subject is assigned to the second treatment.
Though the coin toss is somewhat random, this isn’t taking into account how after 10 flips, you may not get 5 heads and 5 tails, you may get 7 heads and 3 tails or other situations where neither are equal to each other. To fix this, just use a completely random design as it would give you a truly random group of five for each treatment. (2)
Twenty students are to be used to evaluate a new treatment. Ten men are assigned to receive
the treatment and 10 women are assigned to be the controls.
The main thing wrong here is that the random blocked design isn’t right. What I mean is that
with the design, if you have more than one treatment, then you have to have more groups within each block. An easy way to fix this would be by using a random block design, making four groups, 2 for control and 2 for treatment, with the 10 men and 10 women being divided
evenly into each for accurate data.
(3)
An experiment will assign 40 rats to 4 different treatment conditions. The rats arrive from the supplier in batches of 10 rats and the treatment lasts two weeks. The first batch of 10 rats is randomly assigned to one of the four treatments, and data for these rats are collected. After a one-week break, another batch of 10 rats arrives and is assigned to one of the three remaining
treatments. The process continues until the last batch of rats is given the treatment that has not been assigned to the three previous batches.
The main problem here is that there is a chance the groups will have an uneven amount of people in them. Group 1 will, at most if you’re trying to split each batch evenly, have 3 rats, while group 4 will have at least 8, as the groups are closed off each new batch. The way that you fix is by having the groups be of equal size. You can keep the random assignments, but with having the groups it allows for not only have the same amount of data, but it keeps the
2.
(12 pts) Explain (1) what is wrong with each of the following random selection procedures and (2) explain how you would do the random selection correctly. You need to use concepts from the notes, such as simple random sampling, stratified random sampling, to answer these questions. (1)
A population of subjects is put in alphabetical order and a simple random sample of size 10 is taken by selecting the first 10 subjects in the list.
The problem with this is that it isn’t really random, you are choosing your subjects based solely on the first ten people on a list. An easy fix for this is to just do a simple random sampling design. You can keep the alphabetical list, but by using actual randomization, it
