Biostatistic Homework

PBHL-B301 Homework #1                                                                            Name:  

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.

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  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.
    • 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.
    • 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.
    • 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.

 

  1. (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.
    • 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.
    • To determine the reading level of an introductory statistics text, you evaluate all the written material in the third chapter.
    • You want to sample student opinions about a proposed change in procedures for changing majors. You hand out questionnaires to 100 students as they arrive for class at 7:30am.

 

  1. (6 pts) Two drugs were tested to see whether they helped women who had breast cancer without lymph node involvement. The drugs are called TAC (docetaxel, doxorubicin, and cyclophosphamide) and FAC (fluorouracil, doxorubicin, and cyclophosphamide). About half of the 1060 women with breast cancer without lymph node involvement were randomly assigned to TAC and the other half were assigned to FAC. After 77 months, 472 out of 541 of the women assigned to TAC were alive and 425 out of 524 women assigned to FAC were alive (Source: Martin et al., Adjuvant docetaxel for high-risk, non-negative breast cancer, New England Journal of Medicine 363(23): 2200-2210)
    • Find the sample percentages of survival and compare them descriptively.
    • Was this an observational study or an experiment? Explain why. From studies like these, can we conclude a cause-and-effect relationship between the drug type and the survival percentage? Why or why not?

 

 

Download the data file HW1Data.xlsx from Canvas.  This file contains the first name and School of major for students in a certain class.

  1. (2 point)  Fill in the following table with the names and School of major (e.g. Medicine, Public Health, Nursing, Dentistry, Science, etc.) of five of your college friends or acquaintances.  These friends or acquaintances you fill in the table below can be students at IUPUI or any other university.

 

  1 2 3 4 5
Name          
School          

 

 

  1. (2 points)  How many were Public Health students?  Find the proportion of Public Health students in your sample by taking =

 

 

  1. (3 points)  Is the collection of names in #4 a simple random sample (SRS) of college students in the US?  Why or why not?  Do you think there is any bias involved?  If so, how?  Do you think your own major has anything to do with the names that you collected?

 

 

 

For the remaining problems, we will assume that the 25 individuals in HW1Data.xlsx form a “population”. In truth, this is not the case, but we are doing this exercise to illustrate the concepts of sampling and sampling variability.

  1. (5 points) Open the attached Excel file, HW1Data.xlsx, and note the first column, “Student”, which will be the Student Number for selecting simple random samples (SRS’s).  For this problem, you will select SRS’s using the classic “drawing from a hat” method. Create 25 small slips of paper, all of fairly equal size. On these slips of paper, write numbers from 1 to 25 and then fold them in half. Next, put the 25 slips of paper into a hat, a bowl, or something else you can draw from. Finally mix up the paper slips and then hold the hat/bowl up above your eye level and randomly pull out 5 slips of paper.  Write down the names who were selected and the School for each student selected.  Put the slips back into the hat/bowl, mix them up again, and repeat this process for 4 more times, to complete 5 simple random samples (SRSs). Fill in the names and Schools for your 5 SRS’s below (on the next page):

 

SRS #1:

  1 2 3 4 5
Name          
School          

 

SRS #2:

  1 2 3 4 5
Name          
School          

 

SRS #3:

  1 2 3 4 5
Name          
School          

 

SRS #4:

  1 2 3 4 5
Name          
School          

 

SRS #5:

  1 2 3 4 5
Name          
School          

 

  1. (4 points)  Find the sample proportion of Public Health students for each of your SRS’s using the method above from problem #5.  Enter your sample proportions below:

 

Sample proportions:

  SRS #1 SRS #2 SRS #3 SRS #4 SRS #5
         

 

Were all of the sample proportions in problem #8 the same?  Probably not.  Sample statistics will vary from sample to sample.  Our sample size is fairly small, so we have a lot of variability.  The larger the sample size, the smaller the sampling variability will be.  This will be an important fact that we will use all semester. 

 

  1. (4 points)  In most real life situations, we don’t know the population parameters.  However, looking at all the original data in the file HW1Data.xlsx, what is the true population proportion?

 

= ?

 

 

Within problems #7-8 above, how did your sample proportions from SRS #1 through SRS #5 compare to this population proportion?  Were they close?   A larger sample size will also give us more accurate results (sample statistics closer to the true population parameter).

 

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