Chapter 12 Part II Answers

Chapter 12 Part II Answers
Chapter 13 Notes Chapter 12 Part I Answers Chapter 12 Part II Answers

Chapter 13 Experimental Design

Definitions: 1) Observational study - observe outcomes without imposing any treatment 2) Prospective study – Identifying subjects in advance and collecting data as events unfold CORRECTION: #40 of unit questions change word “allowed” to “followed”

Definitions: 3) Retrospective study – Identifying subjects and use data from events that have already occurred 4) Experiment - actively impose some treatment in order to observe the response

100% of daily vitamins & essential oils!
I’ve developed a new rabbit food, Hippity Hop. Helps rabbits develop a shiny coat & gives them more energy as they grow. Hippity Hop Rabbit Food 100% of daily vitamins & essential oils!

Can I just make this claim?
NO What must I do to make this claim? Do an experiment Who (what) should I test this on? Rabbits What do I test? The type of food

5)Experimental unit – the single individual (person, animal, plant, etc.) to which the different treatments are assigned 6) Factor – is the explanatory variable 7) Level – a specific value for the factor

8) Treatment – a specific experimental condition applied to the experimental units.
Each factor/level combination is a treatment 9) Response variable – what you measure after the treatment is applied. What is affected by the factor

I plan to test my new rabbit food. What are my experimental units?
What is my factor? What is the response variable? Rabbits Type of food How well they grow

I’ll use my pet rabbit, Lucky!
Hippity Hop Not good enough. This might have happened any way. Discuss the need for a comparison group. Since Lucky’s coat is shinier & he has more energy, then Hippity Hop is a better rabbit food!

10) Control group – a group that is used to compare the factor against; can be a placebo or the “old” or current item 11) Placebo – a “dummy” treatment that can have no physical effect

WOW! Lucky is bigger & shinier so Hippity Hop is better!
Not good enough. Lucky may have grown bigger with the old food. Old Food Hippity Hop Now I’ll use Lucky & my friend’s rabbit, Flash. Lucky gets Hippity Hop food & Flash gets the old rabbit food. Discuss the need for replication. WOW! Lucky is bigger & shinier so Hippity Hop is better!

The Hippity Hop rabbits have scored higher so it’s the better food!
Not good enough. The rabbits must be randomly assigned. Old Food Hippity Hop The first five rabbits that I catch will get Hippity Hop food and the remaining five will get the old food. Discuss the need for random assignment to treatment groups. The Hippity Hop rabbits have scored higher so it’s the better food!

Much better if the one evaluating doesn’t know which food was given.
Old Food Hippity Hop Number the rabbits from 1 – 10. Place the numbers in a hat. The first five numbers pulled from the hat will be the rabbits that get Hippity Hop food. The remaining rabbits get the old food. 8 5 7 3 9 6 Discuss the need for the evaluator to be blinded 2 4 5 I evaluated the rabbits & found that the rabbits eating Hippity Hop are better than the old food! 10 1 9 7 3 8

12) blinding - method used so that experimental units do not know which treatment they are getting
13) double blind - neither the experimental units nor the evaluator know which treatment was received

Principles of Experimental Design
14. Principles of Experimental Design Control of effects of extraneous variables on the response – by comparing treatment groups to a control group (placebo or “old”) Replication of the experiment on many subjects to quantify the natural variation in the experiment Randomization – the use of chance to assign subjects to treatments

The ONLY way to show cause & effect is with a well-designed, well-controlled experiment!

Example 1: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Experimental units? Factors? Levels? Response variable? How many treatments? Plots of land Type of fertilizer Fertilizer types A, B, & C Yield of crop 3

Example 2: A consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum, glass, and plastic pans in both gas and electric ovens. Experiment units? Factors? Levels? Response variable? Number of treatments? Cake batter Two factors - type of pan & type of oven Type of pan has 3 levels (aluminum, glass, & plastic & type of oven has 2 levels (electric & gas) How evenly the cake bakes 6

Why is the same type of seed used on all 15 plots?
Example 3: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Why is the same type of seed used on all 15 plots? What are other potential extraneous variables? Does this experiment have a placebo? Explain It is part of the controls in the experiment. To control the factor of type of seed. Type of soil; amount of water, sunlight, etc. No, one would compare the three types of fertilizers Type of soil, amount of water, etc. NO – a placebo is not needed in this experiment

Experiment Designs 16. Completely randomized – all experimental units are allocated at random among all treatments Treatment group 1 response Random assignment Treatment group 2 variable Treatment group 3

Completely randomized design
Treatment A Treatment B Treatment C Treatment D Randomly assign experimental units to treatments Completely randomized design

17. Randomized block – units are blocked into groups and then randomly assigned to treatments Random Assignment Treatment 1 Group 1 Treatment 2 Treatment 3 response varaible Treatment 1 Random Assignment Group 2 Treatment 2 Treatment 3

Randomized block design
Treatment B Treatment A Treatment A Treatment B Put into homogeneous groups Randomly assign experimental units to treatments Randomized block design

a special type of block design
18. Matched pairs – a special type of block design match up experimental units according to similar characteristics & randomly assign one to one treatment & the other automatically gets the 2nd treatment

Pair experimental units according to specific characteristics.
Treatment A Treatment B Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B. Pair experimental units according to specific characteristics. This is one way to do a matched pairs design – another way is to have the individual unit do both treatments (as in a taste test).

19) Confounding – When the levels of one factor are associated with the levels of another factor so their effects cannot be separated, we say that these two factors are confounded

Confounding can arise from a badly designed multifactor experiment.
A credit card bank wanted to test the sensitivity of the market to two factors: the annual fee charged for a card and the annual percentage rate charged. The bank sent out 50,000 offers with a low rate and no fee, and 50,000 offers with a higher rate and a $50 fee. Ask for 4 male & 4 female volunteers Randomly assign to treatments – no confounding between gender & deodorant Block by gender & randomly assign – no confounding Block by gender – give females new deodorant & males get current – NOW have confounding! Guess what happened?

What should they have done?
Confounding can arise from a badly designed multifactor experiment. A credit card bank wanted to test the sensitivity of the market to two factors: the annual fee charged for a card and the annual percentage rate charged. The bank sent out 50,000 offers with a low rate and no fee, and 50,000 offers with a higher rate and a $50 fee. People preferred the low-rate, no-fee card. But the bank couldn’t answer their original question. What should they have done? Ask for 4 male & 4 female volunteers Randomly assign to treatments – no confounding between gender & deodorant Block by gender & randomly assign – no confounding Block by gender – give females new deodorant & males get current – NOW have confounding!

Does the bank want to use all 4 possible treatments?
Confounding can arise from a badly designed multifactor experiment. A credit card bank wanted to test the sensitivity of the market to two factors: the annual fee charged for a card and the annual percentage rate charged. The bank sent out 50,000 offers with a low rate and no fee, and 50,000 offers with a higher rate and a $50 fee. People preferred the low-rate, no-fee card. But the bank couldn’t answer their original question. What should they have done? They needed four treatments: - Low rate & no fee - High rate & no fee - Low rate & $50 fee - High rate & $50 fee Ask for 4 male & 4 female volunteers Randomly assign to treatments – no confounding between gender & deodorant Block by gender & randomly assign – no confounding Block by gender – give females new deodorant & males get current – NOW have confounding! Does the bank want to use all 4 possible treatments?

Is this an experiment? Why or why not?
Example 4: An article from USA Today reports the number of victims of violent crimes per 1000 people. 51 victims have never been married, 42 are divorced or separated, 13 are married, and 8 are widowed. Is this an experiment? Why or why not? What is a potential confounding variable? No, no treatment was imposed on people. Age – younger people are more at risk to be victims of violent crimes

Is this an experiment? Why or why not?
Example 5: Four new word-processing programs are to be compared by measuring the speed with which standard tasks can be completed. One hundred volunteers are randomly assigned to one of the four programs and their speeds are measured. Is this an experiment? Why or why not? Yes, a treatment is imposed. Yes, a treatment was imposed Completely randomized one factor, word processing program & 4 levels, the four new programs Speed at which standard tasks can be done What type of design is this? Factors? Levels? Response variable? Completely randomized one factor: word-processing program with 4 levels speed

Can this design be improved?
Example 5: Four new word-processing programs are to be compared by measuring the speed with which standard tasks can be completed. One hundred volunteers are randomly designed to one of the four programs and their speeds are measured. Can this design be improved? a) Speed/expertise of each individual b) Use a matched pairs design where each volunteer uses all four programs in random order Yes, you could a design where each person uses each program in a random order. This is considered a type of matched pair design.

What type of design is this? Why use this method?
Example 6: Suppose that the manufacturer wants to test a new fertilizer against the current one on the market. Ten 2-acre plots of land scattered throughout the county are used. Each plot is subdivided into two subplots, one of which is treated with the current fertilizer, and the other with the new fertilizer. Wheat is planted and the crop yields are measured. What type of design is this? Why use this method? When does randomization occur? Matched - pairs design Each 2-acre plot probably gets equal rainfall. Probably has same soil too. Randomly assigned treatment to first acre of each two-acre plot

Blocking also helps reduce variability.
20. Randomization reduces bias by spreading any uncontrolled variables evenly throughout the treatment groups. 21. Blocking also helps reduce variability.

Chapter 12 Part I Answers a) Population: U.S. citizens
4. (chapter 12) The Gallup Poll interviewed 1423 randomly selected American citizens September 10-14, 1999, and reported that when “asked which type of content bothers them most on TV, 44% of Americans identify ‘violence,’ 23% choose ‘lewd and profane language,’ while 22% say ‘sexual situations.’” a) Population: U.S. citizens b) Parameter of interest: Type of content that bothers most on TV c) Sampling Frame: All U.S. adults d) Sample: 1423 randomly selected U.S. citizens e) Sampling Method: Unknown f) Sources of Bias: None apparent

Chapter 12 Part I Answers a) Population: Adults of drinking age
5. (chapter 12) Researchers waited outside a bar they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the bar and asked whether he or she thought drinking and driving was a serious problem. a) Population: Adults of drinking age b) Parameter of interest: Proportion who think drinking & driving is a serious problem c) Sampling Frame: Adults at particular bar d) Sample: every 10th person leaving the bar e) Sampling Method: Systematic sampling f) Sources of Bias: Only asking adults that have probably been drinking --- Undercoverage

11. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Put a big ad in the newspaper asking people to log their opinions on the PTA website. This is a voluntary response sample. Only those who see the ad, feel strongly about the issue, and have web access will respond.

11. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. b) Randomly select one of the elementary schools and contact every parent by phone. This is cluster sampling, but probably not a good idea. The opinions of parents in one school may not be typical of the opinions of all parents.

11. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. c) Send a survey home with every student, and ask parents to fill it out and return it the next day. This is an attempt at a census, and will probably suffer from nonresponse bias.

11. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. d) Randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. This is stratified sampling. If the follow-up is carried out carefully, the sample should be unbiased.

12. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they favor or oppose the plan. This sampling method suffers from voluntary response bias. Only those who see the show and feel strongly will call.

12. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. b) Hold a PTA meeting at each of the 20 elementary schools and tally the opinions expressed by those who attend the meetings. Although this method may result in a more representative sample than the method in part a), this is still a voluntary response sample. Only strongly motivated parents attend PTA meetings.

12. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. c) Randomly select one class at each elementary school and contact each of those parents. This is multistage sampling, stratified by elementary school and then clustered by grade. This is a good design, as long as the parents in the class respond. There should be follow-up to get the opinions of parents who do not respond.

12. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. d) Go through the district’s enrollment records, selecting every 40th parent. PTA volunteers will go to those homes to interview the people chosen. This is systematic sampling. As long s a starting point is randomized, this method should produce reliable data.

23. Anytime we conduct a survey we must take care to avoid undercoverage. Suppose we plan to select 500 names form the city phone book, call their homes between noon and 4p.m., and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? A SRS is difficult in this case because there is an issue with undercoverage. People with unlisted phone numbers and those without phones are not in the sampling frame. People who are at work, or otherwise away from home, are included in the sampling frame. However, these people could never be in the sample itself.

23. Anytime we conduct a survey we must take care to avoid undercoverage. Suppose we plan to select 500 names form the city phone book, call their homes between noon and 4p.m., and interview whoever answers, anticipating contacts with at least 200 people. b) Describe a more convenient, but still random, sampling strategy. One possibility is to generate random phone numbers and call at random times, although obviously not in the middle of the night. This would take care of the undercoverage of people at work during the day, as well as people with unlisted numbers, although there is still a problem avoiding undercoverage of people without phones.

23. Anytime we conduct a survey we must take care to avoid undercoverage. Suppose we plan to select 500 names form the city phone book, call their homes between noon and 4p.m., and interview whoever answers, anticipating contacts with at least 200 people. c) What kinds of households are likely to be included in the eventual sample of opinion? Who will be excluded? Under the original plan, those families in which one person stays home are more likely to be included. Under the second plan, many more are included. People without phones are still excluded.

23. Anytime we conduct a survey we must take care to avoid undercoverage. Suppose we plan to select 500 names form the city phone book, call their homes between noon and 4p.m., and interview whoever answers, anticipating contacts with at least 200 people. d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? Follow-up of this type greatly improves the chance that a selected household is included, increasing the reliability of the survey.

23. Anytime we conduct a survey we must take care to avoid undercoverage. Suppose we plan to select 500 names form the city phone book, call their homes between noon and 4p.m., and interview whoever answers, anticipating contacts with at least 200 people. e) Random digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded? Random dialers allow people with unlisted phone numbers to be selected, although they may not be the most willing participants. There is a reason that the phone number is unlisted. Time of day will still be an issue, as will people without phones.

28. A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. a) Do you see any danger of bias in the company’s plan? Explain. A small sample will probably consist mostly of laborers, with few foremen, and maybe no project managers. Also, there is a potential for response bias based on the interviewer if a member of management asks directly about discontent. Workers who want to keep their jobs will likely tell the management that everything is fine.

28. A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. b) Propose a sampling strategy that uses a simple random sample. Assign a number 001 to 439 to each employee. Use a random number table to select the sample.

28. A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. c) Why do you think a simple random sample might not provide the representative opinion the company seeks?

28. A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. d) Propose a better sampling strategy. A better strategy would be to stratify the sample by job type. Sample a certain percentage of each job type.

28. A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. e) Listed below are the last names of the project managers. Use random numbers at the bottom to select two people to be interviewed. Be sure to explain your method carefully. 01Barrett 06Bowman 11Chen 02DeLara 07DeRoos 12Grigorov 03Maceli 08Mulvaney 13Pagliarulo 04Rosica 09Smithson 14Tadros 05Williams 10Yamamoto Random Number Table Use two-digits and Ignore and 00 Base on these pre-assigned two-digit numbers and the random number table shown Yamamoto and Maceli would be selected.

Chapter 12 Part II Answers

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