Chapter 13 Notes Chapter 12 Part I 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 unfoldCORRECTION: #40 of unit questions change word “allowed” to “followed”

Definitions:

4) Experiment - actively impose some treatment in order to observe the response

3) Retrospective study – Identifying subjects and use data from events that have already occurred

I’ve developed a new rabbit food, Hippity Hop.

Rabbit Food

Helps rabbits develop a shiny

coat & gives them more energy as

they grow.100% of

daily vitamins & essential

oils!

Can I just make this claim?

What must I do to make this claim?

Who (what) should I test this on?

What do I test?

NO

Do an experiment

Rabbits

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

9) Response variable – what you measure after the treatment is applied.

8) Treatment – a specific experimental condition applied to the experimental units.• Each factor/level combination

is a treatment

• 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

Hippity HopI’ll use my pet rabbit, Lucky!

Since Lucky’s coat is shinier & he has more energy, then Hippity Hop is a better rabbit food!

Not good enough.This might have happened any way.

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

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.

WOW! Lucky is bigger & shinier so Hippity Hop is better!

WOW! Lucky is bigger & shinier so Hippity Hop is better!

Not good enough. Lucky may have grown bigger with the old food.


The first five rabbits that I catch

will get Hippity Hop food and the remaining five will get the old food.

The Hippity Hop rabbits have scored higher so it’s the better food!

Not good enough. The rabbits must be randomly assigned.


Number the rabbits from 1 – 10.

Place the numbers in a hat.

1

2

3

45

6

78

9 10

The first five numbers pulled from the hat will be the rabbits that get

Hippity Hop food.

I evaluated the rabbits & found that the rabbits eating Hippity Hop are better than the old food!

The remaining rabbits get the old food.

39857

Much better if the one evaluating doesn’t know which food was given.

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

• 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

14.

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

The ONLY way to show cause & effect is with a well-designed, well-controlled experiment!!15. 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?

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

Cake batter

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.

Type of soil, amount of water, etc.

NO – a placebo is not needed in this experiment

Experiment Designs

• Completely randomized – all experimental units are allocated at random among all treatments

Ran

dom

ass

ign

men

tTreatment group 1

Treatment group 2

Treatment group 3

response

variable

16.

Treatment C

Treatment B

Completely randomized design

Randomly assign experimental units

to treatments

Treatment A

Treatment D

17.• Randomized block – units are

blocked into groups and then randomly assigned to treatments

Group 1

Group 2

Treatment 1Treatment 2Treatment 3

Treatment 3Treatment 2Treatment 1

response

varaible

Ran

dom

A

ssig

nm

ent

Ran

dom

A

ssig

nm

ent

Treatment B

Randomized block design

Randomly assign experimental units

to treatments

Treatment A

Put into homogeneous groups

Treatment A Treatment B

–match up experimental units according to similar characteristics & randomly assign one to one treatment & the other automatically gets the 2nd treatment

•Matched pairs – a special type of block design

18.

Pair experimental units according to

specific characteristics.

Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B.

Treatment A Treatment B

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.

Guess what happened?


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?


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

Does the bank want to use all 4

possible treatments?

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?

Age – younger people are more at risk to be victims of violent crimes

No, no treatment was imposed on people.

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?What type of design is this?

Factors? Levels?

Response variable?

Yes, a treatment is imposed.

Completely randomized

one factor: word-processing program with 4 levels

speed

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?Yes, you could a design where each person uses each program in a random order.

This is considered a type of matched pair design.

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

Randomly assigned treatment to first acre of each two-acre plot

Each 2-acre plot probably gets equal rainfall. Probably has same soil too.

Randomization reduces bias by spreading any uncontrolled variables evenly throughout the treatment groups.

Blocking also helps reduce variability.

20.

21.


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. citizensb) Parameter of interest: Type of content that bothers most on TVc) Sampling Frame: All U.S. adultsd) Sample: 1423 randomly selected U.S. citizense) Sampling Method: Unknownf) Sources of Bias: None apparent


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 ageb) Parameter of interest: Proportion who think drinking & driving is a serious problemc) Sampling Frame: Adults at particular bard) Sample: every 10th person leaving the bare) Sampling Method: Systematic samplingf) 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 consideringthe 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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.

Chapter 12 Part II Answers28. 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.


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.


c) Why do you think a simple random sample might not provide the representative opinion the company seeks?


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.


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 11Chen02DeLara 07DeRoos 12Grigorov03Maceli 08Mulvaney 13Pagliarulo04Rosica 09Smithson 14Tadros05Williams 10Yamamoto

Random Number Table28914 26687 49104 48827 42036

Use two-digits and Ignore 15-99 and 00Base on these pre-assigned two-digit numbers and the random number table shownYamamoto and Maceli would be selected.

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

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