AP Statistics Experimental Design. Penny Smeltzer

Transcription

1 AP Statistics Experimental Design Penny Smeltzer

2 First step: What are you trying to measure or count? What population are you interested in? Determine the explanatory and response variable How will you select your subjects or experimental units?

3 Simple Random Sample

4 Stratified Random Sample

5 Cluster Sample

6 Cluster Sample

7 Systematic Random Sample Line them up and take every fourth person

8 Other Questions to ask Is blocking needed? If so, why? What treatment is needed for the control group? Should our experiment be blind? double blind?

9 Galapagos land iguana

10 A researcher is interested in the weight of land iguanas. First, he separates the available iguanas by gender. Then he randomly selects 20 male iguanas and 20 female iguanas. Did he achieve a simple random sample? No, this is a stratified random sample.

11 Marine iguanas do not really pay attention to humans. Historically they have had no reason to fear them.

12 Now with the influx of tourists, the iguanas are becoming more timid. Conservationists are interested in the distance at which an iguana begins to show alarm with and without exposure to tourists. Design an experiment. Response variable? The researcher has 100 marine iguana eggs and two habitats with which to work. What are our experimental units? What is the treatment? Explanatory variable?

13 Design a study to determine whether human contact makes a difference in the distance at which iguanas become alarmed.

14 How do we write about randomization? Randomly choose 50 eggs for treatment by throwing them all in a bag, shaking them gently, then pulling out 50. Assign the 50 chosen iguanas the treatment by placing them in an area tourists frequent. Place the remaining 50 iguanas in an area where tourists are not allowed. Wait a month, then measure the distance a person can approach before each iguana shows distress. Compare results. How?

15 Would a diagram be appropriate? What s first? 100 eggs randomly select 50* remaining 50 Place in habitat A Place in habitat B measure alarm distance measure alarm distance compare results *Randomly choose 50 eggs for treatment by throwing them all 100 eggs in a bag, shaking them gently, then pulling out 50. Or number the eggs and use a random number generator to select 50 with no repeats.

16 How could we include blinding in this experiment? Do not let the person measuring the distress response know which treatment group each iguana came from. Should we consider a double blind process? That s just silly!

17 On Isabella, there are both land iguanas and marine iguanas. How might we change our experiment? Why should we?

18 Blocking reduces variation. It s possible that land and marine iguanas react differently to tourists. Why is this important?

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22 A typical U.S. landfill

23 An environmentalist believed education was the key to better recycling habits. He selected two high schools in Austin, Texas. At one school science teachers emphasized the importance of recycling. The other school had science classes as usual. On trash days he randomly selected students from each school and weighed the amount of recycled material from each student s household. Students from the school with more recycling education had significantly more recycling in their household trash. Does this provide enough evidence for the environmentalist to begin a nationwide television ad campaign for recycling? Why or why not?

24 No. We cannot conclude education will improve recycling efforts nationwide since only Austin was studied. We can only generalize to the students of Austin. We did not randomly select students from the entire country.

25 How can we reduce bias? Randomization How do we reduce the effects of confounding variables? Include a control group in our design

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28 How can we reduce variation? Incorporate blocking What is a key difference between an experiment and an observational study? a treatment end here

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31 Deforestation and hunting have limited the habitats for Madagascar s lemur populations. Currently 15 species of lemurs have become extinct and others are in peril. A researcher hopes to plant a new type of bush in the area to help sustain the lemur populations. Before he begins he must show that lemurs will remain healthy on the new food source. He has 12 lemurs available to test his new diet.

32 Lemur # gender species 1 male Black 2 female Black 3 male Mouse 4 male Black 5 female Mouse 6 male Mouse 7 male Black 8 female Black 9 male Mouse 10 female Mouse 11 male Black 12 male Mouse

33 Lemur # gender species 1 male Black 2 female Black 3 male Mouse 4 male Black 5 female Mouse 6 male Mouse 7 male Black 8 female Black 9 male Mouse 10 female Mouse 11 male Black 12 male Mouse a) The researcher will use two treatments; the new plant as food and the native plants as food. He believes that lemur health due to diet may differ with species but not gender so he will block by species. Describe a randomized block design and identify the lemurs by number that will be used for each treatment.

34 The lemurs selected for the new food source are numbered 1, 4, 7, 3, 6, 12. The remaining lemurs will receive the native food source. Compare treatments within each block. Lemur # gender species 1 male Black 2 female Black 3 male Mouse 4 male Black 5 female Mouse 6 male Mouse 7 male Black 8 female Black 9 male Mouse 10 female Mouse 11 male Black 12 male Mouse a) First block by species One block contains lemurs 1, 2, 4, 7, 8, and 11 since they are all Black lemurs. The other block contains lemurs 3, 5, 6, 9, 10, and 12 since they are all mouse lemurs. Randomly select 3 Black lemurs by placing their numbers in a bag and drawing out 3 without replacement. Follow the same procedure to randomly select 3 mouse lemurs.

35 Notice the luxury lodging for scientists in the field.

36 b) Another researcher believes that health due to diet may differ by both species and gender and wants to block by both. Identify the lemurs in each block by number and give the criteria you used to form the blocks.

37 Lemur # gender species 1 male Black 2 female Black 3 male Mouse 4 male Black 5 female Mouse 6 male Mouse 7 male Black 8 female Black 9 male Mouse 10 female Mouse 11 male Black 12 male Mouse There will be 4 blocks: What are they? 1) female mouse lemurs #5 and 10 2)male mouse lemurs #3, 6, 9, and 12 3)female Black lemurs #2 and 8 4) male Black lemurs #1, 4, 7, and 11 Randomly select ½ of the lemurs in each block for the new food source by placing their numbers in a bag and drawing out 1/2 without replacement. Follow the same procedure for each block. The lemurs selected for the new food source are numbered 10, 3, 12, 2, 1, and 7. The remaining lemurs will receive the native food source.

38 How could you sketch out this block design?

39 *random selection female mouse 5, 10 * new food - 10 native food - 5 measure health measure health compare results 12 lemurs male mouse 3,6,9,12 female Black 2,8 * * new food 3,12 measure native food 6,9 health measure new food - 2 health native food - 8 measure health measure health compare results compare results male Black 1,4,7,11 * new food 1,7 native food 4,11 measure health measure health compare results

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41 1. A human resources director of a large company is interested in how often employees use their computers during breaks. She watches a selected group of employees at their desks during the break times. This study would best be described as A)a census B) a survey C) an observational study D) an experiment E) a sample

42 2. A company wants to compare two washing detergents (Brands A and B) to see which best keeps colors from fading. Twenty new, identical red t-shirts will be used in the trials. Ten t-shirts are washed 15 times with Brand A in warm water. The other 10 t-shirts are washed in Brand B in cold water. The amount of fading is rated on a 0 to 100 scale, and the mean for the t-shirts washed in Brand A is compared to the mean for the others. Is this a good experimental design? E) Yes A) No, because the means are not the proper statistics for comparison. B) No, because more than two brands of detergent should be used. C)No, because more temperatures of water should be used. D)No, because water temperature is confounded with brand of detergent.

43 3. The state would like to evaluate the usefulness of a program to randomly test high school athletes for steroid use. Initially, a state agency will test athletes in all 20 schools in Fort Worth, randomly selecting 3 athletes from each school. Is this a simple random sample of student athletes in Fort Worth? A) Yes, because athletes will be chosen at random. B) Yes, because each athlete is equally likely to be chosen. C)Yes, because stratified sampling is a special case of simple random sampling. D)No, because not all possible groups of 60 athletes could be in the sample. E) No, because a random sample of Fort Worth schools is not chosen.

44 4. Which of the following sample designs does NOT contain a source of bias? A) A legislator wishes to know how his district feels about a particular issue. As a result, his office s a long, detailed survey about the issue to a random sample of adults in his district. B) A polling organization uses the telephone directory to randomly select adults for a telephone survey to obtain opinions on the current president. C) All 250 students at a review session are given numbered tickets. Five numbers are chosen randomly, and the individuals with the winning ticket numbers each win a $10 gift card. D) A news show asks viewers to call a toll-free number to express their opinions about their choice for president. E) A teacher asks high school students how often they drink alcohol.

45 5. A college counselor would like to select a simple random sample of all the 525 students in the college. She uses the numbers from 001 to 525 to number the students in a college database and then uses a random number table to choose her sample of 30. What numbers correspond to the first 5 students chosen? A) D) B) E) C)

46 6. Twenty men and 20 women with migraine headaches were subjects in an experiment to determine the effectiveness of a new pain medication. Ten of the 20 men and 10 of the 20 women were chosen at random to receive the new drug. The remaining 10 men and 10 women received a placebo. The decrease in pain was measured for each subject. The design of this experiment is A) completely randomized with one factor, gender B) completely randomized with one factor, drug C) randomized block, blocked by drug and gender D) randomized block, blocked by gender E) randomized block, blocked by drug

47 7. A student organization wants to assess the attitudes of students toward a proposed change in the hours the library is open. they randomly select 50 freshman, 50 sophomores, 50 juniors, and 50 seniors to survey. This situation is described as A) a stratified random sample B) a simple random sample C) a convenience sample D) a systematic random sample E) an observational study

48 8. A group of 420 college students are enrolled in a blind taste test. The school s food service wants to see if they can improve the taste of their lattes. They decide to try two types of coffee beans (Arabica and Robusta); three types of syrup (vanilla, hazelnut, and mocha); and two types of milk (soy and low fat). The best combination of ingredients is sought. The latte experiment will have A) 2 factors, 7 levels, and 420 treatments B) 2 factors, 3 levels, and 12 treatments C) 3 factors, 7 levels, and 420 treatments D) 3 factors, 12 levels, and 420 treatments E) 3 factors, 7 levels, and 12 treatments

49 9. The primary reason for using blocking when designing an experiment is to reduce A) variation B) the need for randomization C) bias D) confounding E) the sensitivity of the experiment

50 10. The head of the admissions office at a small college wants to understand why minority students who visit her school do not eventually enroll. The college holds a preview weekend for students who have been admitted. Two months later, after the students have decided which college to attend, a survey is sent out to all minority students who attended the weekend visit but who did not choose to attend this college. About a third of them returned the survey, with 48% of those indicating that they received a larger scholarship offer elsewhere. Which is true? I. The population of interest is all potential college students. II. This survey design suffered from non-response bias. III. Because it comes from a sample, 48% is a parameter, not a statistic. A) I only B) II only C) I and II only D) II and III only E) I, II, and III

51 First up Experimental Design Know the vocabulary. population vs sample parameter vs statistic placebo control group blocking confounding variables discrete vs continuous observational study vs experiment blind or double blind randomization