Experimental and survey design

Transcription

1 Friday, October 12, 2001 Page: 1 Experimental and survey design 1. There is a positive association between the number of drownings and ice cream sales. This is an example of an association likely caused by: a. coincidence b. cause and effect relationship c. confounding factor d. common cause e. none of the above 2. A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude: a. that the remedy is effective for the treatment of headaches. b. nothing, because the sample size is too small. c. nothing, because there is no control group for comparison. d. that the new treatment is better than aspirin. that the remedy is not effective for the treatment of headaches. 3. A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively: a. a specific storage time, amount of vitamin C, a fruit pack b. a fruit pack, amount of vitamin C, a specific storage time c. random assignment, a fruit pack, amount of vitamin C d. a specific storage time, a fruit pack, amount of vitamin C e. a specific storage time, the nutritionist, amount of vitamin C 4. We wish to investigate if a new medicine is effective in reducing the length and severity of the flu. We take the next 20 patients that come to the walk-in clinic complaining of flu and, after a medical exam to verify that the patients do have the flu, we give them the new medicine and tell them about the new drug we are giving them. One week later, the patients are contacted and 15 patients state the new remedy was helpful in reducing the severity and length of the illness. Which of the following is NOT CORRECT? a. This is a poor experiment because there is no control group. We do not know how many would feel better in a week without treatment. b. This is a poor experiment because it is not double-blinded. The patients may feel relief because they thought the drug should work. c. This is a poor experiment because a convenience sample was selected. Patients who come to the a walk-in clinic may have more severe flu than people who do not. d. This is a poor experiment because we didn't give the remedy to people without the flu to assess its effect in a control group. This is a poor experiment because the sample size is likely to be too small to detect anything but a gross improvement in measuring the 5. A survey is to be undertaken of recent nursing graduates in order to compare the starting salaries of women and men. For each graduate, three variables are to be recorded (among others) sex, starting salary, and area of specialization. a. Sex and starting salary are explanatory variables; area of specialization is a response variable. b. Sex is an explanatory variable; starting salary and area of specialization are response

2 Friday, October 12, 2001 Page: 2 variables. c. Sex is an explanatory variable; starting salary is a response variable; area of specialization is a possible confounding variable. d. Sex is a response variable; starting salary is an explanatory variable; area of specialization is a possible confounding variable. e. Sex and area of specialization are response variables; starting salary is an explanatory variable. 6. Which of the following is CORRECT? a. We do not need to randomize if our sample size is sufficiently large. b. A large sample size always ensures that our sample is representative of the population. c. If all other things are equal, we need a larger sample size for a larger population. d. In a properly chosen sample, an estimate will be less variable with a large sample size and hence more precise. e. In random samples, the randomization ensures that we get precise and accurate estimates. 7. An experimenter wishes to test whether or not two types of fish food (a standard fish food and a new product) work equally well at producing fish of equal weight after a 2-month feeding program. The experimenter has 2 identical fish tanks (1 & 2) to put fish in and is considering how to assign the 40 tagged fish to the tanks. To properly assign the fish, one step would be to: a. put all the odd tagged numbered fish in one tank, the even in the other, and give the standard food type to the odd numbered ones b. obtain pairs of fish whose weights are virtually equal at the start of the experiment and randomly assign one to the group tank 1, the other to tank 2 with the feed assigned at random to the tanks. c. to proceed as in as in (b), but put the heavier of the pair into tank 2. d. assign the fish at random to the two tanks and give the standard feed to tank 1. e. not to proceed as in (b) because using the initial weight in (b) is a non-random process.use the initial length of the fish instead. 8. A researcher wishes to compare the effects of 2 fertilizers on the yield of a soybean crop. She has 20 plots of land available and she decides to use a paired experiment -- using 10 pairs of plots. Thus, she will: a. use a table of random numbers to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots. b. subjectively divide the 20 plots into 10 pairs (making the plots within a block as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots. c. use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each pair. d. flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use a table of random numbers to assign the fertilizers to the 2 plots. e. use a table of random numbers to assign the 2 fertilizers to the 20 plots and then use the table of random numbers a second time to place the plots into 10 pairs. 9. A student wishes to examine the effect of wing width and wing length on the length of flight of a paper airplane. There are 4 different models of airplanes. Which of the following is NOT correct? a. A factor (such as wing width) is an experimental variable under control of the experimenter. b. The order of flights was randomized to remove the influence of any other variables upon the flight distance of each flight. c. It would be better to make four copies of each model of plane to give some feel for the

3 Friday, October 12, 2001 Page: 3 plane-to-plane variations. Flying a single copy four times gives information about the internal variation. d. Interaction between two factors means that the effect of a factor at one level depends on the level of the second factor. e. Planned experiments (where randomization can take place) is one of the strongest pieces of evidence in try to establish a causal relationship. 10. An experiment was conducted where you flew paper airplanes after modifying wing depth and wing length. There were four different models of airplane. One design consideration was the choice between flying each plane four times or making four copies of each model, each of which is flown once. Which of the following is NOT correct? a. Flying multiple copies of each model (i.e. separate planes of each model) could give information on variability in flight due to fabrication effects (i.e. how you made the plane). b. Flying a single copy of each model four times could give information on variability in flight due to changes in initial launch conditions. c. The differences in flight length among the different models gives information on the "effects" of the design factors - wing depth and wing length. d. The response variable is flight length; the explanatory variables are wing depth and wing width. e. Interaction between the effects of wing depth and wing width implies that the effects of wing depth are the same for all wing widths. 11. An experiment was designed an experiment to investigate the effect of the amount of water and seed variety upon subsequent growth of plants. Each plant was potted in a clay plot, and a measured amount of water was given weekly. The height of the plant at the end of the experiment was measured. Which of the following is not correct? a. The response variable is the plant height. b. The explanatory variables are the amount of water and seed variety. c. Randomization was used to eliminate the effect of other possible factors upon the growth of the plants. d. A possible uncontrollable factor in this experiment is any nutrients that might be present in the clay pots. e. Designed experiments give the best evidence of "cause-and-effect" relationships. 12. A survey was conducted by visiting a student parking lot to estimate the proportion of cars that were red. Which of the following is NOT correct? a. If the sampled stall was empty, we can simply choose another stall, at random, to take its place because it is not likely that the stall being vacant is related to a car being red. b. The sample would be representative of the population if 100 cars were chosen regardless if randomization was used or not. c. Even though a random sample was taken from cars in the parking lot, the sample may not be representative of the cars driven by SFU students because the decision to park in B-lot is self-selected. d. If a another sample of cars was chosen, it is likely that a different proportion of cars that are red would be obtained. e. The confidence interval computed gave a 95% confidence interval for the true proportion of cars that were red in the population of cars that park in B-lot (assuming that the sample was selected using the 3 R's). 13. A survey was done to estimate the proportion of cars that are red and are Japanese made in the City of Vancouver by taking a random sample of size 25 from a student parking lot at Simon Fraser University. Which of the following is NOT CORRECT: a. This sample may not be representative of the cars in Vancouver because mainly students park at SFU.

4 Friday, October 12, 2001 Page: 4 b. If the particular stall is vacant, we can simply select another stall at random because it is unlikely that a stall is vacant is related to the color or manufacturer of the car. c. It would be dangerous to simply select the first 25 stalls in the lot closest to the Applied Science Building because there are a number of stall reserved for service vehicles whose primary color is white. d. Different students obtained different answers for their sample proportions. This is an example of a sampling distribution for an estimator. e. The margin of error will depend upon the total number of cars in the lot when we did the sample. 14. Discriminant analysis is a statistical technique, which attempt to find a set of variables to allow you distinguish among groups, e.g. in one of the assignments, you tried to distinguish among authors based on sentence length and other statistics. Which of the following is NOT CORRECT? a. We needed to adjust some variables to a "per 100 word basis" or to a "per sentence basis" to adjust for the different number of words in the texts where authorship is known. b. Potentially useful variables are selected by finding variables whose distribution are as similar as possible for all the authors. c. Another example of this method might be a bank making a decision on granting a student a loan based on characteristics such as grade point average, past credit history, etc. d. We looked at many pairs of plots to find the pair of variables that gave the best separation between the two authors. Because of natural variability, errors can always be made. However, the goal of this analysis is to minimize the costs of misclassification. 15. An experiment was conducted where here you tried to distinguish among authors based on sentence length and other statistics. Which of the following is NOT correct? a. We needed to adjust some variables to a "per 100 word basis" to adjust for the different number of words on a page. b. This was a simplified form of discriminant analysis where, in general, one wishes to distinguish among groups of objects based on characteristics observed. c. Another example of this method might be a bank making a decision on granting a student a loan based on characteristics such as grade point average, past credit history, etc. d. The polygon plot is a way of "enclosing" typical values of the statistics for each author. e. Potentially useful variables are selected by finding variables whose distribution are as similar as possible for all the authors. 16. An experiment was conducted where you analyzed the results of the plant growth experiment after you manipulated the amount of water and seed variety. Which of the following is correct? a. We randomized the plants to plots to eliminate any effect of hidden variables. b. We could determine the best combination of water and seed variety by examining the difference in the plant height in the final week of the experiment. c. The variability in growth among plants of the same variety who received the same amount of water was constant over time. d. The growth of a particular plant in week 3 is likely to be independent (unrelated) of the growth of the same plant in week 2. e. The growth of the plants was linear over time. 17. The following numbers are extracted from a table of random digits:

5 Friday, October 12, 2001 Page: A scientist will be measuring the total amount of woody debris in a random sample of sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02,..., 45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct? a. Her sample is 38, 25, 02, 38, 22 b. Her sample is 38, 68, 35, 02, 22 c. Her sample is 38, 35, 27, 28, 08 d. Her sample is 38, 65, 35, 02, 79 e. Her sample is 38, 35, 02, 22, We wish to draw a sample of size 5 without replacement from a population 50 households. Suppose the households are numbered "01", "02",, "50", and suppose that the relevant line of the random number table is: Digits Then the households selected are: a. households b. households c. households d. households households An experiment to measure the effect of giving growth hormones to girls affected by Turner s Syndrome was carried out recently in Vancouver. All 34 girls in the study were given the growth hormone and their heights were measured at the time the hormone was given and again one year later. No measurements were made on their final adult heights. Which of the following is NOT a problem with this experiment: a. there was no blinding b. there was no control group c. nonresponse bias d. there was insufficient attention to the placebo effect e. Because final heights were not measured, it would be impossible to tell if the hormone affected final height or only accelerated growth and made no difference to final height. 20. Which of the following statements is FALSE? a. Nonresponse can cause bias in surveys because non-respondents often tend to behave differently from people who respond. b. Nonsampling errors are often bigger than the random sampling errors in surveys. c. Slight changes in the wording of questions can make a measurable difference to survey results. d. People will sometimes answer a question differently for different interviewers. e. Sophisticated statistical methods can always correct the results if the population you are sampling from is different from the population of interest, e.g. due to undercoverage. 21. A properly conducted random survey selected 1000 Canadians (from a total population of about 30 million) and 1000 Americans (from a total population of about 300 million). Which of the following is FALSE? a. Randomization ensures that both samples are representative of their respective populations. b. The precision is determined by the ratio of the sample size to the total population size. c. A smaller proportion of the American population has been chosen. Therefore, a

6 Friday, October 12, 2001 Page: 6 particular person has a smaller chance of being selected in America than in Canada. d. A potential stratification variable for both countries could be location - eastern, middle, or western continental. Random digit dialing to select people for the survey could induce biases in the results if the characteristic of interest for the survey is 22. A recent survey by a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important are universities to the Canadian economy". The main problem with using these results to draw conclusions about the general public s perception is: a. selection bias b. insufficient attention to the placebo effect c. no control group d. non-response bias e. interviewer bias