10_w4_s3_chapter_12

10_w4_s3_chapter_12 - Week four Session one(chapter 12 Week...

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Unformatted text preview: Week four Session one (chapter 12) Week 4 Sessions one and two were review and midterm one Professor Esfandiari Major concepts: Population: All the possible entities (example individuals) of interest Sample: A fraction of the population Bias: Under or over-emphasizing some characteristic or attribute of the population. A sample that is biased is not a good representative of the population Randomness: A mean of minimizing bias and ascertaining that on the average the sample represents the population If we draw repeated random samples from the population, you will see that they resemble each other and the population. Sample size is an important consideration here because if the samples are too small, the likelihood that they resemble each other and the overall population decreases. How large of a sample do we need? An issue that we will discuss in detail when discussing margin of error and confidence interval Census: Including everybody in the population in the sample. In that sense the population and the sample become the same and you do have not use any particular method of sampling Summa table of notations for the sam 1e and o ulation Poulation u (read at mue) CA2 (sigma squared> Standard Deviation 0 (sigma) P Correlation coefficient m (Beam) {50 (Beta zero) Different type of samples A H {3" O v O" H "U U) U) U) H > > NI § [\3 ‘6‘ L D“ a ('D 1\./ Simple Random Sample (SRS): Each person has an equal chance of being selected and the choice of one individual is independent of the choice of the other Sampling frame: Is the list of the individuals from which the sample is drawn Repeated random samples differ from each other and this is called sampling variability. For instance, if we choose 50 different sample of size 30 and calculate the mean each time, the thirty means will be different from each other and we will create a variance called the variance of the sample means and show it with [8/2 ( 30]. As the size of the sample increases this variability decreases. As you will see in the future chapters SAZ ( X) = SA2/N (variance of sample means) How do we select a SRS? ° Table of random digits ' The computer can generate an SRS Stratified Random Sampling: The population is divided into a number of strata and them we conduct simple random sampling to choose individuals from each stratum. Each stratum is homogeneous. But, they differ from one another. Cluster sampling: Dividing the population to clusters, choosing representative clusters, and conducting a census like data collection within each cluster; that is all of the individuals in the cluster will be part of the sample. Clusters are heterogonous. But, they resemble the overall population. Multistage sampling: Combining several schemes of sampling is called multistage. Example of different types of samples: You are iven the followin information about a school district Elementa Middle scools Number of Number of schools teachers administrators Number of Number of A, B, C, and D D, E, F, and G each have four each have four elementary elementary staff teachers = 150 = 300 classes at first, classes at sixth, second, third, seventh, and (110 women (200 women fourth and fifth eighth, and and 40 men) and 100 men) grade. ninth grade. Number of Number of students in each students in each class = 40 Total classes in four schools 5*4 = 20 class = 40 Total classes in the four middle schools = 4*4 = 16 Total number Number of of middle middle school school teachers staff = 200 (120 = 180 women and 80 (90 women and men) 90 men Total number Total number of elementary of middle classes in the school classes district = in the district = 20* 4 = 80 Total number of elementary students in the district = 80*40 = 3200 16* 4 = 64 Total number of middle school students = 64*40= 2560 Total number of staff in the district = 500 Total number of teachers in the district = 3 3 0 Examples of different types of sampling: Simple random sample: We want to find out how happy the staff are with then new health insurance plan that the district is proposing. It requires the staff to fill out a rather lengthy questionnaire and participate in focus groups. So, it is not feasible to include all of the 500 in the study. To pick a simple random sample, we could number all of the staff from 1—500 and use a table of random digits to generate the sample of our interest. Suppose we use the table of random digits given on page eight. What we need to do is to close our eyes and choose a number and then go across in rows or go down in columns and choose numbers between 01 to 99. If the number between 01 to 99 happened again we go to the next two digits. One could also have the computer generate a 20% sample (20% of 500 = 100). Stratified Random Sample: Suppose that you want to find out how happy teachers and staff are with the new health plan and you want to know if their level of satisfaction varies with gender. Thus, you need to divide your population of into four strata (male and female teachers and male and female administrators). Then, you need to randomly choose a number of participants within each stratum. Here are you sub—populations (four strata) Male teachers at elementary and middle Male staff at elementary and middle school school level level 90+40= 130 100+80= 180 Female teachers at elementary and middle Female staff at elementary and middle school level school level 110 + 90 = 200 200+120 = 320 Suppose you want to choose a 20% sample from the above population, you would be randomly choosing 26 (20% of 130) from male teachers 40 (20% of 200) from female teachers 36 (20% of 180) from the male staff 64(20% of 320) from female staff Total sample size = 146 Cluster sampling: Suppose now we want to find out how happy the parents of the first second, third, fourth, and fifth grade students are with the education that their children are receiving in the district. Instead of randomly sampling individual students, we randomly sample a first, second, third, fourth, and fifth grade class from each of the four schools within the district and then conduct a census within each cluster. We will do this by having the parents of all the students in the grades selected fill out a short survey to assess the extent to which they are happy with the education that their children are receiving. Multi-stage sampling is combining several schemes of sampling. For example, if we randomly select an elementary school, then from each school randomly select a first, second, fourth and fifth grade, and then from each class randomly select ten out of forty students; this would be multi-stage sampling. Systematic sampling: From a list we randomly select an observation and then systematically select every tenth, twentieth, thirtieth,. . .etc observation. For example: Suppose we want to find out how well people liked a movie. We could randomly select one person among the crowd who leave the movie theatre, and then systematically select individuals until we select the sample of our choice. Systematic sampling is not random because the individuals do not have an equal chance of being selected. For instance if person one and person ten is selected, then the second to ninth person do not have a chance of being selected. What points to consider when building a survey Validity of the survey A valid survey is a survey that helps you ascertain that the question of your interest has been answered. For example, if you want to construct a survey to assess the attitude of the undergraduate students toward academics at UCLA, you have to make sure that the questions really relate to academics and not to social life or other issues at UCLA. Reliability of the survey A reliable survey will result in consistent results over time. That means if you repeat a survey twice within a reasonable time interval, you will get the same results. Pilot: The rule of thumb is that you should always conduct a “pilot study” prior to conducting the study and collecting the data. The pilot will help you revise the survey and find needs to be changed and revised. Some years ago I conducted a study on the attitude of “at risk students” toward “conflict resolution”. Based on the theory of “conflict resolution”, if you have a conflict with somebody, the least constructive way of handling it would be to “pretend that nothing happened”. One of the questions that I had written on the survey was: If I have a conflict with somebody, I pretend that nothing has happened and just go my way. The options were I strongly agree = l I agree = 2 I am not sure = 3 I disagree = 4 I strongly disagree = 5 If they strongly disagreed that meant they had the right attitude toward “conflict resolution”. In my consulting practice, I always share the survey with the relevant personnel and seek their input regarding revising the survey and what needs to be changed. When I shared the survey with the teachers who taught the students in a neighborhood with a lot of gang activity, they all frowned upon how I had decided to score this items. Once I asked why, they said: “If the students think they are going to have an encounter with a gang member, the most constructive way would be not to get into a discussion with them and pretend that nothing happened rather than try to discuss and solve the issue. This is an example of a situation in which what has been proven in theory does not necessarily work in all situations. Another example that I can give you about the importance of piloting a survey is that sometimes in my consulting practice, I noticed that some of the students or adults for whom English is the second language had difficulty understanding the meaning of some words and thus did not follow the questions. I tried to solve this problem by piloting the survey among the students, eliminating the words that were difficult for them, and using words that they understood. A second strategy was that I would have somebody read the survey to them and if they had questions about the meaning of some words, the person who administered the survey, explained the meaning of the words. Other factors that could potentially bias the results studies that are based on surveys include: Samples of convenience: Sampling who is available; not a good representative of the population Under-coverage: A part of population that is less represented Non-response bias: A large fraction of the population that do not response Response bias: Writing survey questions in such a way that the majority are more likely to agree or disagree with. Social desirability of questions could be a potential issue. Exercise to be done in class: Take the following survey and we will discuss it Locus of Control Check the one statement that best describes how you feel. 1 Many of the unhappy things in people's lives are partly due to bad luck People's misfortunes result from the mistakes they make. 2. One of the major reasons why we have wars is because people don't take enough interest in politics. There will always be wars, no matter how hard people try to prevent them. 3 In the long run, people get the respect they deserve in this world. Unfortunately, an individual’s worth often passes unrecognized no matter how hard he tries. 4. The idea that teachers are unfair to students is nonsense. Most students don't realize the extent to which their grades are influenced by accidental happenings. 5. Without the right breaks, one cannot be an effective leader. Capable people who fail to became leaders have not taken advantage of their opportunities. “WWW nmnmwumwummmmmmmm a..." 6 No matter how hard you try, some people just don't like you. People who can't get others to like them don’t understand how to get along with others. WWW mWtNjin.mllmmwmwmm m-wmmuhmw m‘mmfimmmmmumnmn‘immm/mummmmMimwljMMWMWWHNWMIM 7. » I have often found that what is going to happen will happen. Trusting to fate has never turned out as well for me as making a decision to take a definite course of action. 8. In the case of the well prepared student, there is rarely, if ever, such a thing as an unfair test. Many times exam questions tend to be so unrelated to course work that studying is really useless. 9. Becoming a success is a matter of hard work; luck has little or nothing to do with it. Getting a good job depends mainly on being in the right place at the right time. 10. The average citizen can have an influence in government decisions. This world is run by the few people in power and there is not much the little guy can do about it. l 1. When I make plans, I am almost certain that I can make them work. It is not always wise to plan too far ahead because many things turn out to be a matter of luck anyway. ...iMmla...t.lqtlawn—ummm—“wmmumm 12. In my case, getting what I want has little or nothing to do with luck. Many times we might just as well decide what to do by flipping a coin. 13. What happens to me is my own doing. Sometimes I feel that I don't have enough control over the direction my life is taking. nW.mmwWWW-mm».alllitl..ui.iuilnaml"1......mllnllltlljjllltllmm.mmwmmmuliluimmmw.mw.m “WWW 7—16. What did they do? For the following reports .about statistical studies, identify the following items (if posnble). If ' u can’t tell, then say so—this often happens when we read 1 The population )_ The population parameter of interest The sampling frame ' The sample "The sampling method, including Whether or not ran— domization was employed 'Anypotential sources of bias you can detect and any ‘roblems you see in generalizing to the population of terest _ess magazine mailed a questionnaire to the hu- source directors of all Fortune 500 companies, and ved responses from 23% of them. Those responding mad that they did not find that such surveys in- ?Sigriificantly on their work day. V Between quarterly audits, a company k on its accounfing procedures to address any fore they become serious. The accounting 65 Payments on about 120 orders each day. {the supervisor rechecks 10 of the transac— me they were processed properly. fg- Between quarterly audits, a company §Ck on its accounting procedures to address any 13'6fore they become serious. The accounting sses payments on about 120 orders each day. , the supervisor rechecks 10 of the transac- ure they were processed properly. a) Propose a sampling strategy for the supervisor. b) How would you modify that strategy if the company makes both Wholesale and retail sales, requiring dif— ferent bookkeeping procedures? 7, 20. Parent opinion, part 2. Let’s revisit the school system 21. L 22. 23. described in Exercise 19. Four new sampling strategies have been proposed to help the PTA determine whether parents favor requiring elementary students to pass a test in order to be promoted to the next grade. For each, indi- cate 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. b) Hold a PTA meeting at each of the 20 elementary schools, and tally the opinions expressed by those who attend the meetings. c) Randomly select one class at each elementary school and contact each of those parents. (1) Go through the district’s enrollment records, selecting every 40th parent. PTA volunteers will go to those homes to interview the people chosen. Churches. For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, you'll ask to get a list of all current members and contact 100 members at random. a) What kind of design have you used? b) What could go wrong with the design that you have proposed? ' Fish. The US. Fish and Wildlife Service plans to study the kinds of fish being taken out of Saginaw Bay. To do that, they decide to randomly select 5 fishing boats at the end of a randomly chosen fishing day and to count the numbers and types of all the fish 0n those boats. a) What kind of design have they used? b) What could go wrong with the design that they have proposed? Roller coasters. An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) Is it likely to be representative? c) What is the sampling frame? Tables and Selected Formuias TABLE OF RANDOM DIGITS \OOOVIONU‘IHéth-I pikaJQJUJOJmOJCDmUJNNNNNNN NHI—‘v—‘h—lHr—‘I—‘lr—‘l—AH A-94 I: A i i v 1 -| ...
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This note was uploaded on 12/03/2011 for the course STATISTICS 10 taught by Professor Gould during the Fall '11 term at UCLA.

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10_w4_s3_chapter_12 - Week four Session one(chapter 12 Week...

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