1.1. What is survey sampling?

Transcription

1 1.1. What is survey sampling? We learn about the characteristics of interest of a finite population by only examining a subset of units in this population. A finite population is conceptually made of finite number of sampling units each possessing some characteristics. Examples including residents in Canada with their ages as a characteristic.

2 Why do not we examine all units in this population? This is indeed done occasionally. Every ten years, Canada conducts a census of its residents. Here we have used the terminology census which is a practice of collecting information from every unit in the population (if at all possible). It is costly and time consuming to have a census done properly. Census has its disadvantages: (1) cost; (2) timeliness; (3) and can be less precise.

3 Additional considerations by your instructor: One needs a high level of authority to force everyone to participate. It can be hopeless to rearch all units in the population, e.g. Fishing. The method of examining a unit can be destructive, e.g. elasticity of a piece of wood.

4 1.2. Who needs such information? Government is apparently a big consumer of the information obtained in surveys. We repeatedly hear the announcements of unemployment rates of provinces. They are vital for policy makings. Political parties cannot ignore the polls conducted again and again. There are hardly many times when the poll results were off a big margin when an actual election is hold. See Gallup, George Horace ( ) in dictionary. US statistician. A pioneer of opinion research, he developed the Gallup Poll and founded the American Institute of Public Opinion in 1935.

5 1.2. Who needs such information? Environmentalists need such data to convince the public about conservational measures. The biomass of fish is a closely monitored index. Overfishing can have disastrous consequences. Fishery companies, on the other hand, would like to maximize the quota. It can be a life and death issue when a retailer re-stock their goods for the up-coming season. The information on consumer preferences is apparently vital.

6 1.3. Sample surveys are conducted throughout the world (textbook 1.1) Some numbers I learned from internet, news and so on. In the last provincial election, BC liberal was behind NDP according to Gallup poll. All parties made serious effort to change their strategies accordingly. BC teachers are likely still on strike. Both Teacher s union and the BC government are paying close attention to their supporting rates.

7 Statistics Canada messed up with the employment numbers. The latest Canada GDP figure had been very positive. Ontario government intends to use survey data to prove that cigarette companies profited at the cost of provincial healthy care.

8 1.4. Who conduct surveys? Statistics Canada is likely the largest organization whose sole responsibility is to conduct surveys. The U.S Census Bureau is an analogue in the Unites States, only more powerful and has a larger budget. Market research firms keep trying their best to assess preferences of consumers regarding the household purchases.

9 1.5. Common means of taking surveys Telephone surveys are often used for polls on election issues. ( I get many such phone calls every year) Internet is used more and more often now (I am asked by UBC, by NSERC, by Joint Statistical Meeting every year). Post-mail questionaries are less used now but we do receive such requests every year. Person-to-person interview is used but this is a very expensive method. Survey vessels are employed to sample the abundance of fish over open seas. Needless to say, all methods have their shortcomings.

10 1.6. Target population The target population is the collection of all units about which we would like to obtain information. The target population may appear to be well specified initially in many applications. However, once we actually settle down on to design a survey, the issue is far from simple.

11 You might be interested in the average salary of professors working at UBC. In this case, the target population is made of professors who are currently working at UBC. There does not seem to be anything unclear. Yet should we include those professors who have dual appointments with UBC and BC cancer agent? How about those who are not in tenure track but serve as research associate with research teams? How about those who are at leave this year? How about some who are visiting us and somehow get paid partially?

12 On average, how many children does a Canadian woman bear in her life time? I find this question is almost impossible to answer. What do you think? (It is very hard to find the number of children of a particular lady in her life time if she is still alive, particularly, when she is still young enough). What percentage of our UBC graduates find a job with half year?

13 Study Population. In applications, the population we settle on may be called Study Population. The validity of the conclusions of a survey depends on many factors, one of them is how well the study population matches with the target population.

14 Sample frame At least conceptually, a survey is done by first taking a sample from the target population. For this purpose, we may create a frame which is the list of all the units of the population to be surveyed.

15 This leads to the notion of sampling unit. Suppose we wish to find the average household annual income of Canada. What do we mean by a household? Someone has divorced several times, living with his parents and one of his children and a girlfriend.

16 To get the survey properly done, one must forcefully nail down the smallest units that a sample may include or exclude. Here is a definition I find on web: A sampling unit is one of the units into which an aggregate is divided for the purpose of sampling, each unit being regarded as individual and indivisible when the selection is made.

17 I must admit that such concepts are not exactly scientific or mathematical, some ambiguity is unavoidable. According to the same website, the ultimate sampling unit may be defined as the smallest unit which is the subject of sample selection. In a household survey the ultimate sampling unit might be the household.

18 My interpretation is: one may take a sample of a set of blocks in a city. After which, every household is interviewed. In this case, the block is the primary sampling unit and the household is the ultimate sampling unit.

19 Here is the definition given by Cochran which I feel is most accurate: the population must be divided into parts that are called sampling units. These units must cover the whole of the population and they must not overlap, in the sense that every element in the population belongs to one and only one unit.

20 finite populations Generally speaking, a target population in survey context are finite populations. If you keep taking sampling units from it without replacement, sooner or later, the sampling units will be exhausted. In comparison, in experimental design, we study infinite population. If you experiment with planting tomatoes, you never exhaust all tomatoes nor tomato plants.

21 non-finite populations Consider the experiment in which we study whether the temperature has any effect on the probability of obtaining a head when a coin is tossed. There are only two possible outcomes which will be exhausted quickly. Yet you cannot exhaust the samples you can take.

22 finite or not populations?? The line is not so clear in other examples. The finite population may itself be dynamic. When the unemployment information is needed, the population itself changes with time. This above notion works only if you can sample as many units as you like instantly. When the fish abundance over a region of the sea is of interest, the area is artificially divided up. The finiteness is more an artifact rather than a natural fact.

23 1.7. Type of surveys Many of the national and international surveys are usually of the multisubject and multipurpose type. In almost all small and large-scale surveys, before selecting the samples, the population is first divided into a fixed number of strata. For large-scale surveys, well-defined clusters, groups of contiguous units, may be considered in each stratum.

24 The actual procedure of sampling in some situations may be implemented in two, three, or more stages. These are Multistage sampling. In the rotation or successive sampling procedures, observations are made on some of the units selected previously and on some new units sampled at the current period. In longitudinal surveys, observations are made on a selected sample, a panel, over periods of time.

25 1.8. Questionaries, interviews and sample sizes The issue of questionary comes up if the information has to be provided by a respondent included in the sample. Depending on how you design the question, the outcome can differ a lot. There can be as many reasons as you care to enumerate. I will not make a fool of myself here.

26 Interviewing method is apparent another important issue. Similarly, I refer it to textbook. sample sizes: The general principle about the sample size is: when the sample size increases, we obtain more information which leads to more precise statistical inference. In standard situations, statisticians can prescribe a sample size needed to achieve certain level of precisions for the later analysis.

27 1.9. Probability sampling Roughly, a probability sampling does not specify which subset of the units in the population will be measured. Rather, we use a pre-specified sampling plan to select a subset according to some random mechanism.

28 1.9. Non-probability sampling In comparison, a non-probability sampling may have a subset selected according to other principles. For instance, you may feel that one small area in a large field is a good representative area. One elephant out of a dozen is of median size so you want to use her weight to estimate the total weight of the herd.

29 1.10. Sampling errors What we hope to learn is the characteristics of a finite population. We rely on a random subset from this population to infer about such characteristics. Unless it is a very simple situation or you are super-lucky, this subset is not a perfect replication of the target population. The error due to using one sample instead of another possible sample is generally referred as sampling error.

30 1.10. Sampling errors A very important feature of probability sampling is that in addition to providing an estimate of the unknown population quantity, it enables the assessment of the sampling error of the estimate, the standard error. Further, the estimate and its standard error can be used to obtain confidence limits for the unknown population quantity. For a specified probability, these limits provide an interval for the population quantity.

31 1.10. Non-sampling errors Suppose one wishes to learn about the average amount of money students spend on lunch in UBC. He or she may collect information on on every 10th student leaving Student Union Building on some day. No matter how good a job is done there, there is a potential difference between students who visit SUB often and those who do not visit at all.

32 1.10. Non-sampling errors The error caused by mis-match between target population and the study population is non-sample error. The Gallop polls before the last provincial election may erred at unknowingly mis-match the study population and the target population. Those represented in the sample may have a low rate of vote, and those systematically under-represented in the sample may have a higher than average voting rate.

33 1.11. Some sensible but abused terminologies The first one is whether a sample is obtained unbiasedly? In general, unbiasedness means that all units have the same probability to be selected in a survey. This concept is often used loosely, and not applied strictly.

34 If one uses a (home) telephone survey with a target population as everyone living in a specific city, the surveyor may reach house-wives more often. The survey may hence be regarded as biased because of this.

35 The second abused terminology is the representativeness of the sample. My interpretation is: a representative sample can be duplicated many folds to create a finite population which is similar to the target finite population. If one samples students exclusively from those living in a dorm, the resulting sample (units in the sample) is unlikely a representative one for the target population students registered at UBC in year 2015.

36 Likely issues regarding biased sample are: it is often hard to judge whether the sample is strictly unbiased; we may bias the sample purposely to obtain more information and correct the bias at the data analysis stage.

37 My point is: do not fall into the trap by stating naively that because the sample is biased, the conclusion is false. The term representative is problematic. It is hard to have an exact definite of similar to. Therefore, this terminology is defined based on a loose concept similar to.

38 This textbook also asks students whether a survey is valid. Yet the validity is true when the responses are representative. We can easily see that this is not very scientific. Yet my comment itself is very unscientific.

39 In this course, we do have many topics rigorously addressed, and others based on unscientific discussions. Let us feel okay to accept some ambiguity, while feel free to ask your instructor about any specific topics.

40 Learning outcomes The subtitles and boldfaced terminologies form a summary of learning outcomes of this week.