MN 400: Research Methods. CHAPTER 7 Sample Design

Transcription

1 MN 400: Research Methods CHAPTER 7 Sample Design 1

2 Some fundamental terminology Population the entire group of objects about which information is wanted Unit, object any individual member of the population Sample a part of the population used to gain information about the whole Random eliminate human choice by allowing impersonal chance to choose the sample Sampling frame the list of units from which the sample is chosen Variable a characteristic of a unit to be measured for the units in the sample Parameter Summary measure to describe a characteristic of the population 2

3 What is a Good Sample? Accurate: absence of bias Precise estimate: sampling error 3

4 Steps in Sampling Design What is the relevant population? What are the parameters of interest? What is the sampling frame? What is the type of sample? What size sample is needed? How much will it cost? 4

5 Frame Sampling frame the list of units from which the sample is chosen. EXAMPLE: Schools Under coverage: Units in the population but not in the frame Over coverage: Units in the frame that are not in the population Under coverage is a bigger problem? WHY? You will miss them and you do not know how big the problem is. 5

6 Variables A characteristic of a unit to be measured for the units in the sample Qualitative Quantitative (figures) Non-numeric Normally coded Discrete Only some in values, integers Continuous Can be measured often more detail 6

7 Background Independent Stable cause Survey variables Dependent Vary effect EXAMPLE Variable Value Gender Man Civil status Married Number of children Three Income R A variable may well be a background variable in one survey and a survey variable in another.

8 Sampling Population Sampling Sample Random procedure Inference Obtain information about some characteristics of the population. Statistical inference formal methods for drawing conclusions about the population from the sample taking into account the effects of randomisation and other chance variation. 8

9 Sample Size 1. Based on Yamane, 1973, the following is the sample size formula: n = where: n: sample size N: total population e: standard of error (5%) N 1+ N.( e) 2. You take between 5 to 15% of the total population 2 9

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11 Note for Sample size 1. When population is BIG the sample size is SMALLER 2. When population is SMALL the sample size is BIGGER 11

12 Sampling techniques 1. Simple random sampling 2. Systematic random sampling 3. Stratified random sampling 4. Cluster sampling 5. Multi-phase/double phase sampling 6. Opportunity sampling 7. Purposive or judgmental sampling 8. Snowball sampling 12

13 Simple Random Sampling (SRS) Every element (unit) in the population has the same probability of being selected for the sample. This probability is = % n = N sample population size size Each selected element is representing 30 units in the population. Each selected element is representing 30 units in the population. 13

14 Systematic Random sampling Assume a full list of population is available Decide on a sampling fraction 1 in 20 (1 in k) 100 of 3000 = 1 in 30 Select a random number between 1 and k. ( sampling fraction) The starting point (say 4) Starting from no 4, select every k th unit on the list. If N is a multiple of k, every unit has probability of selection. 14

15 Stratified random sample In stratified sampling the population of N units is divided into K sub-populations of N1, N2, N3,..., NK units such that the units within each subpopulation are relatively homogeneous. These sub-populations are non-overlapping and together they comprise the whole of the population, i.e. N1 + N NK = N The sub-populations are called strata. From each stratum a SRS is drawn and the total sample so obtained is called stratified random sampling. 15

16 EXAMPLE Hotels Star grades Manufacture Size, classification subgroups Industry Household Geographic Provinces/districts Ural/rural Race Gender 16

17 Strata don t have to coincide with presentation groups. Choice of strata: Homogeneity similar units in the same group How do we know? Normally as knowledge Certain presentation groups are requested Proportion to strata best for totals Equal size in strata presenting our strata Extremely useful increases accuracy in the inference. Very common at statistical offices. 17

18 Another example of strata sampling: The population under study is divided under known criteria, for example 52% females and 47,6% males is the sex composition of Cambodia. Within this broad strata, people are chosen at random. The strata can become detailed for example, including, age, social class, geographical location. 18

19 For example, Phnom Penh city is divided into five units and the total number of population of Phnom Penh city is 50,000. The percentages of population of the respective five units to the total population are (1) 10%, (2) 15%, (3) 20%, (4) 25% and (5) 30%. Suppose a sample of 10, 000 is drawn, the desired proportional sample may be obtained in the following manner: 19

20 From stratum (unit) one - 10,000(10) = From stratum (unit) two - 10,000(15) = From stratum (unit) three - 10,000(20) = From stratum (unit) four - 10,000(25) = From stratum (unit) five - 10,000(30) = ,000 In disproportionate stratified sampling, an equal number of cases are taken from each stratum regardless of how the stratum is represented in the universe. Thus, in the above example, an equal number of items (2000) from each stratum may be drawn. 20

21 Cluster Sampling Sometimes the population may be spread over a great geographical area so that it is impossible to visit and study. Therefore, the researcher attempts to cluster or group the population though still choosing at random. For example, to examine young girls school drop-out rates, a researcher might first choose a number of cluster schools at random, then within these the number of families to be interviewed in understanding the drop-out rates. 21

22 Double/Multi-phase sampling This usually occurs when a researcher, after an initial study wants to return to the area to ask a small number of sampled people detailed questions. He/she chooses at random a small sub-section of the original sample. 22

23 Other Forms of Sampling Opportunity Sampling Due to financial limitations, research is carried out on conveniently available groups as people living in the neighborhood, shoppers of a supermarket, etc. There is no proper sampling and possibility of Generalization of results to a wider population. Opportunity sampling may produce biased, and Therefore greater likelihood of error. 23

24 Purposive or judgmental sampling Sometimes, it s appropriate to select a sample on the basis of one s own knowledge of the population, its elements, and the nature of the research aims: in short based on one s own judgment and the purpose of the study. For example, a study of street children: while there are many street children in Phnom Penh, it is not practical to interview all of them. Hence, all or a sample of those shopping areas (e.g., markets, supermarkets) may be enough for the research purpose. 24

25 Snowball sampling Most commonly used in qualitative research, this sampling method is appropriate when members of a special population are difficult to locate, e.g., homeless individuals, participants to an NGO radio program, migrant workers, etc. Data is collected on the few members of the target population that can be located and asking those individuals to provide information needed to locate others members of the population. Because this also results in samples with questionable representatives, it is used primary for exploratory purpose 25

26 Determining the sampling size In general the bigger the size, the better because the larger the sample, the lesser the error. But this does not necessary guarantee accuracy of results. 26

27 There really is no fixed rule in establishing The right sample size. Two approached to guard against in deciding the sampling: 1- Specifying a portion of the population to be included in the sample. 2- Taking a particular sample size based on an understanding that it is usual or typical approach to studying a population: 27

28 28 A rule of thumb with regards to this issue is that Representativeness. How well your sample represents the different individuals, families, groups (villages/communities) you are studying is more critical than the numbers that you get. This is because your sample is supposed to be a small Picture of the bigger one that you are attempting to study.