CHAPTER FOUR SAMPLING PROCEDURES March 11, 2015

SAMPLING PROCEDURES –Population and Sampling –The Need for sampling –Characteristics of Good Sampling –Probability Sampling –Non Probability Sampling

4.1. What is population ? The term population refers to the group or units of interest (married couples, English teachers, students of English, clients of FNB) during the time of interest (since 2011, during August 2011, till October A population is a group of individuals persons, objects, or items from which samples are taken for measurement. Defining the population is the essential first step in selecting a sample. This process includes three parts: –Identifying the group of interest –Naming the geographic area where the group is found –Indicating the time period of interest

4.2. What is a sample? A sample is a finite part of a statistical population whose properties are studied to gain information about the whole (Webster, 1985). A set of respondents (people) selected from a larger population for the purpose of a survey.

4.3. What is sampling? Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population.

4.3. What is sampling?

What is sampling?

4.3.2.Sampling Process 8 The sampling process comprises several stages: –Defining the population of concern –Specifying a sampling frame, a set of items or events possible to measure –Specifying a sampling method for selecting items or events from the frame –Determining the sample size –Implementing the sampling plan –Sampling and data collecting –Reviewing the sampling process

SAMPLING FRAME 9 In the most straightforward case, such as the sentencing of a batch of material from production (acceptance sampling by lots), it is possible to identify and measure every single item in the population and to include any one of them in our sample. However, in the more general case this is not possible. There is no way to identify all rats in the set of all rats. Where voting is not compulsory, there is no way to identify which people will actually vote at a forthcoming election (in advance of the election) As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample. The sampling frame must be representative of the population

4.4. What is the purpose of sampling? To draw conclusions about populations from samples, we must use inferential statistics which enables us to determine a population's characteristics by directly observing only a portion (or sample) of the population.

4.4. What is the purpose of sampling? There would be no need for statistical theory if a census rather than a sample was always used to obtain information about populations. But a census may not be practical and is almost never economical. There are six main reasons for sampling instead of doing a census. These are; - 1.Economy 2.Timeliness 3.The large size of many populations 4.Inaccessibility of some of the population 5.Destructiveness of the observation 6.Accuracy

4.5. TYPES OF SAMPLES Probability (Random) Samples 1.Simple random sample 2.Systematic random sample 3.Stratified random sample 4.Multistage sample 5.Multiphase sample 6.Cluster sample Non-Probability Samples 1.Convenience sample 2.Purposive sample 3.Quota

4.5. TYPES OF SAMPLES Probability Sampling What is probability sampling? –A probability sampling method is any method of sampling that utilizes some form of random selection. –In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen. –Humans have long practiced various forms of random selection, such as picking a name out of a hat, or choosing the short straw. –These days, we tend to use computers as the mechanism for generating random numbers as the basis for random selection.

Probability Sampling 1.A simple random sample A simple random sample is obtained by choosing elementary units in such a way that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome. Applicable when population is small, homogeneous & readily available All subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection. It provides for greatest number of possible samples. This is done by assigning a number to each unit in the sampling frame. A table of random number or lottery system is used to determine which units are to be selected. Disadvantages –If sampling frame large, this method impracticable. –Minority subgroups of interest in population may not be present in sample in sufficient numbers for study.

Probability Sampling 2. A systematic random sample A systematic random sample is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals until the desired number of units is obtained. For example, there are 100 students in your class. You want a sample of 20 from these 100 and you have their names listed on a piece of paper may be in an alphabetical order. If you choose to use systematic random sampling, divide 100 by 20, you will get 5. Randomly select any number between 1 and five. Suppose the number you have picked is 4, that will be your starting number. So student number 4 has been selected. From there you will select every 5th name until you reach the last one, number one hundred. You will end up with 20 selected students.

SYSTEMATIC SAMPLING…… 16 As described above, systematic sampling is an EPS method, because all elements have the same probability of selection (in the example given, one in ten). It is not 'simple random sampling' because different subsets of the same size have different selection probabilities - e.g. the set {4,14,24,...,994} has a one-in-ten probability of selection, but the set {4,13,24,34,...} has zero probability of selection.

SYSTEMATIC SAMPLING…… 17 ADVANTAGES: Sample easy to select Suitable sampling frame can be identified easily Sample evenly spread over entire reference population DISADVANTAGES: Sample may be biased if hidden periodicity in population coincides with that of selection. Difficult to assess precision of estimate from one survey.

Probability Sampling 3. A stratified sample Where population embraces a number of distinct categories, the frame can be organized into separate "strata." Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected. Every unit in a stratum has same chance of being selected. Using same sampling fraction for all strata ensures proportionate representation in the sample. Adequate representation of minority subgroups of interest can be ensured by stratification & varying sampling fraction between strata as required.

Probability Sampling 3. A stratified sample Finally, since each stratum is treated as an independent population, different sampling approaches can be applied to different strata. Drawbacks to using stratified sampling. First, sampling frame of entire population has to be prepared separately for each stratum. Second, when examining multiple criteria, stratifying variables may be related to some, but not to others, further complicating the design, and potentially reducing the utility of the strata. Finally, in some cases (such as designs with a large number of strata, or those with a specified minimum sample size per group), stratified sampling can potentially require a larger sample than would other methods

STRATIFIED SAMPLING……. 20 Draw a sample from each stratum

Nonprobability Sampling Any sampling method where some elements of population have no chance of selection (these are sometimes referred to as 'out of coverage'/'undercovered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the selection of elements is nonrandom, nonprobability sampling not allows the estimation of sampling errors.. Example: We visit every household in a given street, and interview the first person to answer the door. In any household with more than one occupant, this is a nonprobability sample, because some people are more likely to answer the door (e.g. an unemployed person who spends most of their time at home is more likely to answer than an employed housemate who might be at work when the interviewer calls) and it's not practical to calculate these probabilities.

Nonprobability Sampling Nonprobability Sampling includes: 1.Purposive Sampling 2.Quota Sampling and 3.Snowball Sampling In addition, nonresponse effects may turn any probability design into a nonprobability design if the characteristics of nonresponse are not well understood, since nonresponse effectively modifies each element's probability of being sampled.

Nonprobability Sampling At least with a probabilistic sample, we know the odds or probability that we have represented the population well. We are able to estimate confidence intervals for the statistic. With nonprobability samples, we may or may not represent the population well, and it will often be hard for us to know how well we've done so.

Nonprobability Sampling 1. Purposive Sampling In purposive sampling, we sample with a purpose in mind. We usually would have one or more specific predefined groups we are seeking. For instance, have you ever run into people in a mall or on the street who are carrying a clipboard and who are stopping various people and asking if they could interview them? Most likely they are conducting a purposive sample (and most likely they are engaged in market research).

Nonprobability Sampling 2. Quota Sampling In quota sampling, you select people non-randomly according to some fixed quota. There are two types of quota sampling: proportional and non proportional.

Nonprobability Sampling 2. Quota Sampling In proportional quota sampling you want to represent the major characteristics of the population by sampling a proportional amount of each. For instance, if you know the population has 40% women and 60% men, and that you want a total sample size of 100, you will continue sampling until you get those percentages and then you will stop. So, if you've already got the 40 women for your sample, but not the sixty men, you will continue to sample men but even if legitimate women respondents come along, you will not sample them because you have already "met your quota." The problem here (as in much purposive sampling) is that you have to decide the specific characteristics on which you will base the quota. Will it be by gender, age, education race, religion, etc.?

Nonprobability Sampling 3. Snowball Sampling In snowball sampling, you begin by identifying someone who meets the criteria for inclusion in your study. You then ask them to recommend others who they may know who also meet the criteria. Although this method would hardly lead to representative samples, there are times when it may be the best method available. Snowball sampling is especially useful when you are trying to reach populations that are inaccessible or hard to find. For instance, if you are studying the homeless, you are not likely to be able to find good lists of homeless people within a specific geographical area. However, if you go to that area and identify one or two, you may find that they know very well who the other homeless people in their vicinity are and how you can find them.

Test Two