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© LOUIS COHEN, LAWRENCE MANION & KEITH MORRISON SAMPLING

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Sample size Sampling error The representativeness of the sample Access to the sample Sampling strategy to be used Probability samples Non-probability samples Sampling in qualitative research Sampling in mixed methods research Planning a sampling strategy STRUCTURE OF THE CHAPTER

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It all depends on: The research purposes, questions and design; The population size; The confidence level and confidence interval required; The likely response rate; The accuracy required (the smallest sampling error sought); The kinds of variables to be used (categorical, continuous); The statistics to be used; HOW LARGE MUST MY SAMPLE BE?

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The number of strata required; The number of variables included in the study; The variability of the factor under study; The kind(s) of sample; The representativeness of the sample; The allowances to be made for attrition and non-response; The need to keep proportionality in a proportionate sample; The kind of research that is being undertaken (qualitative/quantitative/mixed methods). HOW LARGE MUST MY SAMPLE BE?

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N S N S 10 10 400196 15 14 500217 30 281,000278 100 801,500306 2001323,000346 3001695,000357 N = Population; S = Sample Note: As the population increases, the proportion of the population in the sample decreases. SAMPLE SIZE

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Note: As the population increases, the proportion of the population in the sample decreases. PROPORTION OF SAMPLE SIZE TO POPULATION

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SAMPLE SIZE Ensure a sufficiently large sample for each variable. Samples in qualitative research must be large enough to generate ‘thick descriptions’. A large sample does not guarantee representativeness; representativeness depends on the sampling strategy. Sample size also depends on the heterogeneity or homogeneity of the population: if it is highly homogeneous then a smaller sample may be possible.

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SAMPLE SIZE Large samples are preferable when: there are many variables; only small differences or small relationships are expected or predicted; the sample will be broken down into subgroups; the sample is heterogeneous in terms of the variables under study; reliable measures of the dependent variable are unavailable.

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SAMPLE SIZE A weighted sample may be required if there are small sub-groups of populations. A weighted sample: where a higher proportion of the sub-group is sampled, and then the results are subsequently scaled down to be fairer in relation to the whole sample.

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SAMPLE SIZE Sample size depends on the style of research (e.g. surveys may require large samples, ethnographies may require smaller samples). Sample size depends on the numbers of variables to be used, the kinds of variables, and the statistics to be calculated. Sample size depends on the scales being used in measurement (the larger the scale, the larger the sample).

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If many samples are taken from the same population, it is unlikely that they will all have characteristics identical with each other or with the population; their means will be different. Sampling error is the difference between the sample mean and the population mean, due to the chance selection of individuals. Sampling error reduces as the sample size increases. Samples of >25 usually yield a normal sampling distribution of the mean. STANDARD ERROR OF THE SAMPLE

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SAMPLING ERROR Sample size depends on the margin of error and the confidence levels that the researcher is prepared to tolerate.

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Stage One: Draw several number of samples of equal size from a population, to create a sampling distribution. Stage Two: Calculate the Standard Error (SE) of the mean: SDs = standard deviation of the sample (a measure of dispersal around the mean) N = the number in the sample CALCULATING THE STANDARD ERROR OF THE SAMPLE

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If SDs = 13.76 and N = 120 Then The Standard Error (SE) is 1.27. EXAMPLE OF STANDARD ERROR

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NS (95%) S (99%) 50 44 50 100 79 99 200 132 196 500 217 476 1,000 278 907 2,000 322 1,661 5,000 357 3,311 SAMPLE SIZE, CONFIDENCE LEVELS AND SAMPLING ERROR

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What is being represented (e.g. groups, variables, spread of population). If the sample has unequal sub-groups, then it may be necessary equalize the sample by weighting, to represent more fairly the population. THE REPRESENTATIVENESS OF THE SAMPLE

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Is access to the sample permitted, practicable, realistic? Who will give/withhold/deny permission to access the sample? Who are the ‘gatekeepers’? ACCESS TO THE SAMPLE

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Probability sample Non-probability sample SAMPLING STRATEGIES

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Every member of the wider population has an equal chance to be included; choice is made on chance alone. The aim is for generalizability and wide representation. Less risk of bias in the sample. PROBABILITY SAMPLE

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Drawing randomly from a list of the population (e.g.: names from a hat, using a matrix of random numbers). The probability of a member of the population being selected is unaffected by the selection of other members of the population, i.e. each selection is entirely independent of the next. RANDOM SAMPLE

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where f = frequency interval; N = the total number of the wider population; sn = the required number in the sample. Every n th person (e.g. every 4 th person). To find the frequency use the formula: SYSTEMATIC SAMPLING

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In a company of 1,500 employees a sample size of 306 is required (from tables of sample size for random samples). The formula is: This rounds to 5, i.e. every 5 th person.

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Stage 1: Identify those characteristics which appear in the wider population which must also appear in the sample, i.e. divide the wider population into mutually exclusive homogeneous groups. Stage 2: Randomly sample within these groups, the size of each group being determined by judgement or tables of sample size. RANDOM STRATIFED SAMPLE

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N S Total Whole company 1,000 278 278 English employees 800 260 Scottish employees 100 80 Welsh employees 50 44 American employees 50 44 428 THE PROBLEM OF STRATA

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SCHOOLINGSUB-TOTALSAMPLE SIZE No schooling35,020380 Pre-primary6,811364 Primary incomplete80,285384 Primary complete109,561384 Junior secondary94,491384 Senior secondary66,250382 Tertiary, non-degree7,481367 Tertiary, degree23,944379 Special360186 Total424,2033,210 BUT... Total without strata384

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The greater the number of strata, the larger the sample will be. Therefore, keep to as few strata as s necessary. PROBLEMS OF STRATA

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Sampling within a particular cluster (e.g. geographical cluster); Useful where population is large and widely dispersed. CLUSTER SAMPLE

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1. If the target population is 1,000 employees in nine organizations, then the sample size is 278 from the nine organizations. 2. Put the names of the nine organizations on a card each and give each organization a number, then place all the cards in a box. 3. Draw out the first card and put a tally mark by the appropriate organizations on the list. 4. Return the card to the box. 5. Do this 278 times and then total the number of employees required from each organization (the number of tally marks for each organization). STAGED (MULTI-STAGED) SAMPLE

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Organization123456789Total Required number of employees 302145125423164334 278 Go to each organization and ask for the required random number from each.

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Change the sampling strategy at each phase of the research, different samples for different stages of the research, e.g.: Junior employees at stage one, middle management at stage two, senior management at stage 3 (determined by the purposes of the research). MULTI-PHASE SAMPLE

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Members of the wider population are deliberately excluded. The aim is for the sample to represent itself rather than to seek generalizability. Non-probability sampling can be of issues as well as people. NON-PROBABILITY SAMPLE

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Opportunity sample (often those to whom there is easy access). CONVENIENCE SAMPLE

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The non-probability equivalent of stratified sampling. Seeks to represent significant characteristics (strata) of the wider population and to represent these in the proportions in which they can be found in the wider population. QUOTA SAMPLE

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Performing arts:300 students Natural sciences:300 students Humanities:600 students Business & social sciences:500 students Proportions: 3: 3: 6: 5 Minimum required is 3 + 3 + 6 + 5 = 17 EXAMPLE OF A PROPORTIONATE/QUOTA SAMPLE FROM A UNIVERSITY

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Stage 1: Identify those characteristics which appear in the wider population which must also appear in the sample, i.e. divide the wider population into mutually exclusive homogeneous groups, one row for each characteristic. Stage 2: Identify the frequencies and proportions in which the selected characteristics appear in the wider population (as a percentage). HOW TO OBTAIN A PROPORTIONATE (QUOTA) SAMPLE

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Stage 3: Ensure that the same percentages of characteristics appear in the sample. Stage 4: Calculate the totalled percentage and divide it by the highest common factor of the cells in that column. Stage 5: Add together the totals for the column to find out the total. HOW TO OBTAIN A PROPORTIONATE (QUOTA) SAMPLE

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Deliberately chosen for specific purposes. PURPOSIVE SAMPLE

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●Critical case sampling ●Extreme case sampling ●Deviant case sampling ●Boosted sample ●Negative case sampling ●Maximum variation sampling ●Typical case sampling ●Intensity sampling KINDS OF PURPOSIVE SAMPLING

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●Homogeneous sampling ●Reputational case sampling ●Revelatory case sampling ●Politically important case sampling ●Complete collection sampling ●Theoretical sampling ●Confirming and disconfirming case sampling KINDS OF PURPOSIVE SAMPLING

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Identify the group of factors (dimensions) to be sampled, and obtain one respondent (or more) for each group, i.e. a respondent who carries more than one factor, e.g. a junior employee who is a not ‑ native English speaker. DIMENSIONAL SAMPLING

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One sample leads on to more of the same kind of sample. SNOWBALL SAMPLING

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Person 1 Friend/contact 1 contacts his/her own friends/contacts/ Friend/contact 2 contacts his/her own friends/contacts/ Friend/contact 3 contacts his/her own friends/contacts/ 456789 101112 RESEARCHER RESEARCHER HAS 3 CONTACTS THE 3 CONTACTS EACH HAVE 3 CONTACTS SNOWBALL SAMPLING

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Volunteers may be well intentioned, but they do not necessarily represent the wider population. Caution: people volunteer for different motives, e.g.: – wanting to help a friend – interest in the research – wanting to benefit society – revenge on a particular school or headteacher. VOLUNTEER SAMPLING

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The researcher must have sufficient data to be able to generate and ‘ground’ the theory in the research context, i.e. to create theoretical explanation of what is happening in the situation, without having any data that do not fit the theory. The researcher proceeds in gathering more and more data until the theory remains unchanged, until no modifications to the grounded theory are made in light of the constant comparison method. THEORETICAL SAMPLING

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Parallel mixed methods sampling Sequential mixed methods sampling Multilevel mixed methods sampling Stratified purposive sampling Purposeful random sampling Nested sampling designs MIXED METHOD SAMPLING DESIGNS

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Stage One: Decide whether you need a sample, or whether it is possible to have the whole population. Stage Two: Identify the population, its important features (the sampling frame) and its size. Stage Three: Identify the kind of sampling strategy you require (e.g. which variant of probability, non- probability, or mixed methods sample you require). Stage Four: Ensure that access to the sample is guaranteed. If not, be prepared to modify the sampling strategy. PLANNING A SAMPLING STRATEGY

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Stage Five: For probability sampling, identify the confidence level and confidence intervals that you require. For non-probability sampling, identify the people whom you require in the sample. Stage Six: Calculate the numbers required in the sample, allowing for non-response, incomplete or spoiled responses, attrition and sample mortality. Stage Seven: Decide how to gain and manage access and contact. Stage Eight: Be prepared to weight (adjust) the data, once collected. PLANNING A SAMPLING STRATEGY

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