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Research Methods in Education 6th Edition

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  2. 2.  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
  3. 3. 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?
  4. 4.  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?
  5. 5. N S N S 10 10 400 196 15 14 500 217 30 28 1,000 278 100 80 1,500 306 200 132 3,000 346 300 169 5,000 357 N = Population; S = Sample Note: As the population increases, the proportion of the population in the sample decreases. SAMPLE SIZE
  6. 6. 0 1000 2000 3000 4000 5000 6000 SA M PLE PO PU LA TIO N Note: As the population increases, the proportion of the population in the sample decreases. PROPORTION OF SAMPLE SIZE TO POPULATION
  7. 7. 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.
  8. 8. 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.
  9. 9. 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.
  10. 10. 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).
  11. 11.  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
  12. 12. SAMPLING ERROR Sample size depends on the margin of error and the confidence levels that the researcher is prepared to tolerate.
  13. 13.  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 N SD SE s = CALCULATING THE STANDARD ERROR OF THE SAMPLE
  14. 14. If SDs = 13.76 and N = 120 Then The Standard Error (SE) is 1.27. 27.1 120 96.13 === N SD SE s EXAMPLE OF STANDARD ERROR
  15. 15. N S (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
  16. 16.  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
  17. 17.  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
  18. 18.  Probability sample  Non-probability sample SAMPLING STRATEGIES
  19. 19.  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
  20. 20.  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
  21. 21. sn N f = where f = frequency interval; N = the total number of the wider population; sn = the required number in the sample. Every nth person (e.g. every 4th person). To find the frequency use the formula: SYSTEMATIC SAMPLING
  22. 22.  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 5th person. 9.4 306 500,1 ==f
  23. 23.  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
  24. 24. 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
  25. 25. SCHOOLING SUB-TOTAL SAMPLE SIZE No schooling 35,020 380 Pre-primary 6,811 364 Primary incomplete 80,285 384 Primary complete 109,561 384 Junior secondary 94,491 384 Senior secondary 66,250 382 Tertiary, non-degree 7,481 367 Tertiary, degree 23,944 379 Special 360 186 Total 424,203 3,210 BUT . . . Total without strata 384
  26. 26. The greater the number of strata, the larger the sample will be. Therefore, keep to as few strata as s necessary. PROBLEMS OF STRATA
  27. 27. Sampling within a particular cluster (e.g. geographical cluster); Useful where population is large and widely dispersed. CLUSTER SAMPLE
  28. 28. 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
  29. 29. Organization 1 2 3 4 5 6 7 8 9 Total Required number of employees 30 21 45 12 54 23 16 43 34 278 Go to each organization and ask for the required random number from each.
  30. 30.  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
  31. 31.  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
  32. 32.  Opportunity sample (often those to whom there is easy access). CONVENIENCE SAMPLE
  33. 33.  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
  34. 34.  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
  35. 35.  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
  36. 36.  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
  37. 37.  Deliberately chosen for specific purposes. PURPOSIVE SAMPLE
  38. 38. ● 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
  39. 39. ● 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
  40. 40.  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
  41. 41.  One sample leads on to more of the same kind of sample. SNOWBALL SAMPLING
  42. 42. 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/ 4 5 6 7 8 9 10 11 12 RESEARCHER RESEARCHER HAS 3 CONTACTS THE 3 CONTACTS EACH HAVE 3 CONTACTS SNOWBALL SAMPLING
  43. 43.  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
  44. 44.  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
  45. 45.  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
  46. 46. 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
  47. 47. 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