Lecture 2 Sampling Techniques For use in fall

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Lecture 2 Sampling Techniques For use in fall semester 2015 Lecture notes were originally Lecture 2 Sampling Techniques For use in fall semester 2015 Lecture notes were originally designed by Nigel Halpern. This lecture set may be modified during the semester. Last modified: 4 -8 -2015 SCM 300 Survey Design

Lecture Aim & Objectives Aim • To investigate issues relating to sampling techniques for Lecture Aim & Objectives Aim • To investigate issues relating to sampling techniques for survey research Objectives • What is a sample? • How should the sample be obtained? – Sampling considerations – Sampling techniques – Sources of error & degrees of confidence • How large should the sample be? SCM 300 Survey Design

What is Sampling? • Method for selecting people or things from which you plan What is Sampling? • Method for selecting people or things from which you plan to obtain data • Closely associated with quantitative methods – i. e. surveys or experiments • Sometimes associated with qualitative methods – i. e. content analysis & ethnography • Used because it’s rarely feasible or effective to include every person or item in a survey or study SCM 300 Survey Design

Not Feasible or Effective…. . • Travel patterns of UK adults • Need to Not Feasible or Effective…. . • Travel patterns of UK adults • Need to survey 50 mn+ people! – The UK government conducts a Census of Population every 10 years but this costs tens of £mn’s • Even a survey of annual cruise passengers visiting Molde would be costly & time consuming • Sampling provides a feasible & effective solution SCM 300 Survey Design

What is a Sample? “A sample is a portion or sub-set of a larger What is a Sample? “A sample is a portion or sub-set of a larger group called a population” (Fink, 2003; p 33) + + + + ++ + + Note: sampling isn’t necessary when you survey the entire population! SCM 300 Survey Design

What is a Population? • It can consist of human & non-human phenomena – What is a Population? • It can consist of human & non-human phenomena – Organisations, businesses, geographical areas, households, individuals • Examples: – – – – Hotels in Møre og Romsdal (population of hotels) Beaches in Australia (population of beaches) People in Norway (population of Norway) Households in Molde (population of households) Visitors to a resort (population of visitors) Users of a ferry service (population of users) Students at Hi. Molde (population of students) SCM 300 Survey Design

Aims of Sampling • Provide a small & more manageable portion or subset of Aims of Sampling • Provide a small & more manageable portion or subset of the population • Represent the population & be free from bias – Results for the sample should be similar if the survey was conducted on another sample from the same population – i. e. results are repeatable & reliable SCM 300 Survey Design

The Need for Reliable Representation SCM 300 Survey Design The Need for Reliable Representation SCM 300 Survey Design

Extracting a Sample Two main sources • From a sampling frame – A list Extracting a Sample Two main sources • From a sampling frame – A list of all known cases in a population from which a sample can be drawn • Sampled at source – Points in time/space where a potential population is available SCM 300 Survey Design

Typical Sampling Frames • • • Electoral register – individuals over 18 Telephone directories Typical Sampling Frames • • • Electoral register – individuals over 18 Telephone directories – households Royal Mail – households Market research companies – households / postcodes / census areas Businesses – customers Organisations / clubs / trade associations – members Magazines / newsletters – subscribers Local authorities / CCI – households / employers Business / trade directories – businesses Yellow pages – clubs / organisations / businesses Tourism offices – reservations / visitors’ Hotels/accommodation – registration records / reservations SCM 300 Survey Design

Sampling Frames • Only available where there is a finite population – i. e. Sampling Frames • Only available where there is a finite population – i. e. where the population can be clearly defined • Potential problems – List not up-to-date / only up-dated periodically • Lags in registration & deregistration – Clusters of individuals create complexities • e. g. making sure you survey the correct individual in a sampling frame of households – Some cost money to access or are confidential SCM 300 Survey Design

Sampling at Source • Clearly defined population is not the case when sampling at Sampling at Source • Clearly defined population is not the case when sampling at source – i. e. shopping streets, visitor attractions, transport terminals, museums, sporting events, etc • Problems – The population is fairly vague (‘hanging around’) – Individuals present are not listed in any form which would constitute a sampling frame – Sampling is more challenging SCM 300 Survey Design

Sampling Considerations Two key Q’s to address in any sample survey 1. How should Sampling Considerations Two key Q’s to address in any sample survey 1. How should the sample be obtained? a. b. c. d. e. Who or what should be sampled (eligibility criteria)? Who do you survey (profiles & individuals in clusters)? When should sampling take place (timing & timescale)? Where should the survey be administered (location)? What sampling technique do you use (probability versus non-probability)? 2. How large should the sample be? SCM 300 Survey Design

How Should the Sample be Obtained? a. Who or what should be sampled? – How Should the Sample be Obtained? a. Who or what should be sampled? – Therefore defining the eligibility criteria b. Who do you survey? – – Households, visitor attractions, shopping streets, etc will normally have people in clusters as opposed to individuals Ensure that the survey is completed by the correct individual SCM 300 Survey Design

How Should the Sample be Obtained? c. When should the sampling take place? – How Should the Sample be Obtained? c. When should the sampling take place? – – – Time of year, month, day, time Duration of the sampling process Useful to • • Have some prior knowledge of the phenomena to be sampled as results may be biased by particular times of day or year or weekly, monthly & seasonal variations Spread the sampling over different times, days, months, etc to reduce potential for bias SCM 300 Survey Design

How Should the Sample be Obtained? d. Where should the survey be administered? – How Should the Sample be Obtained? d. Where should the survey be administered? – This could be determined by the definition of the population • – On-site surveys should consider location of interviewers • – e. g. surveys sent to postal addresses e. g. recreation areas or tourist attractions tend to have natural or pre-defined entry & exit points If using multiple-interviewers, strict instruction must be given on where to stand SCM 300 Survey Design

How Should the Sample be Obtained? e. What sampling technique should be used? Two How Should the Sample be Obtained? e. What sampling technique should be used? Two main options Probability Techniques 1. Simple random sampling 2. Systematic random sampling 3. Stratified random sampling 4. Cluster sampling 5. Multi-stage sampling SCM 300 Survey Design Non-Probability Techniques 1. Haphazard sampling 2. Purposive sampling a. Judgement sampling b. Quota sampling c. Snowball sampling d. Expert choice sampling

Sampling Techniques • Choice of technique is dependent on 2 Q’s – Is the Sampling Techniques • Choice of technique is dependent on 2 Q’s – Is the population known/clearly defined? – Can the population be listed as a sampling frame? Yes to either Q Allows for Probability Techniques (used with sampling frames) SCM 300 Survey Design No or uncertainty Sampling is complex & based on Non-Probability Techniques (used when sampling at source)

Probability Sampling Techniques 1. Simple random sampling • Each unit has an equal chance Probability Sampling Techniques 1. Simple random sampling • Each unit has an equal chance of selection – – e. g. lottery draw, names pulled from a list Probability of selection is: • • • (sample size/total population)*100 e. g. (100/1, 000)*100 = 10% (a 1 in 10 chance) Should really use a table of random numbers – e. g. see http: //stattrek. com/Tables/Random. aspx SCM 300 Survey Design

Table of Random Numbers Create a sample of 10 from a population of Norway’s Table of Random Numbers Create a sample of 10 from a population of Norway’s top 30 football clubs 01. Ham-Kam 02. Bodø Glimt 03. Hereford United 04. Brann 05. Bryne 06. Lillestrøm 07. Lyn 08. Molde 09. Odd Grenland 10. Stabæk 11. Start 12. Sogndal 13. Vålerenga 14. Viking 15. Aalesund 16. Haugesund 17. Rosenborg 18. Hønefoss 19. Tromsø 20. Sandefjord 21. Åsane 22. Hødd 23. Lørenskog 24. Strømsgodset 25. Frederikstad 26. Mjøndalen 27. Ranheim 28. Tromsdallen 29. Moss 30. Træff 1 7 2 5 8 9 4 0 4 6 3 8 7 0 3 3 2 1 2 7 4 3 7 9 7 1 3 5 5 3 2 2 8 1 5 3 7 9 9 6 6 0 1 7 3 5 4 9 3 1 4 9 2 4 0 9 3 5 4 2 1 9 3 3 6 2 5 2 7 0 3 7 8 3 1 0 6 9 1 4 6 4 2 0 4 7 6 5 3 8 6 4 2 SCM 300 Survey Design

Your turn…. . Create a sample of 10 from a population of England’s top Your turn…. . Create a sample of 10 from a population of England’s top 30 football clubs 01. Chelsea 02. Wigan Athletic 03. Aston Villa 04. Manchester City 05. Reading 06. Carlisle 07. Luton Town 08. Portsmouth 09. Leicester City 10. Derby County 11. Bolton 12. Hereford United 13. Cheltenham 14. Liverpool 15. Fulham 16. Sunderland 17. Middlesborough 18. Arsenal 19. Swindon Town 20. Everton 21. West Ham 22. Millwall 23. Tottenham 24. Birmingham 25. Brighton 26. Blackburn 27. Nottingham Forrest 28. Newcastle 29. Crewe 30. Manchester United 7 2 5 8 9 4 0 4 6 3 8 7 0 3 3 2 1 2 7 4 3 7 9 2 2 3 5 5 3 2 2 8 1 5 3 7 9 9 6 6 0 1 7 3 5 4 9 7 6 4 9 2 4 0 9 3 5 4 2 1 9 3 3 6 2 5 2 7 3 3 7 8 3 1 0 6 9 1 4 6 4 2 0 4 7 6 5 3 8 6 4 2 2 SCM 300 Survey Design

Simple Random Sampling • Quick, cheap n’ easy… • Each unit has an equal Simple Random Sampling • Quick, cheap n’ easy… • Each unit has an equal chance of selection… • Need to list units of the poulation – Difficult to do with a large sampling frame… SCM 300 Survey Design

Probability Sampling Techniques 2. Systematic random sampling • Pull one unit from a list Probability Sampling Techniques 2. Systematic random sampling • Pull one unit from a list at regular intervals – • e. g. every nth name from a membership list Commonly used by production companies to survey product quality SCM 300 Survey Design

Procedure for Systematic Random Sampling SCM 300 Survey Design Procedure for Systematic Random Sampling SCM 300 Survey Design

Example (using a small sampling frame) of 30 students • • Sample 10 from Example (using a small sampling frame) of 30 students • • Sample 10 from a population of 30 30/10=3, select a number between 1 & 3 to start from (e. g. 2), then select every 3 rd number 1. Andy Anderson 2. Anita Ashley 3. Ben Ball 4. Carol Crow 5. David Dent 6. Eddie East 7. Flora Field 8. Gaynor Green 9. Harold Harvey 10. Ineka Ince SCM 300 Survey Design 11. Jai Jones 12. Keith Kent 13. Lorna Law 14. Larry Love 15. Mike Matthews 16. Nigel North 17. Oscar Oliver 18. Paul Plumber 19. Peter Parson 20. Richard Reed 21. Sarah Smith 22. Simon South 23. Tony Tapp 24. Tom Trade 25. Ursula Unger 26. Veronica Vallis 27. Vic Vaxley 28. Wayne West 29. Yen Yeah 30. Zachid

Your turn…. . Sample 6 from the list of 30, starting at 3 1. Your turn…. . Sample 6 from the list of 30, starting at 3 1. Rafael Nadal 2. Kurt Asle Arvessen 3. Thierry Henry 4. Steffi Graff 5. John Carew 6. Bjørn Dæhlie 7. Hermann Maier 8. Roger Federer 9. Andy Murray 10. Thor Hushovd SCM 300 Survey Design 11. Steffen Iversen 12. Alex Zülle 13. Niki Lauda 14. Steffen Kjærgaard 15. Michael Schumacher 16. Guus Hiddink 17. Jacques Villeneuve 18. Katarina Witt 19. David Beckham 20. Renate Götschl 21. Marco Van Basten 22. John Arne Riise 23. John Tavares 24. Fernando Torres 25. Boris Becker 26. Bernard Hinault 27. Emanuel Pogatetz 28. Martina Hingis 29. Arantxa S-Vicario 30. Lewis Hamilton

Probability Sampling Techniques 3. Stratified random sampling • Simple/systematic could miss particular groups when Probability Sampling Techniques 3. Stratified random sampling • Simple/systematic could miss particular groups when using a small population – e. g. mature students • Prior knowledge may suggest that inclusion of a group(s) is necessary – e. g. mature students perform better than others • Stratified random sampling samples according to groups (strata) SCM 300 Survey Design

Procedure for Stratified Random Sampling SCM 300 Survey Design Procedure for Stratified Random Sampling SCM 300 Survey Design

Example Survey a Sample of 400 Households in a County 100 25% 40% 100 Example Survey a Sample of 400 Households in a County 100 25% 40% 100 25% 100 Randomly select an equal amount from each of the 4 districts in the county (e. g. 100 from each for a sample of 400) SCM 300 Survey Design

Problem Associated with Multiple Variables • The sample is representative of a single variable Problem Associated with Multiple Variables • The sample is representative of a single variable but not of others – e. g. representative of the 4 districts in the county but not necessarily of age of residents • Where multiple variables are required, the benefits of stratified random sampling diminish in favour of simple/systematic random sampling • This problem is less likely when creating a large sample SCM 300 Survey Design

Problem Associated with Time & Cost • Stratified divides into groups, then selects units Problem Associated with Time & Cost • Stratified divides into groups, then selects units using random sampling • Random sampling may produce a sample that is geographically dispersed – Especially problematic for face-to-face surveys • e. g. the 100 units selected for the household survey in districts 1 -4 may come from different parts of each district and interviewers may need to travel vast distances between each unit to conduct their surveys • Clustering can overcome this problem SCM 300 Survey Design

Probability Sampling Techniques 4. Cluster sampling • Draw from mutually exclusive sub-groups – e. Probability Sampling Techniques 4. Cluster sampling • Draw from mutually exclusive sub-groups – e. g. the 100 units selected for the household survey in districts 1 -4 will be selected in clusters instead of randomly SCM 300 Survey Design

Example: Stratified versus Cluster 25% 40% 25% 10% Stratified takes an equal amount from Example: Stratified versus Cluster 25% 40% 25% 10% Stratified takes an equal amount from each (e. g. 100 from each for a sample of 400) SCM 300 Survey Design 10% Cluster takes a proportionate amount from each & in clusters (e. g. 16 clusters of 10 from district 1, 4 clusters of 10 from district 2, 10 clusters of 10 from districts 3 & 4, for a sample of 400)

The Problem with Cluster Sampling • Whilst cluster sampling provides huge time & cost The Problem with Cluster Sampling • Whilst cluster sampling provides huge time & cost savings, it is likely to have a much greater potential for sampling error – i. e. certain parts of each district will be excluded SCM 300 Survey Design

Probability Sampling Techniques 5. Multi-stage sampling • Experts increasingly use a combination of probability Probability Sampling Techniques 5. Multi-stage sampling • Experts increasingly use a combination of probability sampling techniques – e. g. sample attitudes to tourists in Norway’s towns • • Draw up a sampling frame of towns in Norway Randomly (simple, systematic or stratified) select an appropriate number of towns Randomly select an appropriate number of electoral wards (geographical units from which politicians are elected) from each town Randomly select an appropriate number of voters from the electoral register of each ward SCM 300 Survey Design

Non-Probability Sampling Techniques 1. Haphazard sampling (accidental, convenience or availability) – Samples drawn at Non-Probability Sampling Techniques 1. Haphazard sampling (accidental, convenience or availability) – Samples drawn at the convenience of the interviewer • – e. g. people on a street that are available & willing to participate This technique should still be systematic • • e. g. stop 1 in every 10 passers-by Don’t just stop those that you fancy. . . ! SCM 300 Survey Design

Non-Probability Sampling Techniques 2. Purposive sampling a. Judgement: samples are believed to possess the Non-Probability Sampling Techniques 2. Purposive sampling a. Judgement: samples are believed to possess the necessary attributes • b. e. g. mature students for a survey on mature students Quota: selection according to a pre-specified sampling frame • • e. g. select 75 out of 100 units aged 21 -25 with the presumption that 75% mature students will be 21 -25 and 25% will be 26+ The problem is that you need to decide which specific characteristics to quota (age, gender, income? ) SCM 300 Survey Design

Non-Probability Sampling Techniques c. Snowball: one sampling unit refers another, who refers another, etc Non-Probability Sampling Techniques c. Snowball: one sampling unit refers another, who refers another, etc • • e. g. expats refer other expats for a survey on expats Not particularly representative but useful when the population is hard to find or access (e. g. the homeless) d. Expert choice: asks experts to choose typical units • • i. e. representative individuals or cities Often referred to as a ‘panel of experts’ This helps elicit views of persons with specific expertise Also means they help to validate & ‘defend’ any results SCM 300 Survey Design

Probability versus Non-probability Sampling Techniques • In probability sampling – Representation is determined by Probability versus Non-probability Sampling Techniques • In probability sampling – Representation is determined by the fact that every unit has an equal chance of being selected, based on probability theory • In non-probability sampling – There is an assumption that there is an even distribution of characteristics within the population – BUT, the population may or may not be represented and it will be hard to know which is true SCM 300 Survey Design

Why Might the Following Approaches to Sampling be Biased? 1. I want to survey Why Might the Following Approaches to Sampling be Biased? 1. I want to survey golf club members attitudes to the quality of the greens and survey a sample of the top 25 players at the club 2. I want to survey people in Molde to find out what they think about my cafe so I survey every 10 th customer in the cafe. Surveys are conducted every Monday morning 3. I survey 2, 500 bus passengers in Ålesund, over a series of times, days and months, to ask what they think about the availability of bus services in Ålesund SCM 300 Survey Design

Sources of Error • Non-sampling errors (i. e. from survey design or delivery) – Sources of Error • Non-sampling errors (i. e. from survey design or delivery) – Non-observation errors: failing to obtain data from certain segments of the population due to non-response or exclusion – Observation errors: inaccurate information obtained from the samples or errors in data processing, analysis or reporting Characteristic Population Sample (% pop) Responses (% sample) 18 -21 years 500 250 (50%) 179 (72%) 22 -25 years 300 150 (50%) 96 (64%) 26+ years 200 100 (50%) 10 (10%) Total 1, 000 500 (50%) 285 (57%) SCM 300 Survey Design

Sources of Error • Sampling error (i. e. from sampling) – Where the sample Sources of Error • Sampling error (i. e. from sampling) – Where the sample drawn may not provide the same estimates of certain characteristics as other same-size samples from the population SCM 300 Survey Design

Example of Sampling Error • Age of Squash club members (n=40): 24, 21, 23, Example of Sampling Error • Age of Squash club members (n=40): 24, 21, 23, 16, 17, 56, 60, 64, 58, 57, 60, 47, 42, 41, 40, 22, 35, 38, 40, 41, 49, 19, 20, 35, 27, 28, 29, 30, 71, 66, 21, 23, 26, 27, 30, 31, 45, 55 • Overall average is 37. 5 years (population parameter) • Average for 5 separate samples of 10 members – 35. 7, 39. 5, 23. 1, 51. 3, 30. 3 (estimates) • Accuracy (AKA standard error) of sample means can be calculated for probability samples SCM 300 Survey Design

Standard Error • Accuracy is often quoted in studies “ 56% of customers were Standard Error • Accuracy is often quoted in studies “ 56% of customers were more than satisfied with service quality; this estimate is subject to a 2% error either way” • The 2% error is called the standard error • Measures statistical accuracy of the sample • Standard error decreases as sample size increases – Zero error when the sample is the population SCM 300 Survey Design

Calculating the Standard Error • Standard error = sdev / (√n) – sdev: standard Calculating the Standard Error • Standard error = sdev / (√n) – sdev: standard deviation of sample mean – n: sample size Example – Random sample of 50 customers have a mean age of 23. 4 and a standard deviation of 9. 7 – Standard error = 9. 7 / (√ 50) = 1. 4 – Therefore, population mean is likely to be 23. 4 +/1. 4 (i. e. range between 22. 0 -24. 8 years) SCM 300 Survey Design

Degrees of Confidence • Standard error doesn’t say how likely it is (i. e. Degrees of Confidence • Standard error doesn’t say how likely it is (i. e. how confident we can be) that the estimated range is correct • We use principles of standard deviation to determine the level of confidence in our estimated range SCM 300 Survey Design

Standard Deviation 68% 95% of responses fall within 2 sdev’s of the mean 95% Standard Deviation 68% 95% of responses fall within 2 sdev’s of the mean 95% 99% -3 sd -2 sd -1 sd Mean +1 sd +2 sd +3 sd SCM 300 Survey Design

Degrees of Confidence • 2 sdev’s means we can be 95% confident (i. e. Degrees of Confidence • 2 sdev’s means we can be 95% confident (i. e. correct 95 times out of 100) that the sample mean will lie within 2 sdev’s of the population mean • Calculating 95% confidence for the earlier example – Where we said that the population mean is likely to be 23. 4 +/-1. 4 (i. e. range between 22. 0 -24. 8 years) – 23. 4 +/- 2. 8 (standard error of 1. 4 x 2) provides a range of 20. 6 to 26. 2 • Therefore, we can be 95% confident that the population mean is between 20. 6 and 26. 2 years • Do the same for the 99% level of confidence…. . SCM 300 Survey Design

Acceptable Level of Confidence? • 68% of all sample means would fall within a Acceptable Level of Confidence? • 68% of all sample means would fall within a range of +/- 1 sdev of the population – This means that we would be 68% confident that the population mean is between 22. 0 & 24. 8 years • The 68% level of confidence means there is a 32% chance of being incorrect • 95% is normally used as the acceptable level of confidence for statistical analysis SCM 300 Survey Design

How Large Should the Sample be? • Sample size is NOT relative to population How Large Should the Sample be? • Sample size is NOT relative to population size! • Sample size is absolute – e. g. provided sampling procedures have been followed, a sample size of 1, 000 is equally valid for a population of British adults (50 mn), London residents (7 mn) or Molde residents (24, 000) • Sample size is determined by – – The availability of resources The purpose of data you intend to collect The required level of accuracy in the results The required level of confidence SCM 300 Survey Design

Resources & Purpose • Availability of resources is self-explanatory • The purpose of data Resources & Purpose • Availability of resources is self-explanatory • The purpose of data you intend to collect – Smaller OK for descriptive info. on attitudes – Larger required for explanations for attitudes • e. g. to investigate satisfaction according to gender, you need sufficient numbers of each gender and each level of satisfaction in order to capture the variation within the population – 5 in each would result in a minimum sample size of 60 (see next slide) SCM 300 Survey Design

Sample Size & Explanations for Attitudes Male Female Total Very Satisfied 5 5 10 Sample Size & Explanations for Attitudes Male Female Total Very Satisfied 5 5 10 Neither 5 5 10 Dissatisfied 5 5 10 Very Dissatisfied 5 5 10 Total 30 60 SCM 300 Survey Design 30

Optimum Size for Probability Samples • Estimating proportions method is one of many methods Optimum Size for Probability Samples • Estimating proportions method is one of many methods used by researchers • Assumes – – No info. on standard error from previous studies Size of population is known Simple or systematic random sampling Sample will be used to estimate proportions • e. g. the percentage of customers that are satisfied • e. g. the percentage of students that like to play squash • e. g. the percentage of voters for a particular party SCM 300 Survey Design

Optimum Size for Probability Samples • Sample size is determined by n = z² Optimum Size for Probability Samples • Sample size is determined by n = z² p(1 -p) H² • Where – – n = sample size needed to achieve the level of reliability p = the population proportion (i. e. % satisfied customers) H = desired level of accuracy z = standard error corresponding to the desired level of confidence (z = 2. 0 for 95%) SCM 300 Survey Design

Optimum Size for Probability Samples Example: sampling levels of customer satisfaction 1. Want to Optimum Size for Probability Samples Example: sampling levels of customer satisfaction 1. Want to estimate % satisfied customers within +/-2% Ø 2. Estimate what proportion of the population are satisfied (50% is normal unless a pilot or previous study suggests otherwise) Ø 3. p = 0. 5 (5 / 100) Select the desired level of confidence Ø 4. H = 0. 02 (2 / 100) z = 2 (z is 2 at the 95% level) Calculate sample size n = 2² 0. 5(1 -0. 5) 0. 02² n = 10, 000 x 0. 25 n = 2, 500 SCM 300 Survey Design Now select 2, 500 samples from the sampling frame using simple or systematic random sampling

Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% 50 13. 7 12. 8 11. 2 8. 4 100 9. 8 9. 7 9. 0 7. 9 5. 9 250 6. 2 6. 1 5. 7 5. 0 3. 7 500 4. 4 4. 3 4. 0 3. 5 2. 6 1, 000 3. 1 3. 0 2. 8 2. 5 1. 9 2, 500 2. 0 1. 9 1. 8 1. 6 1. 2 5, 000 1. 4 1. 3 1. 1 0. 8 10, 000 1. 0 0. 9 0. 8 0. 6 20, 000 0. 7 0. 6 0. 4 40, 000 Could reduce sample size by reducing level of accuracy (e. g. 4. 4% for just 500!) 14. 0 0. 5 0. 4 0. 3 SCM 300 Survey Design

Effect of Changing the Level of Confidence Sample size (50/50%) 99% (z=2. 6) 95% Effect of Changing the Level of Confidence Sample size (50/50%) 99% (z=2. 6) 95% (z=2. 0) 90% (z=1. 6) 50 18. 4 14. 0 11. 8 100 13. 0 9. 8 8. 3 250 8. 2 6. 2 500 5. 8 4. 4 3. 7 1, 000 4. 1 3. 1 2. 6 2, 500 2. 6 2. 0 1. 6 5, 000 1. 8 1. 4 1. 2 10, 000 1. 3 1. 0 0. 8 20, 000 0. 9 0. 7 0. 6 40, 000 0. 6 0. 5 0. 4 SCM 300 Survey Design

Your turn. . . Sampling if students like to play squash Using the ‘estimating Your turn. . . Sampling if students like to play squash Using the ‘estimating proportions methods’, estimate the optimum sample size for a survey on whether students like to play squash. 1. The desired level of accuracy is 5% 2. The same survey from last year found that 20% like to play 3. The desired level of confidence is 95% SCM 300 Survey Design

Result. . . Example: sampling if students like to play squash 1. Want to Result. . . Example: sampling if students like to play squash 1. Want to estimate % students that like to play within +/-5% Ø 2. Estimate what proportion of the population like to play (the same survey from last year found that 20% like to play) Ø 3. p = 0. 2 (2 / 100) Select the desired level of confidence Ø 4. H = 0. 05 (5 / 100) z = 2 (z is 2 at the 95% level) Calculate sample size n = 2² 0. 2(1 -0. 2) 0. 05² n = 1, 600 x 0. 16 n = 256 SCM 300 Survey Design Now select 256 samples from the sampling frame using simple or systematic random sampling

Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% 50 14. 0 13. 7 12. 8 11. 2 8. 4 100 9. 8 9. 7 9. 0 7. 9 5. 9 250 6. 2 6. 1 5. 7 5. 0 3. 7 500 4. 4 4. 3 4. 0 3. 5 2. 6 1, 000 3. 1 3. 0 2. 8 2. 5 1. 9 2, 500 2. 0 1. 9 1. 8 1. 6 1. 2 5, 000 1. 4 1. 3 1. 1 0. 8 10, 000 1. 0 0. 9 0. 8 0. 6 20, 000 0. 7 0. 6 0. 4 40, 000 0. 5 0. 4 0. 3 SCM 300 Survey Design

SUGGESTED APPENDIX Statistical Note on Sample Size & Confidence Intervals This survey has a SUGGESTED APPENDIX Statistical Note on Sample Size & Confidence Intervals This survey has a sample size of 500. All samples are subject to a margin of statistical error. The margins of error, or ‘confidence intervals’, for this survey are as follows: Finding from the survey 95% confidence interval 50/50% 40/60% +/-4. 3% 30/70% +/-4. 0% 20/80% +/-3. 5% 10/90% +/-2. 6% 5/95% +/-4. 4% +/-1. 9% This means, for example, that if 20% of the sample are found to have a particular characteristic, there is an estimated 95% chance that the true population percentage lies in the range 20 +/- 3. 5, i. e. between 16. 5 and 23. 5%. These margins of error have been taken into account in the analysis in this report. Source: Veal (1997; p 215) SCM 300 Survey Design

Dodgy Opinion Polls…. . ? ”Senterpartiet er også i siget med 9 prosent, en Dodgy Opinion Polls…. . ? ”Senterpartiet er også i siget med 9 prosent, en framgang på 2, 2 siden juni” (Tidens Krav, 20/08/07) Meningsmålingen for august er laget av Sentio Research Norge for Tidens Krav, Romsdals Budstikke, Sunnmørsposten og NRK. 500 personer i Møre og Romsdal er intervjuet 13. og 14. august. SCM 300 Survey Design

Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% Optimum Sample Sizes at the 95% Level Sample size 50/50% 40/60% 30/70% 20/80% 10/90% 50 14. 0 13. 7 12. 8 11. 2 8. 4 100 9. 8 9. 7 9. 0 7. 9 5. 9 250 6. 2 6. 1 5. 7 5. 0 3. 7 500 4. 4 4. 3 4. 0 3. 5 2. 6 1, 000 3. 1 3. 0 2. 8 2. 5 1. 9 2, 500 2. 0 1. 9 1. 8 1. 6 1. 2 5, 000 1. 4 1. 3 1. 1 0. 8 10, 000 1. 0 0. 9 0. 8 0. 6 20, 000 0. 7 0. 6 0. 4 40, 000 0. 5 0. 4 0. 3 SCM 300 Survey Design A 2. 2% change is within the margin of error and can therefore be ’down to chance’

Optimum Size for Non-Probability Samples • Optimum sample sizes can’t be determined for nonprobability Optimum Size for Non-Probability Samples • Optimum sample sizes can’t be determined for nonprobability samples – Can use optimum probability samples but levels of accuracy & confidence are relatively meaningless • The equation is based on probabilities • Size is simply based on pragmatic considerations – i. e. resources & purpose of data SCM 300 Survey Design

The Effect of Non-Response on Sample Size • Previous studies may suggest that you The Effect of Non-Response on Sample Size • Previous studies may suggest that you can expect a certain response rate – take this into account – e. g. if you need a sample of 200 and expect a response rate of 40%, you should consider sampling 500 – e. g. if your interested in opinions about a particular event and only 30% of your sample attended the event, sample size should be increased SCM 300 Survey Design

Summary • A small & manageable portion or sub-set – Commonly associated with quantitative Summary • A small & manageable portion or sub-set – Commonly associated with quantitative methods – Applies to human & non-human phenomena – Extracted from a sampling frame or at source • 2 main sampling techniques – Probability & non-probability sampling • 2 main types of error – Non-sampling & sampling errors SCM 300 Survey Design

Summary • Levels of accuracy & confidence – Standard error measures accuracy in sample Summary • Levels of accuracy & confidence – Standard error measures accuracy in sample estimates – Confidence determines likelihood that the estimate is correct • Sample size is absolute – Based on resources available & purpose of data – Also based on desired accuracy & confidence (probability sampling) SCM 300 Survey Design

Recommended Reading • Chapters 1 & 2 in Fink, A. (2003). The Survey Handbook. Recommended Reading • Chapters 1 & 2 in Fink, A. (2003). The Survey Handbook. 2 nd Ed. London: Sage. SCM 300 Survey Design

“Thank you for your attention” Questions. ……. SCM 300 Survey Design “Thank you for your attention” Questions. ……. SCM 300 Survey Design




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