1. Numeracy & Quantitative Methods Laura Lake

2. Probability sample – a method of sampling that uses of random selection so that all units/ cases in the population have an equal probability of being chosen. Non-probability sample – does not involve random selection and methods are not based on the rationale of probability theory. Types of Sampling

3. Why is probability sampling important in quantitative research? Research finding not based on samples that are biased / unrepresentative. Based on a sampling frame it enables research to be replicable or repeatable. Research results can be projected from the sample to the larger population with known levels of certainty/precision ( i.e. standard errors & confidence intervals for survey estimates can be constructed). Probability Sampling in Quantitative Research

4. To achieve this the sampling frame used needs to: ensure that the correct population is being sampled i.e. it addresses the questions of interest accurately covers all members of the population being studied so they have a chance to be sampled. The quality of the population list (sampling frame) i.e. whether it is up-to-date and complete is the most important feature for accuracy in the sampling. Probability Sampling in Quantitative Research

5. Four main types of probability sampling: 1.Simple random sample 2.Systematic sample 3.Stratified random sample 4.Cluster/ multi-stage random sample Types of Probability Sampling

6. Randomly selecting units from a sampling frame. ‘Random’ means mathematically each unit from the sampling frame has an equal probability of being included in the sample. Stages in random sampling: Simple Random Sampling Define population Develop sampling frame Assign each unit a number Randomly select the required amount of random numbers Systematically select random numbers until it meets the sample size requirements

7. Similar to simple random sample. No table of random numbers – select directly from sampling frame. Systematic Sampling Define population Develop sampling frame Decide the sample size Work out what fraction of the frame the sample size represents Select according to fraction (100 sample from 1,000 frame then 10% so every 10 th unit) First unit select by random numbers then every nth unit selected (e.g. every 10 th )

8. ‘Gold standard’ of sampling. Why? Designed to be more representative of the population where the sampling frame is ‘stratified’ according to population variables. Variables selected for stratifying are determined by the characteristics needed by the research. Stratification – splitting the population into the different strata (variables e.g. gender, age, ethnic background). Samples can be stratified across more than one variable. Stratified Random Sample

9. As a random sample: Stratified Random Sample Define population Develop sampling frame according to characteristics required Determine the proportion of each population variable of interest Systematic sampling methods can then be followed to select sample unit

10. Cluster sampling: selecting a sample based on specific, naturally occurring groups (clusters) within a population. - Example: randomly selecting 20 hospitals from a list of all hospitals in England. Multi-stage sampling: cluster sampling repeated at a number of levels. -Example: randomly selecting hospitals by county and then a sample of patients from each selected hospital. Cluster/ multi-stage random sample

11. Three main types of non-probability sampling: 1.Convenience 2.Quota 3.Snowball Non-Probability Sampling

12. A sample selected for ease of access, immediately known population group. + good response rate. – cannot generalise findings (do not know what population group the sample is representative of) so cannot move beyond describing the sample. Convenience Sampling

13. Aim is to sample reflecting proportions of population in different categories or quotas (e.g. gender, age, ethnicity). Used in often in market and opinion poll research. + easy to manage, quick – only reflects population in terms of the quota, possibility of bias in selection, no standard error Quota Sampling

14. Useful when a population is hidden or difficult to gain access to. The contact with an initial group is used to make contact with others. + access to difficult to reach populations (other methods may not yield any results). - not representative of the population and will result in a biased sample as it is self-selecting. Snowball Sampling

15. “How large should my sample be in order for it to be representative”? Larger samples are not necessarily better – how representative a sample it depends on the sampling technique used and the size of the population. Determining sample size is dependent of how much error you are prepared to accept in your sample. Sample Size?

16. The larger the sample size the more likely error in the sample will decrease. But, beyond a certain point increasing sample size does not provide large reductions in sampling error. Accuracy is a reflection of the sampling error and confidence level of the data. Sampling Error and Confidence

17. If a sample has been selected according to probability we can assess the level of confidence. Confidence levels will allow you to state, with a certain level of confidence, that the sample findings would also be found in the population. Sampling Error and Confidence

18. Example: +/ - 3% at 95% confidence level A confidence interval of +/- 3% at the 95% confidence level means that, 95% of the time, the ‘true’ answer will be within 3% of the survey findings. Confidence Intervals Voting behaviour% of poll Labour37% Conservative35% Liberal Democrat22% Other6%

19. Bryman, A. (2008) Social Research Methods. 3 rd Ed. Oxford: Oxford University Press. David, M. and Sutton, C. (2004) Social Research :The Basics. London: Sage. ESRC Survey Measurement Programme. Online: available from Survey Resource Network http://www.surveynet.ac.uk/http://www.surveynet.ac.uk/ Oppenheim, A. (2000) Questionnaire Design, Interviewing and Attitude Measurement. London: Continuum References

20. This resource was created by the University of Plymouth, Learning from WOeRk project. This project is funded by HEFCE as part of the HEA/JISC OER release programme.Learning from WOeRk This resource is licensed under the terms of the Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales license (http://creativecommons.org/licenses/by-nc-sa/2.0/uk/).http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ The resource, where specified below, contains other 3 rd party materials under their own licenses. The licenses and attributions are outlined below: 1.The name of the University of Plymouth and its logos are unregistered trade marks of the University. The University reserves all rights to these items beyond their inclusion in these CC resources. 2.The JISC logo, the and the logo of the Higher Education Academy are licensed under the terms of the Creative Commons Attribution -non-commercial-No Derivative Works 2.0 UK England & Wales license. All reproductions must comply with the terms of that license. Author Laura Lake InstituteUniversity of Plymouth Title Numeracy & Quantitative Methods Sampling: Probability & non-probability sampling Description Overview of probability and non-probability sampling techniques in quantitative research. Date Created March 2011. Educational Level Level 5 Keywords UKOER LFWOERK UOPCPDRM Learning from Woerk WBL Work Based Learning CPD Continuous Professional Development Probability sample, non-probability sample, simple random sample, systematic sample, stratified random sample, cluster/ multi-stage random sample, stratification, convenience sampling, quota sampling, snowball sampling, sampling error, confidence intervals. Creative Commons License Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales license Back page originally developed by the OER phase 1 C-Change project ©University of Plymouth, 2010, some rights reserved