Ali, Syed Asad

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Vol. 62, No. 6, June 2012 624Sample Size Calculation and Sampling TechniquesSyed Asad AliDepartment of Paediatrics and Child Health, Aga Khan University, Karachi.Email: asad.ali@aku.eduLearning ResearchSample Size Calculation and SamplingTechniques:Calculating and justifying sample size for a study can bean intimidating task for new researchers. Nonetheless, it is one ofthe most important aspects of any study. In this article, we aim toprovide basic and fundamental information about calculatingsample size which should be helpful for most research studies. In research studies, a sample has to be obtained if it isnot possible to include all the subjects in the study population.For example, if you want to study the prevalence of smokingin the first year medical students of your medical college, youcould just ask all of the students in that class to fill thequestionnaire, without doing any sampling. However, if youwant to know the prevalence of smoking in all the medicalstudents of Pakistan, then it will be very difficult for you tohave each and every medical student to fill yourquestionnaire. In that case you will need to do sampling. For sampling to work correctly, it is critical that thesample is free from bias. This means that everybody in thestudy population should have a more or less equal chance ofbeing included in the sample. If sample is collected in such away that some members of the study population have lesschance of being included than others, then the resulting sampleis a biased sample, and the results obtained from such a samplewill not be valid or generalizable to the entire study population. While calculating sample size, the first thing to note isthat methods to calculate sample size vary depending on thestudy design. For example, calculating sample size for asurvey has a different methodology than to calculate samplesize for a case control study or a clinical trial. However, thefundamental principles remain the same. There are many statistical softwares and onlinewebsites which can help you in calculating sample size foryour studies (Figure). However, you need to have followingfour parameters in hand before you can use those resources:(1) The effect size (2) The population standard deviation (for continuous data); (3) The desired power of the experiment to detect the625 J Pak Med Assocpostulated effect; (4) The significance level. The effect size reflects the expected difference in thetwo study groups of your study. For example, if you knowthat the current cure rate for disease X with drug A is 20%,and you think that the new drug B will have cure rate of 40%,then your expected effect size for drug B is double that ofdrug A. The larger your expected effect size, the smaller willbe your required sample size. However, if you overestimateyour effect size, you will be at risk of having false negativeresults. While you cannot know the effect size for sure beforedoing the study, you must have some rationale for choosing aparticular estimated effect size. This is done based onpreviously published studies, or your own preliminary data.If you are doing a survey, then the effect size meansthe estimated response rate to your study question in thepopulation. For example, if you are surveying the <15 yearsold population of Karachi for measles antibodies, you willneed to know the total < 15 years old population of Karachiand the estimated prevalence of measles based on yourliterature review. This information will need to be entered inthe sample size calculation formulas available at the listedwebsites or softwares. If you have no idea about the expectedresponse rate for your study question (measles sero-prevalence in the above example), then a response rate(measles seropositivity) of 50% is selected as a convention,as this response rate gives you the maximum sample size. Population Standard Deviation is only needed if youare measuring a continuous variable. It is a measure of howspread out your data is in the study population. This is alsoobtained from previously published studies or your ownpreliminary data. For a yes/no (dichotomous) question, it isnot required to find the standard deviation. The power of the study means the ability to find adifference between the two groups being studied, if there isactually a difference. In the above example of drug A vs. drugB for the Disease X, even if drug B was actually better thandrug A, it is still possible that by chance, they may appear tohave same efficacy in your study which is based on a sample.This possibility is called beta error. If we want to be close to100% sure of our finding (i.e. no beta error), then we willneed a very large sample size. As a convention, scientists areFigure: Approach and online resources for calculating sample size for different study designs. happy to be 80% sure that if there is a true difference in thetwo groups, their study will find it. Hence conventionally,80% power (or 90% in some cases) is taken as standard. 80%power corresponds to a beta error of 20%. The final thing to decide on while calculating samplesize is the significance level. Taking the same example of twodrugs A and B for Disease X, it is possible that while in truth,there was no difference in the cure rates of the drugs A and B,just by chance in your study, drug B shows better cure ratethan drug A. This is called the alpha error. If we have the alphaerror of 0, then we will need a very large sample size. Ingeneral scientists accept the alpha error of 5% in their studies.Alpha error of 5% is also written as significance level of 95%. In calculating sample size, the effect size andpopulation standard deviations have to determined (andjustified) by the scientists with the help of previous literature ortheir own preliminary data, while the power and significancelevel are taken as 80% and 95% respectively as a convention.Once you have the information and references foryour expected effect size and your population standarddeviation, you should go to a relevant statistical software (e.gEpi Info, SPSS etc) or website as indicated in Figure 1. Onceyou feed in your numbers, the programme will give you therequired sample size. The websites also often provide the textthat you can use in your study proposals and papers tocommunicate the methodology of how you calculated yoursample size. However, please note that you have to give thejustification of how you calculated your effect size yourself,with the help of previous research studies in the field. After you get the required sample size estimatefrom the above websites, the next step will be for you toselect an appropriate sampling technique. Sampling frameis the source material from which a sample is drawn. Thereare different methods through which a sample can beselected from a sampling frame. These methods can bebroadly classified as probability and non-probabilitysampling methods. A good example of probabilitysampling technique is simple random selection. Forexample in the above study, if you had a list of all themedical students of Pakistan, you could randomly selectthe students (total number based on your sample sizecalculation) and have them fill the study questionnaire. Ifthis not possible to do because of operational challenges,then there are various other options available. Thesemethods are defined in the table.It is important that the correct sample size calculationsbe done before initiating the study. This is critical foranswering the study questions correctly. Good journals do notaccept studies for publication without proper sample sizecalculations. Sample size calculation is also a requirement forall study proposals. The little effort done in doing formalsample size calculation and defining proper samplingtechniques for your study are one of the most importantaspects of your study.Vol. 62, No. 6, June 2012 626Table: Overview of Sampling Techniques.A probability sampling scheme is one in which every unit in thepopulation has a chance (greater than zero) of being selected in thesample, and this probability can be accurately determined.Examples of Probability SamplingIn a simple random sample, all members of the study populationhave an equal chance of being selected in the sample.Systematic sampling relies on arranging the target populationaccording to some ordering scheme and then selecting elements atregular intervals through that ordered list. Systematic samplinginvolves a random start and then proceeds with the selection ofevery kth element from then onwards.Stratified sampling is used when the study population has numberof distinct categories or strata. For example, if we are drawing asample of Pakistan, then each of its provinces could be consideredas a stratum. In stratified sampling, each stratum is then sampled asan independent sub-population, out of which individual elementscan be randomly selected.Nonprobability sampling is any sampling method where some elements of the populationhave 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.Example of Non-probability SamplingConvenience sampling involves the sample being drawn from that part of the studypopulation which is close to hand. That is, a population is selected because it isreadily available and convenient. The researcher using such a sample cannotscientifically make generalizations about the total population from this samplebecause it would not be representative enough.

Sample size calculation and sampling techniques

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Sample size calculation and sampling techniques

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