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Forum Research research-collins/OF/NH2 01/10/2007 17:19 Page 1 Significance of getting the right sample size Claire Collins gives an overview of the principles and variables that underpin sample size estimation WHAT SAMPLE SIZE DO I NEED? is probably the question I am most often asked; however, reference to the sample size estimation is often excluded from research proposals. The sample size estimation approach depends ,among other things, on the design of the study, descriptive or comparative, independent or matched, and the type of variable being analysed. While some researchers apply the appropriate formulae to calculate the sample size required, most seem to utilise the services of a statistician or one of the available sample size calculators. Whichever you use, you will need to provide certain information in order to determine the sample size required. In a single group study, a precision-based sample size is based on the confidence level and the required width of the confidence interval. In a two-group comparison, the sample size is based on significance level, the minimum difference to be detected at that significance level, and the power to detect that difference. If you are testing for an effect, you need to specify the size of the effect you wish to be able to detect and the probability of detecting it, if it exits (the power of the test). You also need some estimate of the variability between subjects. The four principles underlying sample size therefore are: • Variance and sampling variation: standard deviation (SD) – variability of individual observations of continuous measurements around a mean in a sample; standard error (SE) – variability of a mean or percentage from one sample to another sample. Precision increases as the sample size increases • Effect size: This refers to the estimated difference you expect to see between the two groups under study and is determined from previous experience/studies or on an estimate of what would be of scientific/clinical interest. The bigger the effect, the smaller the sample size required to detect it • Significance: How likely is it that the observed difference is due to chance when the true difference is zero? Type I/α error is where you reject the null hypotheses incorrectly. A 5% level is usual chosen • Power: How likely you are to detect a difference for a given sample size, effect size and level of significance. Note if you increase your sample size by X, your power increases by X. Type II/β error is where you accept the null hypotheses incorrectly. A 20% or lower level is recommended (ie. an 80% or higher power). Often in a study there is more than one variable of inter- √ est. Ideally, one should calculate the sample size required for each and select the largest sample suggested. The alternative is to base the calculation on one key variable but this requires a decision regarding which of the variables will underpin the sample size estimation. Note that many of formulae and examples used in demonstration articles and most sample size tables assume that the sample is being selected using a simple random sample technique and are not applicable to samples selected using alternative techniques. The sample size estimations do not allow for non-contacts and non-response. You should consider increasing your target sample size to allow for these. In addition, your sample may need to be increased to permit internal comparisons (eg. between males and females, etc.). The sample must be sufficiently big enough that an effect of scientific significance will also be statistically significant but not so big that an effect of little scientific importance is statistically detectable. In reality, the size of the sample selected is a balance between precision and feasibility, with consideration given to economic (cost and time resources) and ethical (risk of involvement) concerns. In most circumstances, you are likely to estimate the sample with varying effect size and significance and power levels in order to determine what is best suited to your project, given all considerations. The references below, used to compile this summary piece, contain many examples of sample size calculation. Claire Collins is ICGP director of research References 1. Daly, LE, Bourke, GJ. Interpretation and Uses of Medical Statistics 5th edition. UK, Blackwell Science Ltd., 2000 2. du V Florey, C. Sample size for beginners. BMJ 1993; 306: 1181-1184 3. Israel, GD. Determining sample size. http://edis.ifas.ufl.edu/PD006. University of Florida. Original publication Nov 1992. Reviewed June 2003 4. Lenth, RV. Some practical guidelines for effective sample size determination. www.stat.uiowa.edu/techrep/tr303.pdf. University of Iowa, 2001 FORUM October 2007 25