![]() The six factors listed here are intimately linked so that if we know five of them we can estimate the sixth one. A pilot study may be required for this purpose or expert clinical judgement could be sought.The power of an experiment is the probability that it can detect a treatment effect, if it is present. In some cases it can be based on data from previous studies. Determining the effect size can be a difficult task. Test Effect size Small Medium Large Difference between two means d 0.20 0.50 0.80 Difference between many means f 0.10 0.25 0.40 Chi-squared test w 0.10 0.30 0.50 Pearson's correlation coefficient ρ 0.10 0.30 0.50 Table 1 Small, medium and large effect sizes as defined by Cohen 11 Effect size This is the smallest difference or effect that the researcher considers to be clinically relevant. However, other factors need to be considered, as discussed below. As a rule, larger sample sizes have more statistical power. How large should a sample size be? Unfortunately there is no one simple answer to this question. Recruiting more participants than required would also be a waste of both resources and time. Equally, it would not be ethically acceptable to conduct a study by recruiting thousands of participants when sufficient data could be obtained with hundreds of participants instead. It would not be ethically acceptable to conduct a study that would not be stringent enough to detect a real effect due to a lack of statistical power. Research ethics committees often ask for justification of the study based on sample size estimation and statistical power. Firstly, it is increasingly becoming a requirement for most research proposals, applications for ethical clearance and journal articles. Why is statistical power important? Sample size estimation and statistical power analyses are important for a number of reasons. there is a 20% chance of accepting the null hypothesis in error, i.e. Statistical power is conventionally set at 0.80 or 80% 10 i.e. What is statistical power? Statistical power (P) is defined as: P = 1 – Power is dependent on a number of factors, which will be explained later. A beta () level can be chosen as protection against this type of error. A type II, or false-negative, error occurs if the null hypothesis is accepted incorrectly. There is a 5% chance of this occurring if the alpha level is set at 0.05. ![]() ![]() A type I, or false-positive, error occurs if the null hypothesis is rejected incorrectly. This process however has two potential errors type I and type II. The null hypothesis is only rejected if the probability (P-value) is equal to or less than the alpha level. 8, 9 Statistical analysis is then carried out in order to calculate the probability that the difference or effect was purely due to chance. This is referred to at the alpha level (). ![]() Clearly, a criterion must be set for rejecting the null hypothesis. Instead, a finding is described as “not statistically significant” if the null hypothesis is accepted and “statistically significant” if the alternative hypothesis is accepted. Rarely will you see the terms null and alternative hypothesis used in scientific papers. If analysis indicates that the difference or effect is not likely to have occurred by chance then the null hypothesis is rejected in favour of the alternative hypothesis, stating that a real effect has occurred. Statistical analysis determines whether the null hypothesis is correct or not. This is referred to as the null hypothesis. Convention has it that any difference or effect found in an experiment has been caused by chance alone. The first is the concept of hypothesis testing. 2-7 Basic statistical concepts There are several statistical concepts that must be grasped before reading this article. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi. 1 This article presents a step-by-step guide of the process for determining sample size and statistical power. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. PEERREVIEWED Sample size estimation and statistical power analyses Bhavna Prajapati, Mark Dunne & Richard Armstrong 16/07/10 CLINICAL The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. ![]()
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