It is not a secret that determining the sample size that is optimal for a study is a very responsible and difficult process that requires considerable research. The main of sample size determination is finding such a number of subjects so as to make it possible to get statistically significant results. This process is not easy due to a number of variables that it involves. In particular, there are four of them that will be considered below. The first is the desired level of statistical power. His indicator can be interpreted as the probability that effect of treatment will be detected if there is such. Usually, it is set at 0.80m which means that such probability is equal to 80% (DMS, 2006). Under-powered study, consequently, will have less than 80% of probability, while over-power will have greater indicator. The second variable is the P level, which is the probability of finding a difference that is statistically significant and is a result of chance, not of the treatment. Thus, it concerns the probability of receiving a result that is erroneously significant. This type of error is also referred as the Type I error. Usually this variable is set at 0.05, which is 5% probability of such mistake occurrence. The two variables described above are predetermined. The third, which is treatment variability, and forth, which is error variability, should be estimated so as to successfully complete the process of sample size determination. There are three ways, in which these variables can be obtained. The first is conducting a pilot study.
This method provides the most accurate result for determining the sample size. In order to do it, it is necessary to hold small-scale preliminary study, which will not have statistical significance, but will show the necessary variables. It is strongly recommended to use this method for estimation of treatment and error variability. The second way to do it is studying the relevant literature. In this case, the estimates on the necessary variables can be made on the basis of previously published studies, in which similar studies were conducted and related question were answered. It is recommended to use this method if pilot study cannot be conducted due to some reasons (DMS, 2006). The last way is called rule-of-thumb estimates. In its scope rough approximations, which are also called the rules-of-thumb, which are accepted in each particular field, are used. This type of procedure is the least effective and should be used only if there is no possibility to conduct pilot study and there is no relevant literature in the given field. If upon conducting the necessary procedure it was discovered that treatment variability is large in relation to the error variability, then the sample size can be relatively small, while in such situation it will still be statistically significant. If the situation is the opposite, then it is necessary to take a large sample size so as to receive reliable results.
For this assignment I have chosen two calculators – the first developed by the Creative Research Systems (“Sample Size Calculator,” n.d.) and the second – by the National Statistical Service (NSS, n.d.). The first of them allows to determine sample size by choosing the following variables – confidence level, which can be either 95% or 99%, confidence interval and population. Besides, there is a possibility to find confidence interval in a separate calculator, in which it is necessary to specify the confidence level, sample size, population and percentage. The formula for determining sample size that is used at this website is the following: . Here Z is Z value, which is equal to 1.96 for the confidence level of 95%. P is percentage picking a choice, expressed as decimal. C is the confidence interval expressed in the decimal form. The second calculator that I have chosen has another structure and allows definition of the confidence interval, standard error, relative standard error and sample size upon condition that one of these four variable is already known. The other variables that should be provided are the confidence level, population size and proportion. The last estimate can be left blank, in which case it will be assumed to be 0.5. In order to test the calculators, I have chosen the confidence level of 95%, population size of 1000 and confidence interval of 5%, which is 0.05. Both calculators showed the same result – sample size of 278 people.
At the same time, the second calculator showed relative standard error of 5.10, standard error of 0.02551 and upper and lower values for the confidence interval of 0.55 and 0.45 respectively. Thus, in my point of view, the second calculator is more representative for researchers and should definitely be used if the given variables should also be identified. Still, the first calculator is also effective for the sample size determination. Both of them are easy to use, especially owing to the detailed explanations provided at both websites.
DMS. (2006). Determination of Sample Size. Retrieved from http://web.ncifcrf.gov/rtp/lasp/intra/acuc/fred/Determination_of_Sample.pdf
NSS. (n.d.). Sample Size Calculator. Retrieved from http://www.nss.gov.au/nss/home.NSF/pages/Sample+size+calculator?OpenDocument
Sample Size Calculator. (n.d.). Retrieved from http://www.surveysystem.com/sscalc.htm