## Sample Size Calculators

At Select, we are often asked to help our clients calculate the sample sizes required for a particular survey or study that they plan to undertake. Standard formulae can often be used to calculate the sample size, but these usually require a certain amount of information that you must have before you start your study, trial or survey.

Firstly, you must know how you are going to collect your data (also known as the study design) and what it is that you are trying to estimate. For example, you may wish to estimate the proportion of a specific characteristic of the population of interest or to estimate the difference in the mean effect between a treatment and control group.

You will often also need an initial estimate of the proportion or the mean difference between the two groups that you expect to see, together with an estimate of its variability. This can often be obtained from previous studies or by running a small pilot study.

Once you have all the necessary information, it is often a fairly simple task to calculate the required sample size. So that you can see for yourself how simple sample size calculations can be performed, we’ve put together the following small selection of online sample size calculators. These are all appropriate where you have collected your data using simple random sampling.

Occasionally your study may not fit into these standard calculators. For example, if you are estimating a proportion that you expect to be close to 0 or 1, or if you have a complex sample design with e.g., stratification or clustering. In this case, there are alternative techniques that can be used and you can

## Confidence Interval Calculators

When reporting a point estimate from a sample of data (for example, estimating the mean of your population), it is usually a good idea to provide a confidence interval that quantifies the uncertainty associated with the estimate. The interval is calculated from the sample of data and is the range of values in which we estimate the point estimate to lie given our level of confidence.

To calculate a confidence interval, you will first need the point estimate and, in some cases, its standard deviation. The other important piece of information is the confidence level required, which is the probability that the confidence interval contains the true point estimate. For example, if we are estimating the confidence interval given an estimate of the population mean and the confidence level is 95%, if the study was repeated and the range calculated each time, you would expect the true value to lie within these ranges on 95% of occasions. The higher the confidence level the more certain you can be that the interval contains the true mean.

The basic calculations for a confidence interval remain the same whatever your point estimate. To demonstrate this, we’ve put together the following small selection of online confidence interval calculators. Remember, you can calculate the confidence intervals for many other estimates such as medians, differences or quantiles.

## Basic Statistical Tests

There are an enormous range of statistical tests available and we’ll be developing a few of the most common ones that, with a little guidance, can be easily applied in simple situations. We currently have the following online statistical tests available.