Prior to completing any calculations of two proportions, it is necessary to identify the variables, constants and values for as much of the sampling information as you can possibly identify. The more known information you have, the more accurate the statistical computation will be. The identification process prepares the hard data to be eventually entered into the sample-size calculation as proportions. As an example, imagine that you are sampling people to conduct a study on weight. Rather than coming up with an estimated weight of the group as a whole, a more technical approach would be to identify the weight of each individual in the sample to give you accurate information.
To understand the difference in two proportions of a sample size, you must find the proportion for each sample so that you have two to compare. After this step in the research is completed, you should end up with Proportion 1 and Proportion 2 -- one for each sample -- and then convert the proportion to a decimal fraction for simplicity. In order for the proportions to make sense when the difference is examined, the two samples must have equally sized groups or populations. That is, if one sample group consists of four people, the other group must consist of four people. Having three or five people in the second sample group will skew the data.
The formula to find the difference in two proportions of sample sizes is often computed automatically with statistical calculators or computerized equations. The formula also can be performed manually by breaking down the information that is needed to compute it. In a sample-size calculation, the sample size of the equally sized groups is usually referred to as "n," which acts as the variable. The desired power and desired level of statistical significance is added together, taken to the second power and multiplied by 2 times the standard deviation of the variable outcome. This data is then divided by the difference, squared. The difference is really the difference in the proportions, which is why it becomes useful to have the decimal fractions of each proportion.
When it comes to examining the difference of two sample sizes, researchers also use a secondary approach, which is to find the difference in two means, as opposed to proportions. The means, commonly known as averages, have a similar formula, but instead of dividing the equation by the difference in proportions, the equation is divided by the difference in means. This offers another sort of data for researchers to study in relation to the proportional statistics.