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Sample Size Calculations for the Modular Grant Application Process Outcome Evaluation Study

One purpose of this paper is to describe and illustrate the methods used to determine the sample sizes for the Modular Grant Application Process (MGAP) Outcome Evaluation Study. The sampling strategy for this study involves selecting a simple random sample without replacement from four of the six study populations. (A census was used for the remaining two populations.) This paper also serves as a primer on the factors affect sample size, how sample size is calculated, and the use of the finite population correction (FPC) factor when drawing a simple random sample.

The paper is divided into four sections and uses one of the six study populations

as an example throughout the paper. The first section outlines factors affecting the sample size when using a simple random sampling plan without replacement. The second part illustrates the sample size formula. The third section explains the purpose of the Finite Population Correction (FPC) Factor and depicts its use. The last section describes how we obtained the number of respondents to survey from each of the populations. More specifically, we explain how our expected response rates and anticipated returned emails (called “bounce backs”) are taken into consideration when calculating the final number of respondents to survey. Appendix A shows the sample sizes for all study populations and Appendix B provides web addresses of sample size calculators easily accessible via the Internet. The population used in the examples throughout the paper consists of all principal investigators (PIs) who have applied for and received at least one modular grant (N=16,450). This group is referred to as PIs1.

Factors Affecting Sample Size.

Three factors are used in the sample size calculation and thus, determine the sample size for simple random samples. These factors are: 1) the margin of error, 2) the confidence level, and 3) the proportion (or percentage) of the sample that will chose a given answer to a survey question. Each one of these will be discussed below.

The margin of error (also referred to as the confidence interval) measures the precision with which an estimate from a single sample approximates the population value. For example, in a national voting poll the margin of error might be + or – 3%. This means that if 60% of the people in a sample favor Mr. Smith, you could confident

that, if you surveyed the entire population, between 57% (60-3) and 63% (60+3) of the population would favor Mr. Smith. The margin of error in social science research generally ranges from 3% to 7% and is closely related to sample size. A margin of error will get narrower as the sample size increases. The margin of error selected depends on the precision needed to make population estimates from a sample. If it’s acceptable to have an interval of + or -7% around a given estimate, then the sample size needed will be smaller than if...

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