Sample size is a count the of individual samples or observations in any statistical setting, such as a scientific experiment or a public opinion survey. Though a relatively straightforward concept, choice of sample size is a critical determination for a project. Too small a sample yields unreliable results, while an overly large sample demands a good deal of time and resources.
TL;DR (Too Long; Didn't Read)
Sample size is a direct count of the number of samples measured or observations being made.
The Definition of Sample Size
Sample size measures the number of individual samples measured or observations used in a survey or experiment. For example, if you test 100 samples of soil for evidence of acid rain, your sample size is 100. If an online survey returned 30,500 completed questionnaires, your sample size is 30,500. In statistics, sample size is generally represented by the variable "n".
Calculation of Sample Size
To determine the sample size needed for an experiment or survey, researchers take a number of desired factors into account. First, the total size of the population being studied must be considered -- a survey that is looking to draw conclusions about all of New York state, for example, will need a much larger sample size than one specifically focused on Rochester. Researchers will also need to consider the margin of error, the reliability that the data collected is generally accurate; and the confidence level, the probability that your margin of error is accurate. Finally, researchers must take into account the standard deviation they expect to see in the data. Standard deviation measures how much individual pieces of data vary from the average data measured. For instance, soil samples from one park will likely have a much smaller standard deviation in their nitrogen content than soils collected from across a whole county.
Dangers of Small Sample Size
Large sample sizes are needed for a statistic to be accurate and reliable, especially if its findings are to be extrapolated to a larger population or group of data. Say you were conducting a survey about exercise and interviewed five people, two of whom said they run a marathon annually. If you take this survey to represent the population of the country as a whole, then according to your research, 40 percent of people run at least one marathon annually -- an unexpectedly high percentage. The smaller your sample size, the more likely outliers -- unusual pieces of data -- are to skew your findings.
Sample Size and Margin of Error
The sample size of a statistical survey is also directly related to the survey's margin of error. Margin of error is a percentage that expresses the probability that the data received is accurate. For example, in a survey about religious beliefs, the margin of error is the percentage of responders who can be expected to provide the same answer if the survey was repeated. To determine the margin of error, divide 1 by the square root of the sample size, and then multiply by 100 to get a percentage. For instance, a sample size of 2,400 will have a margin of error of 2.04 percent.