One of the most frequent questions posed to statisticians is “How large should my sample be?” Unfortunately, there is no simple answer. An important issue is whether the study will be of a quan- titative or qualitative nature. Qualitative studies use much smaller samples than quantitative studies. Qualitative studies may use samples that are quite small, sometimes even smaller than 10. After pat- terns and themes have been extracted from the participants and no more new ideas are being uncov- ered, sampling ceases. Generally speaking, quantitative studies seek to obtain sample sizes large enough to talk about the population of interest.
There are no simple rules for determining the desired sample size for a quantitative study. Some factors to be considered are the homogeneity of the population, degree of precision desired by the re- searcher, and type of sampling procedure that will be used. If the population is very homogeneous, or alike, on all variables other than the one being measured, a small sample size may be sufficient. But if the researcher wants to be very precise in generalizing to the population based on sample data, a large sample may be necessary for the sample to represent the population accurately. Finally, when probability sampling methods are used, smaller samples are required than when nonprobability sam- pling techniques are employed.
According to Roscoe (1975), there are few instances in descriptive behavioral research when a sample size smaller than 30 or larger than 500 can be justified. A sample size of 100 ensures the benefits of the central limit theorem (see Chapter 15). Sample sizes as small as 30 are generally adequate to en- sure that the sampling distribution of the mean will closely approximate the normal curve (Shott, 1990).
Large sample sizes may be needed in the following instances:
1. Many uncontrolled variables are present. The researcher thinks age may influence study results, but is not able to control for this variable.
2. Small differences are expected in members of the population on the variable of interest. Small, but important, differences between members of the population may not be uncovered when small samples are used.
3. The population must be divided into subgroups. Sample sizes must be increased to assure inclu- sion of members of each of the subgroups.
4. Dropout rate among subjects is expected to be high. This problem is especially likely to occur in longitudinal studies.
5. Statistical tests are used that require minimum sample sizes. Certain statistical tests require mini- mum numbers of responses in each cell of the data.
Although large samples are desirable, the law of diminishing returns applies. A sample of 100, or 10%, may be necessary to obtain the required precision desired for a population of 1,000. A 10% sample of a population of 1 million would require 100,000 elements. This would be a huge sample and would be unnecessary. In fact, samples of 5,000 or 6,000 are often sufficient to estimate the char- acteristics of the entire population of the United States. The next time you see a Gallup survey report, make a note of the number of participants who were included in the sample. A more important issue than the size of the sample is the representativeness of the sample. Election results can be predicted with very small percentages of votes counted because the polled voters have been thoroughly exam- ined for representativeness in voting behavior. Does it make you angry when you see the media pre- dict the winner of an election when only 25% of the votes are in?
It is always wise to set the sample size a little bit larger than what is actually desired (to allow for nonresponse or subject dropout). Also, an absolute minimum sample size should be declared at the be- ginning of a study. Should the study be conducted if only five people agree to participate? The researcher must make the decision about the minimum acceptable sample size before data collection begins.
Power analysisis a procedure that can be used to determine the needed sample size for a re- search study. Researchers want to ensure that they have enough sample elements to detect a differ- ence or a correlation, if one actually exists between groups or within groups on some variable of interest. This procedure is very important in experimental studies. The power of a statistical test is its ability to detect statistical significance in a study, when it is present. When power is low, the likeli- hood of making a type II error is high (see Chapter 15). One factor that influences the power of a test is the sample size that was used in the study. In many studies, researchers erroneously conclude that no significant difference exists between the experimental and the control group when, in fact, a differ- ence would have been detected if the sample had been larger.
Connelly (2008) asserted that a tradeoff exists between obtaining the desired sample size and the amount of time and resources available for a study. She also contended that it would be unethical to sample more people than is really needed, especially if the study is invasive.