Week 3

Sample Size In: Encyclopedia of Research Design

By: Ashley Acheson Edited by: Neil J. Salkind Book Title: Encyclopedia of Research Design Chapter Title: "Sample Size" Pub. Date: 2012 Access Date: May 24, 2020 Publishing Company: SAGE Publications, Inc. City: Thousand Oaks Print ISBN: 9781412961271 Online ISBN: 9781412961288 DOI: https://dx.doi.org/10.4135/9781412961288 Print pages: 1300-1301

© 2010 SAGE Publications, Inc. All Rights Reserved. This PDF has been generated from SAGE Research Methods. Please note that the pagination of the online version will vary from the pagination of the print book.

Sample size refers to the number of subjects in a study. If there is only one sample, then the sample size is designated with the letter “N.” If there are samples of multiple populations, then each sample size is designated with the letter “n.” When there are multiple population samples, then the total sample size of all samples combined is designated by the letter “N.”

A study's sample size, or the number of participants or subjects to include in a study, is a crucial aspect of an experimental design. Running a study with too small of a sample runs numerous risks including not accurately reflecting the population a sample was drawn from, failing to find a real effect because of inadequate statistical power, and finding apparent effects that cannot be replicated in subsequent experiments. However, using more subjects than necessary is a costly drain on resources that slows completion of studies. Furthermore, if an experimental manipulation might pose some risk or cause discomfort to subjects, it is also ethically preferable to use the minimum sample size necessary. This entry focuses on the factors that determine necessary sample size.

Magnitude of Expected Effect

In general, when possible it is preferable to design an experiment looking for large effects that can be more easily detected with relatively small sample sizes. However, in many cases, small to modest effects can still be very important. For instance, important psychological processes might be associated with relatively subtle changes in detectible biological measures, such as the relatively minor changes in blood oxygen level dependent signaling (BOLD) that corresponds with neural activity. Additionally, treatments that produce relatively modest clinical improvements could still significantly benefit and improve the quality of life of afflicted individuals. Likewise, an even slightly more accurate diagnosis process could save countless lives. For studies looking to detect relatively small to modest effects, larger sample sizes will be needed.

Variability

The variability of data is a crucial factor for estimating what sample size is needed. The sample sizes needed in descriptive studies are dependent on the variability of measures of interests in the population at large. If the measures of interest are narrowly distributed in the population, then smaller sample sizes might be sufficient to predict these measures accurately. Alternatively, if these measures are broadly distributed in the population, then larger sample sizes are needed to predict these measures accurately.

For example, suppose a group of forestry students wished to determine the average tree height on a Christmas tree farm and in an adjacent forest. All the trees on this Christmas tree farm are 4-year-old Douglas firs, whereas the trees in the forest are of various ages and species. The students could likely measure relatively few trees in the Christmas tree farm and have an accurate idea of the average tree height, whereas they would likely have to measure many more trees in the forest to determine the average tree height there.

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In experimental studies, the more variable data are across subjects, the more subjects will be needed to detect a given effect. One means of reducing variability across subjects and thereby reducing the sample size required to detect an effect is to use a within-subject design. Within-subject designs, or repeated testing on the same subjects across the different phases of the experiment, reduces variability across subjects by allowing each subject to serve as his or her own control. Care must be taken to control for possible carryover effects from prior testing that might influence later measures.

For example, let us suppose a researcher wishes to test the effects of a novel drug on performance on a memory task. Under baseline conditions, there is a fair amount of variability in performance across subjects, but each subject scores about the same each time he or she performs the task. Using a within-subjects design and comparing each subject under placebo and drug conditions helps control for variability between subjects and allows the researcher to use a smaller sample size than would be necessary in a between-subject design with separate placebo and drug groups.

Statistical Criteria

A larger sample size will be needed to detect a significant finding as the alpha level (p value criteria for determining significance) becomes more conservative (i.e., going from maximum acceptable p value of .05 to .01 or .001). This is a potential issue when alpha corrections are needed because of multiple statistical comparisons. A smaller sample size is necessary for one-tailed than two-tailed statistical comparisons. However, one-tailed statistical comparisons are only appropriate when it is known a priori that any difference between comparison groups is possible in only one direction.

Sample Size Estimation

There are several commercially available software programs for estimating required sample sizes based on study design, estimated effect size, desired statistical power, and significance thresholds. In addition, free estimation programs might be found through a search using an Internet search engine.

Ashley Acheson

http://dx.doi.org/10.4135/9781412961288.n396 See also

• One-Tailed Test • p Value • Two-Tailed Test • Variability, Measure of • Single-Subject Design • Within-Subjects Designs

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Further Readings

Eng, J. Sample size estimation: how many individuals should be studied? (2003).227,309–313.

Lenth, R. V. Some practical guidelines for effective sample size determination. (2001).55,187–193.

Polgar, S., &Thomas, S. A.(2008). Introduction to research in the health sciences (5th ed.). Toronto, Ontario, Canada: Elsevier.

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SAGE Research Methods

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