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.

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.

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