The sample size required to detect a reasonable experimental effect (i.e., departure from the null hypothesis), with a reasonable level of power, is calculated, while allowing for a reasonable margin of error.Sample size planning is an essential part of designing research studies that can actively answer scientific of questions of interest and contribute meaningfully to a research literature.Power and required sample size for a reasonable range of effects is investigated.The type of analysis and null hypothesis are specified.In some such situations, a 'window of opportunity' may close before the sample size can be adjusted upward.Īcross a wide variety of analytic situations, power analysis and sample size estimation involve steps that are fundamentally the same: Only later does the experimenter realize that a small change in p requires a huge increase in N, and that the planning for the experiment was optimistic. 6 will not require substantial differences in N. The experimenter budgets for a sample size of, say, 220, and imagines that minor departures of p from. For example, imagine that the experimenter had estimated the required sample size on the basis of reliably (with power of. It is much better to be aware of the overall performance of the statistical test against a range of possibilities before beginning an experiment, than to be informed of an unpleasant reality after the fact.

Obviously, then, required sample size is somewhat difficult to pinpoint in this situation. 50) requires an N greater than 800, but reliable detection of a difference of. To be able to reliably detect a difference of. The preceding graph demonstrates how the required N drops off rapidly as p varies from. The following graph shows power as a function of sample sizes ranging from 20 to 2000, using a 'normal approximation' to the exact binomial distribution. You might start with a graph that covers a very wide range of sample sizes, to get a general idea of how the statistical test behaves. Graphical analysis can shed a considerable amount of light on the capabilities of a statistical test to provide the desired information under such circumstances.įor example, the researcher could plot power against sample size, under the assumption that the true level is. In the example discussed in the preceding section, the goal, from the standpoint of the politician, is to plan a study that can decide, with a low probability of error, whether the support level is greater than. Power Analysis allows the convenient construction of a wide range of power and sample size graphs. Intelligent analysis of power and sample size requires the construction, and careful evaluation, of graphs relating power, sample size, the amount by which the null hypothesis is wrong (i.e., the experimental effect), and other factors such as Type I error rate. 70 is much different than that required to reliably detect a p of. It might then be that the sample size required for a p of. For example, suppose the function relating required sample size to p is particularly steep in this case. In practice, of course, we would be foolish to perform only one power calculation, based on one hypothetical value. In the preceding discussion, we arrived at a necessary sample size of 607 under the assumption that p is precisely.

Sample size power analysis