How large should the sample be?

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How large should the sample be? A general standard is that in an experimental design, we should have at least 25 subjects per condition. We have two conditions: participation and nonparticipation in the patient education program. We need at least (25 x 2 =) 50 subjects. However, some people contacted may decline to participate in an information program. Typically less than half of the people contacted agree to participate. Therefore, the researcher needs to contact at least 50 subjects per condition. So the sample size is at least (50 x 2 =) 100.
Another standard is that we need to have a larger sample size if the intervention is not expected to have a large effect. It would be safe to assume that the patient education program will produce at best a small change in the use of ER for nonemergency treatment. It is unlikely that an educational program, no matter how good it is, will bring about a large change in people’s habits of accessing care, especially when they are ill and in pain.
A small change in the dependent variable may not show up in a small sample. A small sample may not show a significant statistical difference between the two groups in the study. For example, visits to ER for nonemergency treatment may decrease by 3 in the group that did not receive the intervention and by 8 in the group that did receive the intervention. Is the difference large enough to draw conclusions about the effectiveness of the intervention? For a larger sample size, differences in the two groups are more likely to be statistically significant. So it would be a good idea to at least double the number of study participants. Therefore, the sample size is now 200. Statistical formulas (to determine the sample size in an objective way) take into consideration the two main points discussed herein, namely, error rate and the expected difference between the groups.
Another consideration is whether the event related to the dependent variable is rare. Though ERs of large hospitals are busy places, for an individual, a visit to ER may be rare. In this case, the number of visits tracked may be so small for both groups in the study that we can’t find a statistically significant difference between them. This problem does not require an increase in sample size, however. We can simply extend the period of study from 6 months to 8 months or 9 months to account for the effect of frequency of visits.
The researcher may want to ask additional questions. For example, are uninsured patients less likely to change their ER utilization patterns in response to the intervention? If yes, is there a gender difference? Such questions add new variables to the study. In this case, the variables are insurance status and gender. If the study is to find statistically significant differences between these categories, the sample size will have to increase again. However, these variables must be considered when designing the studies and selecting the sample. The researcher would want the number of insured and uninsured to be relatively similar in both the experimental and control groups
Representative Sample

What type of subjects should be included in the sample? Researchers study a sample because it is not practical to study the whole population. But the aim is to reach a conclusion that applies to the population. The sample, then, should represent the population so that what is true of the sample may be assumed to be true of the population.
Think for a moment of the opinion polls in newspapers or on television. Do the participants in these polls form a representative sample of the population? The sample is drawn from only the regular readers of one newspaper or regular viewers of one television program. Readers often choose newspapers that match their own beliefs. This certainly makes the sample non-representative. The results of an opinion poll cannot be generalized to the whole population.
In an experiment, not only the whole sample but also the experimental group and the control group must be representative of the population. It may seem at first that the only way to draw a representative sample is to list hundreds of characteristics for the population and make sure that they appear in the sample. But things are not so difficult as we will see.
The researcher may pick up subjects at random from the population. This is a random sample. When large enough, a random sample is representative of the population. Because subjects are not selected on any criterion, there is little danger that a group is completely left out if the sampling is done in a truly random, unbiased fashion.

Sample Characteristics