Chapter 17

Primary Studies:

Estimating Sample Size

Importance of Sample Size

An adequate number of study participants is required

to achieve valid and significant results.

Importance of Sample Size

The goal is to recruit just the right number of participants based on statistical estimations of how many people are required to answer the study question with a specified level of certainty.

•If more participants are recruited than are statistically required, resources are wasted. •If too few participants are recruited, the whole study will be almost worthless because there will not be enough statistical power to answer the study question.

Bigger Samples Are Better

Large samples from a population are usually better than small ones at yielding a sample mean close to the true population value.

FIGURE 17- 1 Sample Size and Means

Bigger Samples Are Better

• When the sample size is small, the sample mean may be quite far from the mean in the total population from which the sample was drawn. This is represented by a wide confidence interval that reaches far from the sample mean.

• When the sample size is large, the sample mean is expected to be close to the population mean, and the confidence interval will be narrower.

FIGURE 17- 2 Larger Samples from a Population Have a Narrower 95% Confidence Interval Than Smaller Samples

Sample Size Estimation

A sample size calculator – more accurately called a sample size estimator – should be used to identify an appropriate sample size goal.

Sample size estimators suggest an appropriate minimum sample size based on a series of “best guesses” the researcher makes about the expected characteristics of the sample population.

When in doubt, err on the size of a larger sample!

FIGURE 17- 3 Examples of Sample Size Calculation

Power Estimation

Another way to check for sample size requirements is to work backward from the number of participants likely to be recruited to see whether that sample size provides adequate statistical power for the study design.

Statistical power is the ability of a statistical test to detect significant differences in a population when differences really do exist.

Power Estimation

Sometimes a sample population does not capture the true experience of the population:•Type 1 errors (α) occur when a study population yields a significant statistical test result when one does not exist in the source population. •Type 2 errors (β) occur when a statistical test of data from the study population finds no significant result when one actually exists in the source population.•Power = 1 – β

FIGURE 17- 4 Power and Errors

FIGURE 17- 5 Examples of Power Calculation

Refining the Study Approach

• Be prepared to rethink the study question, study approach, and/or target and source populations if the power for the estimated number of participants is not sufficient.