What relationship exists between the expected population deviation rate and sample size?

Int J Ayurveda Res. 2010 Jan-Mar; 1[1]: 55–57.

INTRODUCTION

One of the pivotal aspects of planning a clinical study is the calculation of the sample size. It is naturally neither practical nor feasible to study the whole population in any study. Hence, a set of participants is selected from the population, which is less in number [size] but adequately represents the population from which it is drawn so that true inferences about the population can be made from the results obtained. This set of individuals is known as the “sample.”

In a statistical context, the “population” is defined as the complete set of people [e.g., Indians], the “target population” is a subset of individuals with specific clinical and demographic characteristics in whom you want to study your intervention [e.g., males, between ages 45 and 60, with blood pressure between 140 mmHg systolic and 90 mmHg diastolic], and “sample” is a further subset of the target population which we would like to include in the study. Thus a “sample” is a portion, piece, or segment that is representative of a whole.

ATTRIBUTES OF A SAMPLE

• Every individual in the chosen population should have an equal chance to be included in the sample.

• Ideally, choice of one participant should not affect the chance of another's selection [hence we try to select the sample randomly – thus, it is important to note that random sampling does not describe the sample or its size as much as it describes how the sample is chosen].

The sample size, the topic of this article, is, simply put, the number of participants in a sample. It is a basic statistical principle with which we define the sample size before we start a clinical study so as to avoid bias in interpreting results. If we include very few subjects in a study, the results cannot be generalized to the population as this sample will not represent the size of the target population. Further, the study then may not be able to detect the difference between test groups, making the study unethical.

On the other hand, if we study more subjects than required, we put more individuals to the risk of the intervention, also making the study unethical, and waste precious resources, including the researchers’ time.

The calculation of an adequate sample size thus becomes crucial in any clinical study and is the process by which we calculate the optimum number of participants required to be able to arrive at ethically and scientifically valid results. This article describes the principles and methods used to calculate the sample size.

Generally, the sample size for any study depends on the:[1]

• Acceptable level of significance

• Power of the study

• Expected effect size

• Underlying event rate in the population

• Standard deviation in the population.

Some more factors that can be considered while calculating the final sample size include the expected drop-out rate, an unequal allocation ratio, and the objective and design of the study.[2]

LEVEL OF SIGNIFICANCE

Everyone is familiar with the “p” value. This is the “level of significance” and prior to starting a study we set an acceptable value for this “p.” When we say, for example, we will accept a p