How often have you gone frantically scouring for a statistician who will "calculate" that magical number? The number that will answer all research questions - the sample size
Before we decide its size, let us understand what we mean by a "sample" and how to "construct" it. Ideally, to answer a research question, like the prevalence of say diabetes in Mumbai or Delhi or even India, or whether lung cancer is associated with smoking, we should study the entire population to get the perfect answer. This is obviously not practical. So we choose a sample, study it, and then extrapolate the results to predict the results in the population. A common enough example that we see in our day-to-day lives, are the exit polls run by agencies during elections. All the voters are not polled instead a well-planned "representative" sample is chosen to predict the outcomes of the elections. Apart from being impractical, the non-statistical challenges of working with whole populations include cost, manpower and time considerations. It is also unethical to study an entire population when a representative subset of the population (sample) can easily and accurately answer the research question.
Characteristics of a Good Sample
Before we discuss how to calculate the sample size (and actually do this in real life) it is mandatory to understand and apply the characteristics of a "good" or "appropriate" sample.
Thus, a sample should have all the following characteristics to answer the research question, namely
i. Be representative of the population to which the results will be eventually generalized.
ii. Give reliable, valid and accurateresults.
iii. Be of an appropriate size neither so small that you miss the results or be so large as to be unethical, impractical and unwieldy. In other words, the sample should be sufficiently large to provide statistical stability or reliability.
Types of Sampling Techniques
How to actually choose an individual patient to be in the sample [or not] is very important to be defined when the research study is planned. Broadly, there are two types of sampling methods (Probability and Non probability techniques), each having multiple subtypes, each with their own advantages and disadvantages. The choice of which sampling technique is to be used will again depend on the research question, the population you want to study and the feasibility of doing a particular type of sampling.
1. Non-Probability Sampling: When members of a population do not have an equal chance of being selected in a study, this is called non-probability sampling and is useful for pilot studies, proof of concept studies, qualitative research, and for hypothesis generation study. The advantages of this technique include that it is relatively quick, easy and inexpensive to use. Also, it is possibly the only sampling technique that can be used for a particular research question or population (like when studying IV drug use in adolescents, sexual behavior in school going children, among others) as the sensitive nature of the research question would mean that these participants would necessarily need to be located through methods that are "non random" in nature.
The main disadvantage of this technique is that results obtained from this type of a sample may not be amenable to generalization and is less representative of the population. Most importantly it is prone to sampling bias as the researcher may deliberately choose the individual that will participate in the study and thus shift the results to what he/she desires. When non-probability sampling has been used, it is necessary to describe in the final manuscript how the sample was different from an ideal sample that should have been randomly selected. It is also useful to describe the characteristics of the individuals who might have been be left out during the selection process or the individuals who are overrepresented in the sample. These are limitations of a study and must be stated.
Non-probability sampling methods include:
i. Convenience sampling
ii. Sequential sampling
iii. Quota sampling
iv. Judgmental sampling and
v. Snowball sampling
In convenience sampling individuals are selected because of their accessibility to the researcher.It is the most common of all sampling techniques and among the non-probability sampling techniques, researchers prefer it because participants are readily available making the recruitment faster. A common example of convenience sampling is using students or patients attending your clinic as participants.
Sequential sampling occurs when the researcher selects a single or a group of individuals (in the latter case, this is called as group sequential sampling in a given time frame, performs the study, and after analysis of results may select another group of individuals in a different time frame, if needed). In this method, the researcher is able to fine tune his research methods because he can continue to select participants and gain vital insights into the study.The sample size, n, is not fixed in advance, nor is the timeframe of data collection. For example, if the researcher wishes to study coping mechanisms to the social and curricular stresses of newly admitted medical students, he may conduct the study in one batch over one year, and then repeat it in the next year with the next batch of students to gain better insights with improved tools of investigation.
Quota sampling is a technique where the sample chosen has the same proportions of individuals with characteristics under study as the entire population. Thus, for example, if we want to study the level of autonomy amongst men and women in the city of Mumbai, we first identify the proportion of men and women in the general population in the city (say from the census data) and then choose a sample that has the same proportions to answer our research question.
When the researcher selects individuals to be studied based on their knowledge and professional judgment, it is called Judgmental sampling. This type of sampling technique is also known as purposive or authoritative sampling.The process simply involves purposively handpicking individuals from the population based on the researcher's understanding, experience and judgment. For example, if a researcher wants to identify challenges in conduct of clinical research in academic set-ups in Mumbai, he would handpick seasoned researchers from reputed institutes based on his knowledge of the researchers. This method can be used when one knows that aonly limited number of individuals possess the trait of interest (in our example, this would be knowledge and experience in clinical research in academic institutes). Naturally, this technique is limited by the extent and accuracy in defining the judgmental capacity of the researcher and there is no standardized way to evaluate the reliability of the expert or the authority.
Snowball samplingalso called as chain referral sampling is used when identification of potential participants is difficult.After the researcher identifies the initial participant or informant, he/shethen asks for assistance from this person to help identify people with a similar trait of interest.For example, you want to study the HIV prevalence among MSMs, you may opt to use snowball sampling as it would be difficult to locate these participants due to the sensitive nature of the research question that may preclude people from readily agreeing to make themselves available for participation. This method is especially useful to reach populations, such as MSMs, or commercial sex workers (CSWs) who are otherwise difficult to reach with traditional sampling methods. However, the researcher has limited control on sampling and has to rely mainly on the previous participant and their referral patterns. Here, more than other non-probability sampling methods, representativeness is even less certain as the researcher has no idea of the true distribution of the population and of the sample. In fact, because we rely on referrals, it is highly possible that we end up with participants all sharing similar traits and characteristics.
2. Probability Sampling: When every individual in a population has an equal chance of being selected as a participant, it is called probability sampling and is probably the default method for analytical studies (like randomized controlled trials). It is also the appropriate technique when the study is designed estimate the population parameters since it is representative of the population.This method ensures randomness or unpredictability in the choice of participant selection and helps minimize selection bias. This sampling technique also ensures the validity of the statistical methods after the research is completed.
The disadvantages are mainly non-statistical in nature and include the need for time, resources, finances and manpower.
Probability sampling methods include:
i. Simple Random Sampling
ii. Systematic Sampling
iii. Stratified Sampling
iv. Cluster Sampling
v. Disproportional Sampling
When each member of the population has an equal chance of being selected as a participant, it is called Simple Random Sampling. The process of sampling occurs in one step with each participant getting selected independent of other potential participants in the population.The process itself can be done in different ways, for example, lottery method. However, a computer software can do a random selection of participants from your population.
One of the most important advantages of this method is that this is considered to be a "fair" way to select a sample that is closest to (or most representative of) the population in characteristics, since every member is given an equal opportunityto be selected. However, one must have the entire population (N) to be able to select "randomly" the sample from it. If the population is very large, this technique becomes cumbersome and inaccurate. For example, if we want to study the sale of antibiotics at chemists shops without prescription in E ward of Mumbai city, we would first need to list all the chemists shops that exist in the ward and then choose a random sample either by lottery method of using a computer generated randomization list.
In the systematic samplingmethod, which is also a random sampling technique, where the researcher first randomly picks the first shop from the population and then goes on to select the n'th (say the 10th) chemist shop in the E ward so as to cover the desired sample.This is relatively an easy process and can be done manually. The n'th number has to be fixed and decided à priori.This process of obtaining the systematic sample is much like an arithmetic progression and gives us an adequate representation of the population unless,in very rare instances, certain traits of the population are repeated for every n'th unit.In our example, suppose in addition we are also studying the most expensive drugs sold at the chemists shop. If every 10th shop is located near a hospital which is an oncology or critical care hospital, we would get skewed results. However, this is highly unlikely to happen in real life.
When the entire population is divided into different subgroups or strata, and then randomly select the final subjects proportionally from the different strata, this is called stratified sampling technique. For example, you want to study the sleeping patterns among resident medical officers of an academic institute. A simple random sample may be representative of residents, but it is possible that we do not get adequate numbers of residents of each of the specialities represented. Hence, if we want to study them speciality wise, which is so important in this case (i.e. anatomy residents would be quite different from gynaecology and obstetrics residents or community medicine residents would differ from surgical residents) we would need an adequate number, randomly selected from each speciality. It is important that the strata are non-overlapping and use simple random sampling within each stratum.
In cluster sampling, a group (called cluster) of participants that represent the populationwherein the population is divided into groups that are already clustered in certain geographical areas (living in areas of poor hygiene and sanitation) or time frames (e.g. born during the world war), and a sample is taken from each group.For example, if we wanted to study the herd immunity patterns for typhoid after vaccination, it would be appropriate to make geographic clusters of the city and then sample each cluster for the outcome. It is important here, that we make the distinction between stratified sampling and cluster sampling which appear similar. The former involves division of the population into strata according to one or more variables that are in turn related to the variables that we are interested in. Each stratum is then sampled. In cluster sampling, the population is divided into clusters, but only few clusters are actually studied. The error thus is much lower with stratified sampling as variation within the cluster/s chosen will be apparent only after the sample is chosen. Often times, both sampling techniques methods are employed together.
Disproportional sampling is a type of stratified random sampling wherein the size of the sample from each stratum is "disproportional" to the size of that stratum within the population. This usually stems from the fact that the sizes of the strata are unequal to begin with. With this type of sampling, some strata are then "oversampled" relative to other strata to achieve balance. Let us say, for example, that in a medical college, a 1st MBBS class has 140 girls and 60 boys. A researcher needs to study 20% of the class, i.e.40 students to answer a particular research question. If 20% of girls and 20% of boys were to be chosen by him, this would lead to 28 girls and 12 boys respectively being chosen, and thus an under-representation of boys. Instead, if he were to chose 20 girls and 20 boys, this becomes disproportionality sampling.
The choice of the sampling method or strategy to be used for a particular study should be defined in advance in the research protocol. Since multiple factors impact the choice of the sampling method, it is best to list potential sampling strategies in advance and then use the one method that is the most likely to answer the study objectives. Table 1 summarises the differences between the two methods.