A simple random sample (SRS) is the most basic probabilistic option used for creating a sample from a population. Each SRS is made of individuals drawn from a larger population (represented by the variable *N*), completely at random. As a result, said individuals have an equal chance of being selected throughout the sampling process. The benefit of SRS is that as a result, the investigator is guaranteed to choose a sample which is representative of the population, which ensures statistically valid conclusions.

### Example

An investigator wishes to draw multiple samples consisting of 5 people each from a village of 100. (Here, the variable *n *is used to represent the size of the sample; thus village size *N*=100 and sample size *n*=5). By randomizing the selection procedure, any member of this village has an equal chance of being selected as part of this first sample, and an equal chance off being selected for the next sample of the same size (and so on).

To prepare for SRS, researchers can randomise the sample selection process using several different techniques. One approach for small studies is to use a lottery technique, in which each member of population *N* is assigned a unique number that is written down on a scrap of paper, mixed with the other numbers, and selected at random for inclusion into a sample. This can, however, prove cumbersome in larger populations – here, a better strategy might be to use a random number generator, which can be found in the back of most statistics textbooks or online (see links below).

Finally, as all members of a population have an equal probability of being included in each sample, investigators drawing multiple samples may wish to deliberately exclude individuals from being selected more than once. This is known as SRS “without replacement”, or SRSWOR. (Conversely, SRS “with replacement” – SRSWR – allows for the possibility of the same individual being selected multiple times over different samples).

### Advice

#### Advice for CHOOSING this option (tips and traps)

- SRS requires a complete sampling frame – a list of all those subjects in a population you wish to measure (individuals, homes, schools, etc). This complete sampling frame may be missing or incomplete; if so, it is worth either attempting to obtain the missing data or consider alternative statistical approaches.
- Beyond this need for a complete frame, however, SRS requires little advance knowledge of the population, and may thus prove attractive to investigators.
- Confirm in advance that the population in question is relatively homogenous. If not, and you are concerned with sampling enough individuals of a particular group (e.g. both men and women, or adolescents and adults), then consider the use of stratified random sampling instead.
- If you are unable to sample enough individuals in the same timeframe, then consider an alternative design (multistage or snowballing, for example).

#### Advice for USING this option (tips and traps)

- Make sure that you have taken steps to ensure the randomness of your sample. Most statistical inference is based off of the randomness of the research design. If randomness is not maintained statistical inferences and claims of causality become much more difficult.
- Whichever option is used to decide to select individuals/observations, it is very important that those selected are indeed surveyed. While the selection of the sample is random, the sample is no longer random if the people selected refuse to participate. If a phone survey is utilized, keep calling the selected individuals. If in person or via mail, keep coming back or mailing for a response (within reason). All reasonable steps should be taken to survey those who were selected. Otherwise the sample is no longer random as individuals who were chosen randomly to be studied opt out, leaving you with those who proactively volunteered to participate. This is a self-selection issue that will bias the results of the study and cannot be fixed later.

### Resources

#### Guide

- An Introduction to the use of Randomized Control Trials to Evaluate Development Interventions - This guide provides a non-technical introduction to RCTs. It briefly covers what is meant by impact evaluation, before examining the problem of selection bias and how it can be dealt with through experimental and quasi-experimental designs
- "Simple Random Sampling", Yale University Statistics - this course paper defines a few different simplified sampling options

#### Tools

- Research Randomizer - Research Randomizer is an online, free service offered to students and researchers interested in conducting random assignment and random sampling

### Sources

Agresti, A and Finlay, B. *(2008) Statistical Options for the Social Sciences, 4 ^{th} edition.* Upper Saddle River, NJ: Prentice Hall.

Taylor-Powell E. (1998), *Sampling, *Program Development and Evaluation, Madison Wisconsin, Cooperative Extention, University of Wisconsin-Extension. Retrieved from www.mymande.org/?q=node/98

White H. (2011) , *An introduction to the use of randomized control trials to evaluate development intervention* International Initiative for Impact Evaluation 3ie, New Delhi, Global Development Network.

Urbaniak, G. C., & Plous, S. (2011). Research Randomizer (Version 3.0) [Computer software]. Retrieved on July 10 2012, from http://www.randomizer.org/