Simple Random Sample

What is a Simple Random Sample?

A simple random sample is an unbiased surveying technique that defines a subgroup of a population where the prospect of getting selected is equal for all the members of the population. Here, the sample selection process is entirely based on chance or luck. A simple random sample will yield a more representative result in cases where the entire population is homogenous.

Since the members of a simple random sample are chosen randomly by chance, all the members in the population set have an equal probability of being chosen. The statistical accuracy of the sample improves as the size of the sample is increased.

A simple random sample is similar to a random sample, except that each member of a population may not have an equal chance of being chosen in a random sample.

Steps for Creating Simple Random Samples

1. Define the population.

Depending on the sampling criteria, choose a group about which conclusions are needed to be drawn. For example, assume that a researcher wants to learn about students’ career aspirations studying at a specific university.

There are roughly 15,000 students in the university, which will be considered the population and denoted by N. The sampling frame would be all 15,000 students. Each student would be known as a unit.

2. Choose a sample size.

Since surveying the entire population of 15,000 students would be difficult, the researcher instead selects a sample size depending on their budget and time available for surveys. The larger the sample, the more statistically certain it will be.  Alternatively, a statistical tool can be used to determine the appropriate size of the sample. Let us assume that the statistical tool suggested the researcher use a sample of 300 students.

3. List the population.

In order to select a sample of 300 students, all 15,000 students need to be identified. Certain permissions may be required to carry out the study of some populations. In our example, the researcher may need to get permission from Student Records or any other relevant department so that privacy rules are not breached.

4. Allocate numbers to each unit.

Each unit of the population is marked with consecutive numbers from 1 to N. In the example, the researcher needs to assign numbers from 1 to 15,000.

5. Select sample.

To make the process of selecting a bias-free simple random sample, either of the following approaches can be used:

Lottery method

When the population list is prepared, each member of the population is marked with a number. The numbers are drawn randomly from the box to select samples. In our example, the researcher needs to choose 300 students from a total of 15,000 students. All the students are assigned a number. The researcher will randomly draw 200 numbers out of a box filled with numbers from 1 to 15,000.

However, the method can be very tedious for large populations if done manually. Hence, software is used for selecting simple random samples for relatively large populations. The software assigns numbers to each member and selects numbers at random.

Using random numbers

For this, a list of random numbers is required. The list can be found using either random number tables or software that generates random numbers. The random number generator software is preferred since human interference is not required.

In our case, the researcher needs to either select 300 random numbers from a random number table or generate 300 random numbers using the software. Assume that the first four numbers from the table were 0015, 0123, 2015, and 3002. It implies the researcher would select the 15^th, 0123^rd, 2015^th, and 3002^nd students from the prepared list. It continues until 300 students are selected.

Advantages of a Single Random Sample

A single random sample reduces the risk of human bias while selecting units for the sample. A simple random sample fairly represents the population under study, assuming that limited data is missing. Since the units of the sample are chosen using the theory of probability or chance, statistical inferences on the population can be made from the sample.

Disadvantages of a Single Random Sample

A simple random sample can be chosen only if a population list is complete and available. Obtaining a complete list of the population can be difficult sometimes due to various reasons – restrictions on accessibility, private policy protections, or a lengthy process of obtaining permissions. 

Sometimes researchers are interested in more than one list of populations, and it becomes time-consuming and difficult to merge all the sub-lists and generate a final list that is to be used to choose a sample. Moreover, the required lists may not be available in the public domain and may be expensive to purchase.

Additional Resources

Thank you for reading CFI’s guide to Simple Random Sample. To help you become a world-class analyst and advance your career to your fullest potential, check these additional resources:

• Hypothesis Testing
• Sampling Errors
• Statistical Significance
• Basic Statistics Concepts in Finance
• See all data science resources