# Simple Random Sample

A subgroup of a population where the prospect of getting selected is equal for all the members of the subgroup

## What is a Simple Random Sample?

A simple random sample defines a subgroup of a population where the prospect of getting selected is equal for all the members of the subgroup. Here, the sample selection process is entirely based on chance or luck. A simple random sample is preferable in cases where the entire population is homogenous. Since the members of a simple random sample are chosen randomly, all the members in the population set have an equal probability of being chosen. For the appropriate selection of a simple random sample, the size of the sample should be at least a few hundred.

Since it is not easy to work with such large sample sizes, the practical implementation of a simple random sample becomes difficult. A simple random sample is analogous to a random sample except that in a random sample, each member may not have an equal chance of being chosen.

### Summary

• A simple random sample defines a subgroup of a population where the prospect of getting selected is equal for all the members of the subgroup.
• Since the sample is selected at random, a simple random sample fairly represents the population under study, assuming that limited data is missing.
• A simple random sample can be chosen randomly from the population list or by using a list of random numbers.

### Steps for Creating Simple Random Samples

#### 1. Describe 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 the career aspirations of students studying at a specific university.

There are roughly 15,000 students in the university, which is 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 sample size

Since studying the entire population of 15,000 students is difficult, the researcher will select a sample size depending on his/her budget and time available for surveys. Alternatively, a statistical tool can be used to determine the size of the sample. Let us assume that the statistical tool suggested the researcher consider 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 take permission from Student Records or any other relevant department.

#### 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 15th, 0123rd, 2015th, and 3002nd 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 attaining 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.