Random sampling is a statistical method of selecting a sample of data from a larger set in such a way that each data point has an equal chance of being selected, so that the sample represents the population from which it was drawn.

## Overview: What is random sampling?

Random sampling is a method of choosing a sample of observations from a population to draw assumptions and make inferences about the population. The primary feature of random sampling is that the selection of observations must occur in a *random* way such that they do not differ in any significant way from the rest of the population that was not selected.

### The different methods of conducting random sampling are as follows:

**Simple random sampling** – In this sampling method, each item in the population has an equal probability of getting selected in the sample. First, you must assign a unique identifier to each item. Then you can use a random number table or a computerized random number generator to select your random samples.

**Systematic Random Sampling** – This technique is good for process sampling whereby you would randomly select your items using a fixed periodicity of time. For example, you might decide to randomly select ten items every hour from a production line.

**Stratified Random Sampling** – If you suspect there are unique differences between items in your population, you might use this sampling strategy to assure you get a balanced representation of the population. If you suspect that men and women may have different opinions on a subject, and women make up a greater proportion of your population, you may want to stratify your sample and randomly select men and women based on their proportion in the population.

**Clustered Sampling** – Cluster sampling is like stratified sampling. Here, the population is divided into a large number of subgroups. After that, some of these subgroups are randomly selected and simple random samples are then gathered within these subgroups. These subgroups are known as *clusters*. This method will reduce the overall cost of your sampling.

## 5 benefits of random sampling

Random sampling is a common method of selecting samples from a population. Here are some of the benefits of random sampling.

### 1. Representativeness

Random samples are representative of the population from which they are drawn, allowing accurate inferences about the population.

### 2. Reduced Bias

Random sampling reduces the possibility of selection bias, leading to more accurate results.

### 3. Increased Precision

The larger the sample size, the more precise the results will be.

### 4. Improved Generalizability

Random sampling allows the results to be generalizable to the larger population.

### 5. Increased Reliability

The random selection of data points ensures the sample is representative of the population, increasing the reliability of results.

## Why is random sampling important to understand?

Here are a few thoughts regarding the importance of understanding how to use random sampling.

### Validity of results

Understanding random sampling helps ensure that a representative sample is selected, leading to valid and accurate results.

### Bias reduction

Random sampling minimizes the potential for bias, allowing for a fair and objective representation of the population being studied.

### Estimation of population parameters

With a random sample, one can estimate population parameters, such as mean and standard deviation, with a high degree of accuracy.

### Generalization

Results from a well-conducted random sample can be generalized to the entire population, providing insights into the population as a whole.

### Improved decision-making

By understanding random sampling, one can make better-informed decisions, as the results are based on a representative sample and not just a small, unrepresentative subset.

## An industry example of random sampling

A major healthcare system was preparing for an audit of their medical records. One of the items the auditors wanted to know was the percentage of medical documents which contained errors. The Six Sigma Master Black Belt (MBB) was asked to design a plan for sampling the hundreds of thousands of medical records kept in the computer.

The MBB knew that he couldn’t examine them all, so he chose to do a simple random sampling. Since the records each had a unique reference number, he put all the reference numbers in an Excel worksheet and numbered them from 1 to 350,000 which was the total count of records.

The MBB then calculated the appropriate sample size. Since a similar exercise was done during the last audit, the MBB knew there was about a 13% defective rate last time, so he used that number to calculate his sample, along with a desired 95% confidence level and a 5% precision level. Using the appropriate sample size formula, it was decided that 174 records needed to be examined.

Using the Excel random selection function, the MBB randomly identified the 174 records. The Records Supervisor pulled those documents and examined each one for errors. She found 19 of the 174, or about 11% contained one or more errors. This information was then used during the audit.

## 7 Best practices when thinking about random sampling

Here are several tips for effectively utilizing random sampling in your organization:

### 1. Define the population

Clearly define the population from which the sample will be drawn.

### 2. Determine sample size

Determine the size of the sample based on the size of the population and the desired level of confidence and precision.

### 3. Random Selection

Use a random selection method, such as a random number generator or random number tables, to select data points from the population.

### 4. Avoid Selection Bias

Be mindful of potential sources of selection bias and take steps to minimize it, such as stratified sampling or oversampling.

### 5. Verify Independence

Verify that the data points in the sample are independent and not correlated.

### 6. Replication

Replicate the sampling process to increase the reliability of results.

### 7. Document methodology

Document the sampling methodology and include it in any reports or publications to ensure transparency and reproducibility.

## Frequently Asked Questions (FAQ) about random sampling

### What is the difference between random sampling and stratified sampling?

Random sampling involves selecting data points from the population randomly, whereas stratified sampling involves dividing the population into subgroups (strata) and selecting data points from each subgroup in a random manner.

### How does random sampling ensure representativeness?

Random sampling ensures representativeness by giving each data point in the population an equal chance of being selected, so that the sample accurately reflects the population from which it was drawn.

### How can random sampling help reduce bias?

Random sampling helps reduce bias by giving each data point in the population an equal chance of being selected, reducing the likelihood of certain data points being overrepresented or underrepresented in the sample.

## Reviewing random sampling

Random sampling is a statistical method in which data points are selected from a larger population in a random manner, ensuring that each data point has an equal chance of being selected. This method reduces the possibility of selection bias and provides a representative sample of the population, allowing for valid inferences and generalizations to be made.

The sample size is determined based on the size of the population and the desired level of precision and confidence. To maximize the benefits of random sampling, best practices include defining the population, determining the sample size, using a random selection method, avoiding selection bias, verifying independence, replicating the sampling process, and documenting the methodology.