# What is a Simple Random Sample?

A simple random sample is a set of elements with an equal probability of being picked from a population.

## 🤔 Understanding simple random sample

A simple random sample is a smaller segment of a population in which each element of the population is just as likely to be picked as any other. It’s a basic tool in an analyst’s toolkit designed to obtain an unbiased sample by selecting items entirely at random from the larger population. A common way to create simple random samples is the lottery method — giving each element a number and then selecting numbers at random. Big populations may require a computer to complete simple random sampling. A simple random sample should be a representative sample of a population, allowing you to make inferences about the characteristics of the larger group. It can be a practical way to study a large group without surveying the entire population.

There are typically about 900 graduate students that enroll at Harvard Business School (HBS) each year. To better address the needs of its students, HBS may need to get feedback every so often. However, trying to get answers from every single one of the 900 students may be impractical and delay necessary decisions. Creating a simple random sample, in which each of the 900 students has an equal probability of being selected, may be an efficient way for HBS to get a representative sample of its entire student body.

## Takeaway

A simple random sample is like a bag of jelly beans…

Out of the millions of jelly beans made at the candy factory, a couple of dozen end up together in a bag to be sold at the candy store. They are chosen at random and are representative of all the jelly beans that were made.

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## What is a simple random sample?

A simple random sample is a subgroup from a much larger group in which every item has an equal probability of being selected. Analysts use simple random sampling to build an unbiased sample and make inferences about the larger group.

When a population is small, it’s relatively easy to create a simple random sample. First, you can number all items in the population sequentially. Next, write each number on a small piece of paper and drop them all into a “lottery bowl.” Establish a total number for your sample and draw one piece of paper from the bowl until you reach your target sample size. Match the numbers with the items on your list, and now you have your simple random sample.

Alternatively, you can select numbers using a random number table in a statistics textbook, or create a random number generator on a computer — the “RANDBETWEEN” formula in Excel is an example of doing this.

Simple random sampling allows you to study a large group without having to take a look at every single item or person within the group. Computer software often facilitates the process, letting you save your work, make edits, and handle large amounts of data.

For example, the Russell 2000 is an index that captures the stock performance of 2,000 of the smaller publicly traded U.S. companies. To get a better sense of this index, you can carefully analyze a smaller, unbiased subset of companies that are representative of the index as a whole.

Here are the three steps to create a simple random sample of 100 companies using Excel. First, copy and paste all 2,000 company names into a spreadsheet. Second, assign each company a number from one to 2,000. Finally, generate 100 random numbers using “=RANDBETWEEN(1,2000).” Match each of the 100 numbers with the corresponding company, and you now have a simple random sample of 100 companies from the Russell 2000.

While researchers use simple random sampling to create an unbiased sample, they are aware that there is still room for sampling error. For example, a simple random sample of 100 HBS students may show you that 20% of them like tacos. One might conclude that 20% of the total population of 900 HBS students like tacos. However, the actual percentage of HBS students loving tacos could be 22%. A researcher is generally willing to accept this potential room for error in exchange for not having to survey an entire population.

## What is the difference between a simple random and stratified random sample?

Simple random sampling is one of many different ways you can sample a population. Another one is stratified random sampling, in which you divide the population into “strata” — smaller groups with shared traits. Then, you select randomly from each subgroup to make sure that every group in the whole population is represented.

A stratified random sample is useful when you need to ensure that a sample truly represents all subgroups in a population. Unlike simple random sampling, stratified random sampling requires that you classify the population into non-overlapping categories before creating a sample.

For example, imagine that in a population of 1,000 items, there are four distinct groups that share their own similar traits. To ensure your sample reflects the various traits, you can create a stratified random sample of 100 items by first dividing the 1,000 items into four categories and then randomly choosing an equal amount of items from each of the categories. To avoid skewing the sample, each one of the 1,000 items can only belong to one category.

Stratified random sampling can be useful with a diverse population. Unlike the Nasdaq, an index mostly made up of tech companies, the S&P 500 represents companies from a broad range of sectors. If your goal is to get a good sense of the stocks that make the S&P 500, then a sample of only companies in the consumer staples sector (think Procter & Gamble Co. and Kroger Co.) would be misrepresenting the broader set.

Since the S&P 500 includes other industries, such as financials, health care, and tech, stratified random sampling may be more appropriate than simple random sampling to study this index.

## What is the difference between simple random and random sample?

There are many different types of random samples — a simple random sample is just one. So all simple random samples are random samples, but not all random samples are simple random samples.

In a simple random sample, there is a set of predetermined rules that you have to follow to ensure that every element of the population has an equal probability of being chosen. A random sample only requires that every item in a population has a greater than zero chance of being drawn. Unlike in a simple random sample, that probability may or may not be equal for every item.

In simple random sampling, every element of a 1,000-item set has an equal probability of one in 1,000 to be selected. In other forms of random sampling, some elements may have a 2% probability of being selected, others 3%, and so on. Simple random sampling is theoretically simpler to implement, since each item is given the same probability.

## What is replacement?

Replacement refers to the action of putting a drawn item back into the population and then selecting the next one. When a researcher performs sampling with replacement, there’s a probability that items in the population may be included in the sample more than once.

When drawing random numbers to select an item for a simple random sample, there is a possibility that an element may be chosen more than once. Since simple random sampling requires that each item have an equal chance of being drawn, a researcher typically performs simple random sampling without replacement. That means that once a researcher draws an item from the population, then that item isn’t put back into the pool of available items to be selected for the sample.

## What are the advantages and disadvantages of simple random samples?

Two of the most notable advantages of a simple random sample are its ease of use and perceived sense of fairness. The rules to build a sample are clear, and you don’t have to worry about additional steps, such as classifying the population into mutually exclusive subgroups as in stratified random sampling.

When creating a simple random sample, a researcher seeks to build an unbiased sample. Generally, you would trust the results of a study made with an unbiased sample more than the findings of one built around a skewed sample. Simple random sampling could be considered a fair-minded way to select a sample because every element of the population has the same probability of being chosen.

On the other hand, two of the most notable disadvantages of a simple random sample are that the skewing of data may still occur and that implementation may be nearly impossible or cost-prohibitive. For example, a company with 500 employees may be equally split into 250 workers under age 50 and 250 workers aged 50 and up. A simple random sample of 100 workers may end up including only 20 workers who are at least 50 years old. In that case, the sample may be skewed and not truly representative of all employees.

Additionally, trying to gather a simple random sample may be challenging under certain scenarios, such as the U.S. Census. The Census Bureau estimated the U.S. population to be over 328 million as of July 1, 2019. Since the Census Bureau has limited staff and resources, simple random sampling would likely prove too complicated and expensive to gather a snapshot of the U.S. population. This is why the Census Bureau uses various sampling techniques in the planning, development, and implementation of its programs and surveys involved in the census.

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