What Is a Simple Random Sample?

What Is a Simple Random Sample?

Let me explain what a simple random sample is. It's a subset of a statistical population where each member has an equal probability of being chosen, and it's designed to give you an unbiased representation of the whole group.

You select this group from a larger population, ensuring every individual has the same chance. This approach helps you fairly represent the entire population without introducing bias.

Key Takeaways

Here's what you need to know: A simple random sample pulls a small, random portion from the entire population to stand in for the whole data set, with each member having an equal shot at being picked. You can create one using lotteries or random draws. But watch out for sampling errors if the sample doesn't mirror the population accurately. We determine these samples by assigning sequential values to each item and then randomly selecting them. And remember, there are alternatives like systematic, stratified, and cluster sampling if this doesn't fit your needs.

Understanding a Simple Random Sample

You can create a simple random sample in a few ways. With the lottery method, assign each population member a number and pick them randomly. For instance, if you're at a company with 250 employees and you draw 25 names from a hat, that's a simple random sample because everyone has an equal chance.

This method shows up in science for randomized control tests or blinded experiments. In the employee example, you'd number them from 1 to 250 and randomly select 25 numbers. Since selections are random, each person in the population has the same probability, which usually gives you a balanced subset that represents the larger group well.

For big populations, doing this manually is tough, so use a computer-generated process instead. It follows the same logic as the lottery but with machines handling the numbers and selections.

Room for Error

You have to account for error in simple random samples, shown as a plus or minus variance, which is sampling error. Say you're surveying 1,000 high school students for left-handedness and sample 100, finding eight left-handed—that suggests 8% overall, but the true average might be 10%.

This applies to any topic, like green eyes or disabilities; you'll get a probability with variance. To be 100% accurate, you'd survey everyone, which is often impractical. Even though simple random sampling aims for no bias, selection bias can creep in if the sample isn't inclusive enough, so you might need extra techniques.

How to Conduct a Simple Random Sample

Follow these six steps in order to conduct a simple random sample. First, define your population—the group you want to study, like the largest U.S. companies in the S&P 500 if you're looking at stock performance over 20 years.

Second, choose your sample size, making sure it's large enough to represent the population but fits your resources. For the S&P 500, you might pick 20 companies.

Third, determine the population units by listing all items, such as copying S&P 500 companies into a spreadsheet.

Fourth, assign numerical values sequentially, like numbering companies 1 to 500 based on the CEO's surname alphabetically.

Fifth, select random values—for 20 items, pick 20 numbers from 1 to 500 using a random method.

Sixth, identify your sample by matching those random numbers to the population items.

Random Sampling Techniques

For selecting random values, don't just pick them yourself to avoid bias. Use methods like a random lottery with ping pong balls or slips in a box, physical tools like dice or coins, random number tables from books, online generators, or Excel's RANDBETWEEN function.

Consider getting help from a colleague to spot any biases you might miss.

Simple Random vs. Other Sampling Methods

Compare simple random to stratified random sampling, which divides the population into strata based on shared traits and picks proportionally from each. This ensures representation from subgroups, like industries in the S&P 500, without overlap.

Versus systematic sampling, which picks a random starting point and then selects at regular intervals, like every 37th company, to avoid clustering that might happen in simple random.

Against cluster sampling, which groups similar items and samples within clusters, either in one or two stages, potentially adding more randomness or deeper analysis than simple random.

Advantages and Disadvantages of Simple Random Samples

The biggest advantage is ease of use—no need to subdivide the population like in stratified methods. It's fair because everyone has an equal chance, reducing sampling bias.

But disadvantages include possible sampling errors if the sample doesn't reflect the population, like drawing all men from a mixed group. It's better for unknown populations, but for known ones, other methods account for differences better. Plus, for large populations, it's time-consuming and costly, and assigning numbers can be tricky.

Frequently Asked Questions

Why is it simple? It's the easiest way to get a representative sample from a population. Drawbacks include access issues, time, costs, and potential bias. A stratified sample divides into groups for better subgroup representation. Random samples help make unbiased generalizations about populations without surveying everyone.

The Bottom Line

Simple random sampling is the basic way to analyze a population with equal selection probability. More complex methods fix its issues, but for smaller populations, nothing beats its simplicity.