What Is a Simple Random Sample?

A simple random sample is a group selected from a larger population where every individual has an equal chance of being chosen. This type of sample aims to fairly represent the whole population without bias.

Understanding a Simple Random Sample

Researchers can create a 澳洲幸运5开奖号码历史查询:simple random sample using a couple of methods. With a lottery method, each member of the population is assigned a number, 🦋and numbers are then selected at rando♑m.

An example of a simple random sample would be to choose the names of 25 employees out of a hat from a company of 250 employees. In this case the 澳洲幸运5开奖号码历史查询:population is all 250 employees, andღ the sample is random because each employee has an equal chance of being chosen. Random sampling is used in science to conduct randomized control tests or for blinded experiments.

The example in which the names of 25 e♎mployees out of 250 are chosen out of a hat is an example of the lottery method at work. Each of the 250 employees would be assigned a number between one and 250, after which 25 of those numbers would be chosen at random.

Because individuals wh🅷o make up the subset o🔯f the larger group are chosen at random, each individual in the large population set has the same probability of being selected. In most cases this creates a balanced subset that carries the greatest potential for representing the larger group as a whole.

A manual lottery method can be quite onerous for larger populations. Selecting a random sample from a large population usually requires a computer-generated process. The same methodology as the lottery method is used, only the number assignments and subsequent selections are performed by computers, not humans.

Room for Error

With a simple random sample, there has to be room for error represented by a plus and minus variance (澳洲幸运5开奖号码历史查询:sampling error). For example, if a survey is taken to determine how many students are left-handed in a high school of 1,000 students, random sampling can determin💎e that eight out of the 100 sampled are left-handed. The conclusion would then be that 8% of the student population of the high school are left-handed, when in fact the global average would be closer to 10%.

The same is true regardless of the subject ma🌜tter. A survey on the percentage of the student population that has green eyes or a physical disability would result in a mathematical probability based on a simple random survey, but always with a plus or minus variance. The only way to have 100% accuracy rate would be to survey all 1,000 students which, while possible, would be impractical.

How to Conduct a Simple Random Sample

The simple random sampling process entails six steps, each performed in seqꦉuenti𒁃al order.

Step 1: Define the Population

The starting point of statistical analysis is to determine the population base. This is the group about which you wish to learn more, confirm a hypothesis,💮 or determine a statistical outcome. This step is simply to identify what that population base is and ensure that the group will adequately cover the outcome you are trying to ascertain.

Example: You want to learn how the stocks of the largest companies in the United States have performed over the past 20 years. Your populatioꦕn would be the largest companies in the United States as determined by the S&P 500.

Step 2: Choose the Sample Size

Before picking the units within a population, we need to determine how many to select. This sample size may be constrained by the amount of time, 澳洲幸运5开奖号码历史查询:capital rationing, or other resources available to analyze the sample. However, be mindful to pick a sample size large enough to be genuinely representative of the population. In the example above, there are constraints in analyzing🌠 the performance for every stock in the S&P 500, so we only want to analyze a subset of this population.

Example: Your sample size will be🔥 20 companies from the S&𒆙amp;P 500.

Step 3: Determine Population Units

In our example the items within the population are easy to determine, as they've already been identified for us (i.e., the companies listed within the S&P 500). However, imagine analyzing the students currently enrolled at a university or food products being sold at a grocery store. This step entails crafting the entire list of all items within your population.

Example: Using exchange information, you copy the coไmpanies comprising the S&P 500 into🤡 an Excel spreadsheet.

Step 4: Assign Numerical Values

The simple random sample process calls for every unit within the population to receive an unrelated numerical value. This is often assigned based on how the data may be filtered. For example, you could assign the numbers one to 500 to the companies based on 澳洲幸运5开奖号码历史查询:market cap, alphabetical order, or company formation date. How the v꧒alues are assigned isn𝓰’t relevant; all that matters is that each value is sequential and has an equal chance of being selected.

Example: You assign the numbers one through 500 to the companies in the S&P 500 based on alphabetical order of the current CEO's surname, with the first company receiving the value one and the last company receiving the value 500.

Step 5: Select Random Values

In step 2 we chose 20 as the number of items we wanted to analyze withi♛n our p𝔍opulation. We now randomly select 20 number values out of the 500. There are multiple ways to do this, as discussed later in this article.

Example: Using a random number table (see below), you select the numbers 2, 7, 17, 67, 68, 75, 77, 87, 92, 101, 145, 201, 222, 232, 311, 333, 376,♛ 401, 478, and 489.

Step 6: Identify the Sample

Each of the rando✨m variables selected in the prior step corresponds to an item within our population. The grꦜoup sample is selected by identifying which random values were chosen and which population items those values match.

Example: Your sample consists of the companies that correspond to𓄧 the values chosen in step 5.

Random Sampling Techniques

There is no single method for determining the ﷽random values to be selected in step 5. The analyst can’t choose completely random numbers on their own, as there may be factors influencin💎g their decision. For example, the analyst’s wedding anniversary may be the 24th, so they may consciously (or subconsciously) pick the random value 24. Instead, the analyst may choose one of the following methods:

• Random lottery: Each population number receives an equivalent item, say a ping pong ball or slip of paper, on which it is written, and those items are stored in a box. Random numbers are then selected by pulling items from the container without looking at them.
• Physical methods: Simple, early methods of random selection may use dice, flipping coins, or spinning wheels. Each outcome is assigned a value or outcome relating to the population.
• Random number table: Many statistics and research books contain sample tables with randomized numbers.
• Online random number generator: Many online tools exist where an analyst inputs first the population size and then the sample size to be selected.
• Random numbers from Excel: Numbers can be selected in Excel using the =RANDBETWEEN formula. A cell containing =RANDBETWEEN(1,5) will select a single random number between one and 5.

Simple Random vs. Other Sampling Methods

Simple Random vs. Stratified Random Sample

A simple random sample is used to represent the entire data population. A stratified random sample divides the popula🌌tion into smaller groups, known as “strata,” based on shared characteristics.

Unlike simple random samples, stratified random samples are used with populations that can be easily broken into different subgroups or subsets. These groups are based on certain criteria, then elements from each are randomly chosen in proportion to the group’s 🍸size versus the population. In our example above, S&P 500 companies could have subsets defined by type of industry or geographical region of the company’s headquarters.

This method of sampling means there will be selections from each different group—the size of which is based on its proportion to the entire population. Researchers must ensure that the strata do not overlap. Every point in the population must only belong to one stratum, because they should be 澳洲幸运5开奖号码历史查询:mutually exclusive. Overlapping strata would increase th💜e likelihood that some data are included, thus skewing the sample.

Simple Random vs. Systematic Sampling

澳洲幸运5开奖号码历史查询:Systematic sampling entails selecting a single random variable that determines the interval of how the population items are selected. For example, if the number 37 was chosen, the 37t🔯h company on the list sorted by last name of the CEO would be selected by the sample. Then, the🌌 74th (i.e., the next 37th) and the 111st (i.e. the next 37th after that) would be added as well.

Simple random sampling does not have a starting point; therefore, there is the risk that the population items selected at random may cluster. In our example there may be an abundance of CEOs with a last name that starts with the letter 'F.' Systematic sampling strives to even further reduce bias by ensuring that these clusters do not happen.

Simple Random vs. Cluster Sampling

澳洲幸运5开奖号码历史查询:Cluster sampling (also known as “multistage random sampling”) can occur as a one-stage or two-stage cluster. In the forme🌟r, items within a population are put into comparable groupings (using our example, companies are grouped by year ༺formed), then sampling occurs within these clusters.

Two-stage cluster sampling occurs when clusters are formed through random selection. The population is not clustered with other ༺similar items. Sample items are then randomly selected within each cluster.

Simple random sampling does not cluster any population sets. Clustering (especially two-stage clustering) can enhance the randomness of sample items. In addition, cluster sampling may provide a deeper analysis on a specific snapshot of 🌳a population, which may or may not enhance the analysis.

Advantages and Disadvantages of Simple Random Sa🙈mples

While simple random samples are 📖easy to use, they do come with key disadvantages that can render the data useless.

Advantages of a Simple Random Sample

Ease of use represents the biggest advantage of simple random sampling. Unlike more complicated sampling methods, such as stratified random sampling and probability sampling, there is no ne♑ed to divide the population into subpopulations or take any other additional steps before selecting members of the population at random.

A simple random sample is meant to be an unbiased rꦅepresentation of a group. It is considered a fair way to select a samꦰple from a larger population, as every member of the population has an equal chance of getting selected. Therefore, it has less chance of sampling bias.

Disadvantages of a Simple Random Sample

A sampling error can occur with a simple random sample if the sample does not end up accu♑rately reflecting the population it is supposed to represent. For example, in a simple random sample of 25 employees, it would be possible to draw 25 men even if the population consisted of 125 women, 125 men, and 125 nonbinary people.

For this reason simple random sampling is more commonly used when t🅷he researcher knows little about the population. If the researcher knows more, it is better to use a different sampling technique, such as stratified random sampling, which helps to account for the differences within the population, such as age, race, or gender.

Other disadvantages include the fact that for sampling from large populations, the process can be time-consuming and costly compared with other methods. Researchers may find that a project not worth the endeavor of its 澳洲幸运5开奖号码历史查询:cost-benefit analysis does not generate positive results.

As every unit has to be assigned an identifying or sequential number pri🅠or to the selection process, this task may be difficult based on the method of data collection or size of the data set.

The Bottom Line

Simple random sampling is the most basic form of🀅 analyzing a population, allowing 🔥every item within it to have the same probability of being selected. There are also more complicated sampling methods that attempt to correct for possible shortcomings in the simple method. However, they don’t match the ease of simple random sampling for smaller populations.