# Simple Random Sampling

Definition and Different Approaches

Simple random sampling is the most basic and common type of sampling method used in quantitative social science research and in scientific research generallyThe main benefit of the simple random sample is that each member of the population has an equal chance of being chosen for the study. This means that it guarantees that the sample chosen is representative of the population and that the sample is selected in an unbiased way. In turn, the statistical conclusions drawn from the analysis of the sample will ​be valid.​

There are multiple ways of creating a simple random sample. These include the lottery method, using a random number table, using a computer, and sampling with or without replacement.

## Lottery Method of Sampling

The lottery method of creating a simple random sample is exactly what it sounds like. A researcher randomly picks numbers, with each number corresponding to a subject or item, in order to create the sample. To create a sample this way, the researcher must ensure that the numbers are well mixed before selecting the sample population.

## Using a Random Number Table

One of the most convenient ways of creating a simple random sample is to use a random number table. These are commonly found at the back of textbooks on the topics of statistics or research methods. Most random number tables will have as many as 10,000 random numbers. These will be composed of integers between zero and nine and arranged in groups of five. These tables are carefully created to ensure that each number is equally probable, so using it is a way to produce a random sample required for valid research outcomes.

To create a simple random sample using a random number table just follow these steps.

1. Number each member of the population 1 to N.
2. Determine the population size and sample size.
3. Select a starting point on the random number table. (The best way to do this is to close your eyes and point randomly onto the page. Whichever number your finger is touching is the number you start with.)
4. Choose a direction in which to read (up to down, left to right, or right to left).
5. Select the first n numbers (however many numbers are in your sample) whose last X digits are between 0 and N. For instance, if N is a 3 digit number, then X would be 3. Put another way, if your population contained 350 people, you would use numbers from the table whose last 3 digits were between 0 and 350. If the number on the table was 23957, you would not use it because the last 3 digits (957) is greater than 350. You would skip this number and move to the next one. If the number is 84301, you would use it and you would select the person in the population who is assigned the number 301.
6. Continue this way through the table until you have selected your entire sample, whatever your n is. The numbers you selected then correspond to the numbers assigned to the members of your population, and those selected become your sample.

## Using a Computer

In practice, the lottery method of selecting a random sample can be quite burdensome if done by hand. Typically, the population being studied is large and choosing a random sample by hand would be very time-consuming. Instead, there are several computer programs that can assign numbers and select n random numbers quickly and easily. Many can be found online for free.

## Sampling With Replacement

Sampling with replacement is a method of random sampling in which members or items of the population can be chosen more than once for inclusion in the sample. Let’s say we have 100 names each written on a piece of paper. All of those pieces of paper are put into a bowl and mixed up. The researcher picks a name from the bowl, records the information to include that person in the sample, then puts the name back in the bowl, mixes up the names, and selects another piece of paper. The person that was just sampled has the same chance of being selected again. This is known as sampling with replacement.

## Sampling Without Replacement

Sampling without replacement is a method of random sampling in which members or items of the population can only be selected one time for inclusion in the sample. Using the same example above, let’s say we put the 100 pieces of paper in a bowl, mix them up, and randomly select one name to include in the sample. This time, however, we record the information to include that person in the sample and then set that piece of paper aside rather than putting it back into the bowl. Here, each element of the population can only be selected one time.

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