# Simple Random Sampling

Simple random sampling is the most widely-used probability sampling method, probably because it is easy to implement and easy to analyze.

## Key Definitions

To understand simple random sampling, you need to first understand a few key definitions.

• The total set of observations that can be made is called the population.
• A sample is a set of observations drawn from a population.
• A parameter is a measurable characteristic of a population, such as a mean or standard deviation.
• A statistic is a measurable characteristic of a sample, such as a mean or standard deviation.
• A sampling method is a procedure for selecting sample elements from a population.
• A random number is a number determined totally by chance, with no predictable relationship to any other number.
• A random number table is a list of numbers, composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers in the list are arranged so that each digit has no predictable relationship to the digits that preceded it or to the digits that followed it. In short, the digits are arranged randomly. The numbers in a random number table are random numbers.

## Simple Random Sampling

Simple random sampling refers to a sampling method that has the following properties.

• The population consists of N objects.
• The sample consists of n objects.
• All possible samples of n objects are equally likely to occur.

An important benefit of simple random sampling is that it allows researchers to use statistical methods to analyze sample results. For example, given a simple random sample, researchers can use statistical methods to define a confidence interval around a sample mean. Statistical analysis is not appropriate when non-random sampling methods are used.

There are many ways to obtain a simple random sample. One way would be the lottery method. Each of the N population members is assigned a unique number. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n numbers. Population members having the selected numbers are included in the sample.

## Random Number Generator

In practice, the lottery method described above can be cumbersome, particularly with large sample sizes. As an alternative, use Stat Trek's Random Number Generator. With the Random Number Generator, you can select up to random numbers quickly and easily. This tool is provided at no cost - free!! To access the Random Number Generator, simply click on the button below. It can also be found under the Stat Tools tab, which appears in the header of every Stat Trek web page.

## Sampling With Replacement and Without Replacement

Suppose we use the lottery method described above to select a simple random sample. After we pick a number from the bowl, we can put the number aside or we can put it back into the bowl. If we put the number back in the bowl, it may be selected more than once; if we put it aside, it can selected only one time.

When a population element can be selected more than one time, we are sampling with replacement. When a population element can be selected only one time, we are sampling without replacement.