Difference Between Simple Random Sample and Systematic Random Sample

Simple Random Sample vs Systematic Random Sample
 

Data is one of the most important things in statistics. Due to practical difficulties it will not be possible to make use of data from a whole population when a hypothesis is tested. Therefore, data values from samples are taken to make inferences about a population. Since, not all data are used; there is an uncertainty (which is called the sampling error) in the inferences made. In order to minimize such uncertainties, it is important that unbiased samples be chosen.

When individuals are chosen for a sample in such a way that each individual in the population has an equal probability of getting selected, then such a sample is called a random sample. For example, consider the case where 10 houses out of 100 houses in a neighborhood are to be chosen as a sample. The number of each house is written in pieces of paper, and all the 100 pieces are in a basket. One randomly chooses 10 different pieces of paper with replacement from the basket. Then the chosen 10 numbers will be a random sample.

Simple random sampling and systematic random sampling are both sampling techniques, which result in random samples with a few different qualities.

What is a Simple Random Sample?

A simple random sample is a random sample chosen in such a way that each of the samples of that sample-size (that can be chosen from the population) has an equal probability of being selected as the sample. This sampling technique requires the reach throughout the total scope of the population. In other words, the population should be sufficiently small, temporally and spatially, to do simple random sampling efficiently. Looking back at the example, in the second paragraph, it can be seen that what is done there is simple random sampling and the sample of 10 houses drawn in that way is a simple random sample. 

For example, consider the case of testing light bulbs produced by a company, for lifetime. The population under consideration is all the light bulbs produced by the company. But in this case, some bulbs are yet to be produced and some bulbs are already sold. So the sampling is temporally limited to the bulbs currently in stocks. In this case, simple random sampling cannot be done, since it is impossible to make sure that, for each k, each sample of size k has equal probability of being selected as a sample to be investigated. 

What is a Systematic Random Sample?

Random samples chosen with systematic pattern are called systematic random samples. There are several steps in choosing a sample using this method.

• Index the population (numbers should be assigned randomly)
• Calculate the max-value of the sampling interval (the number of individuals in the population divided by the number of individuals to be chosen for the sample.)
• Select a random number between 1 and the max-value.
• Repeatedly add the max value to select the rest of the individuals.
• Choose the sample by selecting the individuals corresponding to the number sequence obtained.

For example, consider selection of 10 houses out of 100 houses. Then, houses are numbered from 1 to 100, to find a systematic random sample. Then, max-value is ¹⁰⁰/₁₀ = 10. Now, choose a number randomly in the range 1-10. It can be done by drawing lots. Say, 7 is the number obtained as a result. The random sample is the houses numbered 7, 17, 27, 37, 47, 57, 67, 77, 87, and 97.