Video Transcript
A research group is conducting a study on the average income of employees in Egypt. They use a random number generator to select a sample of 2,000 people. Is this considered a stratified sample?
To determine whether the sample obtained by the research group is considered a stratified sample or not, let’s remind ourselves of how we define a stratified random sample. We can then compare the method the research group used to obtain their sample with our definition to see if the two methods match.
We use a stratified random sample when a population naturally subdivides into nonoverlapping groups or strata. A random sample is selected from each group or stratum proportional to the size of the stratum within the population. These individual samples then combine into one representative sample of the population. So that’s stratified random sampling. Now let’s compare this with our research group’s method.
The research group use a random number generator to select a sample of 2,000 people. Now a random number generator is a mathematical program or process designed to produce a set of numbers with no pattern. The research group is conducting a study on the average income of employees in Egypt. So let’s suppose that 30 million people are listed as employed in Egypt and that each employee is associated with a single number from one to 30 million in the list of employees. Since the group would like a sample of 2,000 people, the random number generator produces 2,000 distinct numbers between one and 30 million. The 2,000 employees associated with these numbers make up the random sample.
So now let’s compare this method with stratified sampling. Was our population of employees subdivided into groups before sampling? No, the list of employees was not divided into groups before sampling. So no subdivision occurred in the sampling. In fact, the random numbers generated were between one and 30 million, so the sample was taken directly from the population. And since no subdivision occurred, a random sample was not selected from the groups, since there were no groups. And there was no combination of samples since there was one single sample. Our answer then must be no, this is not considered a stratified sample.
