Question

For the Stratified Sampling technique,

• give the steps that are required, and identify the step(s) in which randomness plays a role for this technique.
• Use your own terms to give at least one advantage, at least one disadvantage, (5 points)
• and give an example showing how randomization can help this sampling avoid bias.

Answer 1

Steps involved in Stratified sampling or Stratified random sampling:

1.

The elements of the population are divided into small sub-groups called strata based on the homogeneity (similarity) so that the elements within each sub-group are homogeneous and the elements among different sub-groups formed are heterogeneous.

2.

And the elements are randomly selected from each of these strata either proportionately or disproportionately. Selecting proportionately means - from each strata the number of elements chosen are proportionate to the number of such elements in the population. Disproportionately means selecting any number of elements from each strata irrespective of how many such elements are present in the population. When we do not know about how many of each characteristic elements are present in the population, then obviously our selection would be disproportionate.

3.

Combine all these elements together to form a sample that contains all the characteristics of the population.

4.

Conduct appropriate tests for this sample to draw inference about the population. That is, do what you wanted to do with the sample.

Advantage:

This sampling technique is used when we want to represent the population in its entirety with all different characteristics.

For example, in a school of boys and girls with different classes, if we need a sample, we divide it into strata of classes and also boys and girls in each class and then randomly pick the samples from each strata. Here, the population is all students of the school. Sampling technique is stratified random sampling. Sample is all the students who are randomly selected from each strata.

The strength of this sampling technique is that it better represents the population than the simple random sample. It enables us to compare the statistics among these different characteristics such as comparing mean marks of girls with that of boys and further testing of significance and deciding which sub-group of the population (boys or girls) contributed more to the overall marks of the school in a certain competition among schools. It is especially used when population is composed of different characteristics.

Disadvantage:

One can't always classify every member of the population into a sub-group. Determining an exhaustive and definitive list of characteristics of an entire population cannot be always possible due to overlapping which is a major issue when there are subjects that fall into multiple strata (sub-groups). When the random sampling is performed, those that are in multiple sub-groups are more likely to be chosen and thus, misrepresents the population.

Randomization can help this sampling avoid bias:

Randomization in stratified sampling technique is same as randomization in simple random sampling and has the same advantages. The randomness governs the selection process where each member of the particular attribute (characteristic) in the population has an equal probability of selection. This is true with every attribute of the population so that everyone has equal chance of selection so that bias is avoided.