Equal implies that the probability of selection of each element in the population is the same; that is, the choice of an element in the sample is not influenced by other considerations such as personal preference. Probability
The concept of independence means that the choice of one element is not dependent upon the choice of another element in the sampling; that is, the selection or rejection of one element does not affect the inclusion or exclusion of another.
To explain these concepts let us take an example. Suppose there are 80 students in the class. Assume 20 of these refuse to participate in your study that is; you have consented them and to respect their rights they won't be able to participate. You want the entire population of 80 students in your study but, as 20 refuse to participate, you can only use a sample of 60 students.
The 20 students who refuse to participate could have strong feelings about the issues you wish to explore, but your findings will not reflect their opinions. Their exclusion from your study means that each of the 80 students does not have an equal chance of selection. Therefore, your sample does not represent the total class. The same could apply to a community. In a community, in addition to the refusal to participate, let us assume that you are unable to identify all the residents living in the community. If a significant proportion of people cannot be included in the sampling population because they either cannot be identified or refuse to participate, then any sample drawn will not give each element in the sampling population an equal chance of being selected in the sample. Hence, the sample will not be representative of the total community.
THE CONCEPT OF INDEPENDENCE: To understand the concept of an independent chance of selection, let us assume that there are five students in the class who are extremely close friends. If one of them is selected but refuses to participate because the other four are not chosen, and you are therefore forced to select either the five or none, then your sample will not be considered an independent sample since the selection of one is dependent upon the selection of others.
The same could happen in the community where a small group says that either all of them or none of them will participate in the study. In these situations where you are forced either to include or to exclude a part of the sampling population, the sample is not considered to be independent, and hence is not representative of the sampling population. However, if the number of refusals is fairly small, in practical terms, it should not make the sample non-representative. In practice there are always some people who do not want to participate in the study but you only need to worry if the number is significantly large.
A sample can only be considered a random/probability sample (and therefore representative of the population under study) if both these conditions are met. Otherwise, bias can be introduced into the study. Bias
There are two main advantages of random/probability samples:
1. As they represent the total sampling population, the inferences drawn from such samples can be generalised to the total sampling population.
2. Some statistical tests based upon the theory of probability can be applied only to data collected from random samples. Some of these tests are important for establishing conclusive correlations.
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