Simple random sample

Simple random sampling, statistically speaking, requires that all the elements in the population having an equal probability of being included in the sample. The idea of drawing names from a hat may evoke a process resembling simple random sampling. Unless the names are drawn with replacement, however, this process is not simple random sampling. The reason lies in the elements of the population not having equal probability.

For instance, if I have 10 names in the hat, the probability of any one name being drawn is 1 out of 10. After the first name is drawn, there are nine names left in the hat changing the probability of anyone being selected as the second name is 1 out of 9. Since different names have different probabilities depending on the sequence in which the drawing is done, the resulting sample will not be a simple random sample. The solution lies in drawing a name and after noting it, dropping it back into the hat. For a large population, the best method may be to number the elements sequentially and use numbers coming from a table of random numbers for selection. Since these numbers, which can fill a large book, are true random numbers with no discernable pattern, the selection will be random.

Simple random sampling is not an efficient method since it does not consider the available information about the population. It best suits situations where the population is fairly homogeneous and not much information is available about the population. If these conditions are not true, stratified sampling may be a better choice.