As the name suggests, we pick the sample, at random. There is no pattern, and it’s a purely random selection. For instance, you wanted to survey vaccination uptake. You could put 100 names of all eligible people in a hat and pull out a few to sample them. For instance, in machine learning, when you split your data into a training set and a test set you use the principle of simple random sampling.
Let’s look at the two subtypes of simple random sampling:
Simple random sampling with replacement
Here, in a sample size N, you select an element of the population and return it to the population. This implies that each element of the population could theoretically be selected more than once. Each time we select an individual, we have the whole selected population available to select from. Typically, when the population itself is small, we use this technique.
Simple random sampling without replacement
Here, once you select an individual from the population, you don’t return it. With each passing selection, the available population decreases by 1. This also implies that for a sample size N, we repeat the selection process N times. When the population size is large, we go for this without-replacement method of simple random sampling.