Systematic Sample vs Simple Random Sample
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Systematic sample
Collecting data and study design
A systematic sample orders the population, picks a random starting point, then selects every kth individual from that point onward.
Systematic sampling chooses one random start and then follows a fixed interval, which is handy when a full list is hard to number in advance. For example, standing at a store entrance and surveying every 10th customer after a random start is a systematic sample. The gap between selections, often written (the sampling interval), is set so the selections cover the whole population. It can fail if the list has a repeating pattern that lines up with the interval.
Simple random sample
Collecting data and study design
A simple random sample is selected so that every possible sample of the given size has an equal chance of being the one chosen.
In a simple random sample, often shortened to SRS, each individual and each group of individuals is equally likely to be picked. For example, numbering all 500 students at a school and using a random number generator to select 30 of them produces an SRS. This equal-chance selection removes selection bias and is what justifies the standard error formulas used later in inference. It usually requires a list of the whole population to sample from.