There are several types of probability sampling. In this video, I'll discuss the two simplest types, simple random sampling and systematic sampling. The most basic form of probability sampling is simple random sampling. In simple random sampling, each element in the sampling frame has an equal and independent probability of being included in the sample. Independent means the selection of any single element does not depend on another element being selected first. In other words, every possible combination of elements is equally likely to be sampled. To obtain a simple random sample, we could write every unique combination of sampled elements on a separate card, shuffling the cards, and then blindly drawing one card. Of course, if the population is large, then writing out all possible combinations is just too much work. Fortunately, an equivalent method is to randomly select individual elements. This can be done using random number tables still found in the back of some statistics books, but these tables have come obsolete. We can now generate random number sequences with a computer. For example, if our population consists of 12 million registered taxpayers, then we can generate a sequence of 200 unique random numbers between one and 12 million. Systematic sampling is a related method aimed to obtain a random sample also. In systematic sampling, only the first element is selected using a random number. The other elements are selected by systematically skipping a certain number of elements. Suppose we want to sample the quality of cat food on an assembly line. A random number gives us a starting point, say, the seventh bag. We then sample each tenth bag. So we select bag number seven, 17, 27, etc. It would much harder to select elements according to random numbers, say, bag number seven, 30, 36, 41, et cetera, especially if the assembly line moves very fast. With this approach, each element has an equal probability of being selected, but the probabilities are no longer independent. Element 17, 27, 37, et cetera, are only chosen if seven is chosen as the starting point. This is not a real problem. It just requires a little more statistical work to determine things like the margin of error. The real problem with systematic sampling is that it only results in a truly random sample if there's absolutely no pattern to the list of elements. What if the assembly line alternately produces cat food made with fish and cat food made with beef? Let's say all odd-numbered elements are made with fish. In our example, we would never sample the quality of cat food made with beef. Of course, this an exaggerated example, but it illustrates that systematic sampling can be dangerous. A preexisting list or ordering of elements can always contain a pattern that were unaware of, resulting in a biased sample. So, systematic sampling only results in a truly random sample if it's absolutely certain that the list of elements is ordered randomly. We can make sure of this by randomly reordering the entire list. We can generate a sequence of random numbers of the same size as the list and then select elements from this list using systematic sampling. Of course, this is equivalent to random selection directly from the original list using random numbers. Unless we can be sure that the list is truly random, systematic sampling should not be considered a form of probability sampling. Instead, it should be considered a form of non-probability sampling.