Independent vs Dependent Sampling Methods
There are two simple methods for sampling distributions or groups of people: independent and dependent samples. People often confused them, and are unsure of which is which. We will cover the easy way to keep them straight.
For independent sampling, each group of cookies sampled below is independent from the previous group.
For instance, an example of independent sampling would be if someone was to randomly eat a vanilla cookie, replacing it with another cookie afterward. This is because initially the probability of getting a vanilla cookie was half, and it remained the same after the event (eating/replacing a cookie). This means that the next time a person reaches for a cookie, they have the same equal probability of picking a vanilla cookie.
For dependent sampling, the probability of getting a particular type of cookie is conditional on what has already happened, and occurs without replacement. An example would be someone taking a vanilla cookie without replacing it. On our cookie sheet, the first person has a one out of two (or 50%) chance of getting a vanilla cookie, while the second person only has 5 out of 11 (or 45%) chance, since there is one less vanilla cookie.
Another way to think about independent sampling might be that if you are a strong, independent person, you are not influenced by others, meaning the probability of making a decision is solely up to you. Conversely, if you are dependent on others, your choice is influenced by other people. Consider picking a college: if you are independently wealthy, your choice is not controlled by money and is independent of it. However, if you are not independently wealthy, your choice of college will be impacted and is dependent on your wealth.
Independent: The probability stays the same each time you sample.
Dependent: The probability changes each time you sample.