We might try to estimate the time to graduation for Lancaster undergraduates in the last 5 years by collecting a sample of students. All graduates in the last 5 years represent the population, and graduates who are selected for review are collectively called the sample. In general, we always seek to randomly select a sample from a population. The most basic type of random selection is equivalent to how raffles are conducted. For example, in selecting graduates, we could write each graduate’s name on a raffle ticket and draw 100 tickets. The selected names would represent a random sample of 100 graduates.
Why pick a sample randomly? Why not just pick a sample by hand? Consider the following scenario.
Suppose we ask a student who happens to be majoring in medicine to select several graduates for the study. What kind of students do you think she might collect? Do you think her sample would be representative of all graduates?
Answer. Perhaps she would pick a disproportionate number of graduates from health-related fields. Or perhaps her selection would be well-representative of the population. When selecting samples by hand, we run the risk of picking a biased sample, even if that bias is unintentional or difficult to discern. If someone was permitted to pick and choose exactly which graduates were included in the sample, it is entirely possible that the sample could be skewed to that person’s interests, which may be entirely unintentional. This introduces bias into a sample. Sampling randomly helps resolve this problem. The most basic random sample is called a simple random sample, and which is equivalent to using a raffle to select cases. This means that each case in the population has an equal chance of being included and there is no implied connection between the cases in the sample.
The act of taking a simple random sample helps minimize bias, however, bias can crop up in other ways. Even when people are picked at random, e.g. for surveys, caution must be exampled if the non-response is high. For instance, if only 30% of the people randomly sampled for a survey actually respond, then it is unclear whether the results are representative of the entire population. This non-response bias can skew results.
Another common downfall is a convenience sample, where individuals who are easily accessible are more likely to be included in the sample. For instance, if a political survey is done by stopping people walking in Lancaster, this will not represent all of the Lancaster and Fleetwood constituency. It is often difficult to discern what sub-population a convenience sample represents.
We can easily access ratings for products, sellers, and companies through websites. These ratings are based only on those people who go out of their way to provide a rating. If 50% of online reviews for a product are negative, do you think this means that 50% of buyers are dissatisfied with the product?
Answer. Answers will vary. From our own anecdotal experiences, we believe people tend to rant more about products that fell below expectations than rave about those that perform as expected. For this reason, we suspect there is a negative bias in product ratings on sites like Amazon. However, since our experiences may not be representative, we also keep an open mind.