INFERENTIAL STATISTICS are “quantitative techniques [that can be used] to generalize from a sample to a population” (Meier, Brudney, and Bohte, 2011, p. 173). When done correctly and with a large enough sample, the results obtained from a sample can be generalized to the population from which the sample was taken, with a known MARGIN OF ERROR that provides a range around a sample estimate within which the true population parameter is expected to lie (once this range is added to our point estimate, we call it a CONFIDENCE INTERVAL) and a CONFIDENCE LEVEL that indicates the probability that the population parameter falls within this interval. Margin of error, confidence intervals, and confidence levels help quantify how precise our estimates are.
For example, every time you hear a news broadcast report the President Biden’s job approval rating, you are receiving inferences based on a sample of the population. Naturally, it would be too costly and take too long to contact everyone in the United States to ask them how well Biden is doing as president. Instead, a random sample of Americans is used to generate Biden’s job approval rating. Then, depending on the sample size, the MOE is calculated; this accounts for variability in their estimates that results from not asking every American how well Biden is doing. If CNN reports that Biden’s job approval is 44% with a ±3 MOE with a confidence level of 95%, we are 95% confident that the true job approval rating lies between 41% and 47%.