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Estimating with uncertainty with certainty: confidence intervals for population parameters
Most findings are based on samples; in other words, we always have incomplete knowledge about the population of interest.
Imagine now a statistical method in which we can state that “we have some confidence” that the true parameter of interest (say mean height of humans, or trees, etc) is between two values:
Making the claims we just did, i.e., building confidence (intervals) for the true population statistic of interest (e.g., mean) requires that we trust our sample estimates (accuracy) & increase precision when possible.
The way we can trust samples is through random sampling (accuracy is assured) and increasing sample size (increase precision).
Statistical populations with relatively smaller variances increase precision, but this is a luxury that researchers don’t always control. Or perhaps possible by defining more specific problems: e.g., average height of humans versus average height of adult humans.
If sampling is random and if the frequency distribution of the population is roughly normal, then exactly 95% out of the infinite possible sample intervals will contain the true population parameter in the way we calculate confidence intervals!!
What is a Confidence Interval? by Mike Marin
Understanding Confidence, by Nic Petty
Slides above contain parts 1 and 2 of the lecture (The video mentioned during the lecture is “What is a Confidence Interval?” by Mike Marin is posted above.