Overview
On this page, we start to discuss the field of “Inferential Statistics”, i.e. the art of making estimates about unknown values of a certain population by considering incomplete information, for example coming from a so-called sample.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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Distinguish between a statistic (a property of an incomplete data set, typically a sample drawn from a population being studied) and a parameter (a property of a complete data set, typically the entire population being studied).
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Understand that a statistic can be treated as a random variable with a probability distribution, since its value depends on the sample that happens to have been chosen by chance, while a parameter can be treated as a definite single value which is unaffected by the random sampling process. This is the basis of frequentist statistics.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Understand the definition of a simple random sample, and be able to constuct the sampling distribution of any statistic on a very small population of three of four individuals by using this definition.
To prepare for class
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Watch the following short video (by Rahul Patwari) which introduces the subject of Inferential Statistics (and compares it with Descriptive Statistics), and explains the concepts of population, parameter, sample, and statistic, as well as the most important examples of these:
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Watch the following video (by Brendan Cordy) which uses the so-called “German Tank Problem” (also called Locomotive Problem) to introduce the basic ideas about statistical estimates:
After class
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Watch the following video (by Brendan Cordy) which explains the concept of a Simple Random Sample (SRS) and discusses some examples of when this does not actually apply in reality:
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Watch the following video (by jbstatistics) which explains the sampling distribution of a parameter, and how to find it, either approximatively or (at least in principle) precisely:
