This summer, I am teaching an undergraduate stats class, which is a first class in stats to cover three units, descriptive statistics, probability and statistical inference. The course webpage is here.
The following paragraph is from the thesis of Michael Phillip Lesnick. It explains the relationship among the three units:
Recall first that in statistics, we distinguish between descriptive statistics and statistical inference. Descriptive statistics, as the name suggests, is that part of statistics concerned with defining and studying descriptors of data. It involves no probability theory and aims simply to offer tools for describing, summarizing, and visualizing data. Statistical inference, on the other hand, concerns the more sophisticated enterprise of estimating descriptors of an unknown probability distribution from random samples of the distribution. The theory and methods of statistical inference are built on the tools of descriptive statistics: The estimators considered in statistical inference are of course, when stripped of their inferential interpretation, merely descriptors of data.
For the teaching of such low level course, it is really challenging. There is one thing I want to share here is the post written by Dr Nic, which says that we’d better to use real data collected from the students as a source of data for use in class examples, exercises and testing. This is really a good idea. And today I saw a paper on Significance, discussing about why statistics lectures confuse students. It’s also very good reference for stats teachers.