Statistical thinking = detective work + skepticism + alternative explanations.
Ask questions.
Do not trust intuition blindly.
There are two kinds of variation:
measurement variation: caused by how we measure or collect data.
random variation: caused by the underlying process itself.
A big part of statistics is figuring out whether variation is just noise or reflects something real and controllable.
Probability starts from the larger world/model and asks what outcomes are likely.
Statistics starts from observed data and tries to infer something about the larger world.
Descriptive statistics summarize what you observed.
Inferential statistics use the sample to reason about the broader population.
The “4 out of 5 dentists” example is especially good because it shows why intuition can be misleading: even when each dentist independently agrees 80% of the time, exactly four out of five agreeing is only about 41%, not 80%.
The broad takeaway I’d keep for the final post is:
Statistical thinking is not mainly about formulas. It is a disciplined habit of questioning what you see, considering alternative explanations, and resisting intuitive conclusions that feel obvious but may be wrong.
Statistical thinking = detective work + skepticism + alternative explanations.