Statistics

statistics

Definition

Statistics

Statistics is the discipline concerned with the description of and inference from data. Given observed data $D=(x_1,\dots ,x_n)$, description summarises properties of $D$, while inference uses $D$ to draw conclusions about the wider population or process from which it arose.

Direction of Reasoning

$$D=(x_1,\dots ,x_n)\text{ observed}⟶\text{conclusions about an unknown population or model}.$$

Statistics collects data and observes events to draw probabilistic conclusions about the whole population. This reverses the direction of probability theory: it begins with partial observations rather than a completely specified model.

Character

• Data collection, model choice, and interpretation require judgement.
• Different valid methods and assumptions can produce different conclusions.
• Consequently, a statistical question need not have a single correct answer.