## Why it is so successful in science?

In some sense it offers a first line of defense against being fooled by randomness, separating signal from noise.

## Definition

• p-values tell you how surprising the data is, assuming there is no effect.
• formal definition:
A p-value is the probability of getting the observed or more extreme data, assuming the null hypothesis is true.

## Example

Does driving while calling increase the risk of a car accident?

• The difference is never exactly zero. A difference of e.g., 0.11 means:
1. Probably just random noise.
2. Probably a real difference

## Null hypthesis

• Assuming null hypthesis is true， means most of the data will fall between these two critical values.

## Important notes

1. A p-value is the probability of the data, not the probability of a theory.
2. You can’t get the probability the null hypothesis is true, given the data, from a p-value.
3. A single p-value is not enough to declare a scientific discovery; only when we can repeatedly observe something, we can consider it a reliable observation.

## How to use pValue correctly?

1. Use p-values as a rule to guide behavior in the long run.
2. 不能说，因为$p < x$,所以理论正确。应该说，因为$p < x$,所以结果符合预期。

## Hwo to calculate pValue?

• 假设：硬币是公平的
• 检验：认为假设是成立的，然后扔十次，看结果与假设是否相符

## 什么是显著水平$\alpha$?

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