**Link**: Statistical test

## Hypothesiss testing

Below chart illustrate the recover time of drug A and drug B. What hypothesis we could draw from below chart?

People taking drug A need 15 more hours on average to recover than who taking drug B.

However, if we repeat the experiment many times and get opposite result, we can confidently **reject** this hypothesis.

If we have data that is similar to the hypothesis but not exactly the same, then we say it’s **fail to reject the hypothesis**.

## Null hypothesis

The hypothesis that there is **no difference** between things is called **Null hypothesis**.

With null hypothesis, we don’t need lots of preliminary data to make such statement because details are not needed in this hypothesis.

Example of default and balance: meaning p of default is not related to the variable balance.

In this case:

- Z-value > 2, meaning it statistically significant from 0, so rejects $H_{0}$
- P-value < 0.05, confirmed its significanty (used as evidence to reject $H_{0}$)

Abstract

Null hypothesis can be anything, it’s just a term to describe an outcome. It’s usually related to “whether it happened/not happened” because it’s easier to calculate the p-value for testing hypothesis.

### Null hypothesis and alternative hypothesis

Null hypothesis and Alternative hypotheses are paired. It can be think of they are two different distribution, and our goal is to **pick the best distribution** from the two.

No matter whether it’s linear/logistic/normal distribution, we can think of this way. In **null hypothesis**, the $β_{0}$ parameter is 0, representing one kind of distribution. While it’s equal to others, it represents other forms of distribution.