很基础很基础的统计学 - 假设检验 T-test

在开始之前，我们先看看什么时候要用到T - test什么时候用Z：

当 σ known： 用Z

当σ unknown，n 小于等于 50，用t ；n大于50，用Z

再说说一些字母代表的含义

P-value

P-value: the probability of observing the statistic (or more extreme) given that the null hypothesis is true.

p-value是一个几率，这个几率是在说，当H0为真，我们发现这个事情的概率，所以P-value 值越低，我们的原假设H0就越荒谬。

Significance level α: 

a threshold probability (e.g. 0.05, or 0.1) that determines whether or not the evidence is overwhelming.

– Typically given

R方

R2 measures how well the regression line fits the data.

For example, R2= 0.90. 

This means that 90% of the variation in 因变量 is due to the variation in 自变量. 

The other 10% of the variation remains unexplained. (0 ≤ R2≤ 1)

R2 is one of several statistics that should be used in evaluating the quality of the regression model. 

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假设检验的步骤

计算confidence interval 用Z的情况：

假设检验：

Step 1. Formulate the hypothesis– Null Hypothesis (H0)

– Alternate Hypothesis (HA)

Step 2. Set the criteria for a decision

Step 3. Acquire an objective test statistic (e.g. from evidence)

Step 4. Does the objective test statistic represent overwhelming evidence against the Null Hypothesis? (i.e., p-value < α? or equivalently, compare the test statistic with the critical z-value or t-value)

– If yes, reject the null (H0) and accept the alternative (HA) as the truth.

– If no, accept the null (H0) as the truth.

总结：