==== Pearson相关的显著性检验 (Significance test of Pearson correlation)====
  * 相关系数的显著性检验包括两种情况：

  - 比较样本相关系数r和总体相关系数ρ，推论总体间是否相关；
  - 比较两个样本相关系数r<sub>1</sub>和r<sub>2</sub>,推论它们所属的总体ρ<sub>1</sub>和ρ<sub>2</sub>是否有差异。

  * The significance test of the correlation coefficient includes two cases:

  - Compare the sample correlation coefficient r and the population correlation coefficient ρ to infer whether the population is correlated;
  - Compare the sample correlation coefficient r<sub>1</sub> and another sample correlation coefficient r<sub>2</sub> to infer whether the populations ρ<sub>1</sub> and ρ<sub>2</sub> to which they belong are different.

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  * 当对相关方向没有预测时，，我们使用双尾检验，虚无假设和备择假设为: H<sub>0</sub>: ρ=0，H<sub>1</sub>: ρ≠0;

  * 当对相关方向有预测时，我们使用单尾检验，虚无假设和备择假设为：H<sub>0</sub>: ρ≥(≤)0，H<sub>1</sub>: ρ<(>)0。

  * When there is no prediction of the relevant direction, we use the two-tailed test, the null hypothesis and the alternative hypothesis are: H<sub>0</sub>: ρ=0，H<sub>1</sub>: ρ≠0;

  * When there is a prediction of the relevant direction, we use the one-tailed test, the null hypothesis and the alternative hypothesis are: H<sub>0</sub>: ρ≥(≤)0，H<sub>1</sub>: ρ<(>)0

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  * 两种进行假设检验的方法(Two methods of hypothesis testing)：

  - 根据r值查Pearson相关临界值表(Check Pearson correlation critical value table according to r value)；
  - 计算出t值，查t值临界值表，t值的计算方法如下：
{{ ::t值计算.jpg?nolink&200 |}}
Calculate the t value, check the t value critical value table, the calculation method of t value is as above.


需注意的是查表时的自由度为(n-2)。

Notice: The degree of freedom when looking up the table is (n-2).
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