• 相关系数的显著性检验包括两种情况：

1. 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；
2. 比较两个样本相关系数r₁和r₂,推论它们所属的总体ρ₁和ρ₂是否有差异。

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

1. Compare the sample correlation coefficient r and the population correlation coefficient ρ to infer whether the population is correlated;
2. Compare the sample correlation coefficient r₁ and another sample correlation coefficient r₂ to infer whether the populations ρ₁ and ρ₂ to which they belong are different.

• 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: H₀: ρ=0，H₁: 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：H₀: ρ≥(≤)0，H₁: 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: H₀: ρ=0，H₁: 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: H₀: ρ≥(≤)0，H₁: ρ<(>)0

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

1. 根据r值查Pearson相关临界值表(Check Pearson correlation critical value table according to r value)；
2. 计算出t值，查t值临界值表，t值的计算方法如下：

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).