卡方匹配度(拟合优度)检验（Chi-square match (goodness of fit) test）

• 卡方可以用来检验频率的观测分布和理论分布之间的拟合优度。

• 定义公式：统计量𝜒^2=Σ [(fo-fe)^2/fe]（观察次数fo，期望次数fe=pn），自由度df=C-1（C：类目的个数）。

• 检验局限：①对样本量敏感（样本量很大时会得到显著结果）；②不能确定因果关系。

• 卡方检验的效应量Cramer's V: V={𝜒^2/[n*min(c-1,r-1)]}^1/2

• 卡方检验的计算步骤：①提出假设；②根据虚无假设𝐻o，选择相应的统计模型；③确定显著性水平α（α确定后，否定域也随之确定）；④基于𝐻o所设定的统计模型，计算检验统计量的值；⑤做出决策。
• Chi-square match (goodness of fit) test

—- The chi square can be used to test the goodness of fit between the observed and theoretical distributions of frequency.

* Definition formula: statistic 𝜒^2=Σ [(FO-Fe)^2/fe] (observed number fo, expected number fe=pn), degrees of freedom df=C-1 (C: number of class objects).

* Test limitations : ① Sensitive to sample size (significant results can be obtained when sample size is large); The causal relationship cannot be determined.

* * * chi-square test the effect of Cramer 's V: V * * = {𝜒 ^ 2 / (n * min (r - c - 1, 1)]} ^ 1/2

* Calculation steps of Chi-square test: ① Put forward the hypothesis; ② According to the null hypothesis 𝐻o, select the corresponding statistical model; (3) The significance level α is determined (after α is determined, the negative domain is also determined); ④ The values of the test statistics are calculated based on the statistical model set by 𝐻o; ⑤ Make decisions.