==== 二因素方差分析过程 Two-factor ANOVA procedure ====

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=== 1、陈述假设stated hypothesis ===
二因素方差分析的假设有三：

Three assumptions were made for the two-factor ANOVA:

  - 因素A的主效应(Main effect of factor A)：虚无假设(null hypothesis)为H<sub>0</sub>: μ<sub>A1</sub>=μ<sub>A2</sub>=...
  - 因素B的主效应(Main effect of factor B)：虚无假设(null hypothesis)为H<sub>0</sub>: μ<sub>B1</sub>=μ<sub>B2</sub>=...
  - 因素A和因素B的交互作用:交互作用的虚无假设通常用文字来表示，即因素A(B)对因变量的影响不因因素B(A)的变化而变化。
    * Interaction of factor A and factor B:The null hypothesis for the interaction is usually stated in words, i.e., the effect of factor A(B) on the dependent variable does not change as a result of changes in factor B(A).


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=== 2、计算相关统计量 Calculation of relevant statistics ===
  * 自由度的计算  Calculation of degrees of freedom{{ ::自由度1.jpg?nolink&300 |}}
{{ ::自由度2.jpg?nolink&300 |}}
{{ ::自由度3.jpg?nolink&300 |}}
  * 根据公式计算所需的统计量  Calculation of the required statistic according to the formula
{{ ::ss1.jpg?nolink&200 |}}
{{ ::ss2.jpg?nolink&400 |}}
{{ :ss3.jpg?nolink&400 |}}
  * 确定显著性水平α  Determination of the significance level α
  * 确定临界F值  Determination of critical F-value
//这里临界F值有三个，分别是F<sub>critA</sub>、F<sub>critB</sub>、F<sub>critA×B</sub>。//
   
//Here the critical F-values are three, which areF<sub>critA</sub>、F<sub>critB</sub>、F<sub>critA×B</sub>.//
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=== 3、计算F统计量 Calculating the F-statistic ===
  * 根据前面算出的各个值作出如下所示的方差分析表  The ANOVA table shown below was made based on the individual values calculated earlier:
{{ ::方差分析表2_2_.jpg?nolink&400 |}}

  * 画出交互作用图  Draw the interaction diagram

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=== 4、得出检验结论 Drawing test conclusions ===
根据算出的各个F值与相应F临界值的比较结果决定是否接受虚无假设。

The decision to accept the null hypothesis is based on the results of the comparison of the calculated individual F values with the corresponding F critical values.

注意当因素之间的交互效应显著时要进行简单主效应分析，即确定一个因素水平，对另一因素的不同水平作单因素ANOVA。

Note that when the interaction effect between factors is significant a simple main effects analysis is performed, i.e., a factor level is determined and a one-factor ANOVA is done for a different level of another factor.