PsychStatsWiki

二因素方差分析的假设有三：

Three assumptions were made for the two-factor ANOVA:

1. 因素A的主效应(Main effect of factor A)：虚无假设(null hypothesis)为H₀: μ_A1=μ_A2=…
2. 因素B的主效应(Main effect of factor B)：虚无假设(null hypothesis)为H₀: μ_B1=μ_B2=…
3. 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).

• 自由度的计算 Calculation of degrees of freedom

• 根据公式计算所需的统计量 Calculation of the required statistic according to the formula

• 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_critA、F_critB、F_critA×B。

Here the critical F-values are three, which areF_critA、F_critB、F_critA×B.

• 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:

• 画出交互作用图 Draw the interaction diagram

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.