SPSS多元方差分析

SPSS数据统计分析与实践主讲：周涛副教授

北京师范大学资源学院

2007-11-6

教学网站：/Courses/SPSS

第九章多元方差分析

GLM Multivariate Analysis

多元方差分析－问题的提出

z T检验、单因素方差分析、多因素方差分析只针对一个因变量，而有时往往要对多个相关的因变量进行相关分析。

z例如：在评价素质教育的效果时，因变量包括语文成绩、数学成绩……。

z虽然有时可以对各个因变量单独进行方差分析（单因素或多因素），但这种处理存在如下的弊端：

多元方差分析－问题的提出

z虽然有时可以对各个因变量单独进行方差分析（单因素或多因素），但这种处理存在如下的弊端：

z检验效率低；

z犯第一类错误的概率增大；

z一元分析结果不一致时，难以下结论；

z忽略了变量间相关关系；

z有时多个观察指标的联合分布存在差异，但单独对每个指标进行统计学检验时却没有统计学意义；反之亦然。

多元方差分析－问题的提出

解决策略：

1.一种解决办法是：使用因子分析先对因变量

中蕴含的信息进行浓缩，然后对提取的公因子进行后续的一元方差分析；

2.另一种解决办法是：采用多元方差分析

（Multivariate Analysis Of Variance，

MANOVA）

多元方差分析对数据的要求

the GLM Multivariate procedure assumes:

z The values of errors are independent of each other across observations and the independent variables in the model. Good study design generally avoids violation of this assumption.

z The covariance (协方差) of dependent variables is constant across cells. This can be particularly important when there are unequal cell sizes; that is, different numbers of observations across factor-level combinations.

z Across the dependent variables, the errors have a multivariate normal distribution with a mean of 0.

SPSS GLM Multivariate Analysis

z The GLM Multivariate procedure provides analysis of variance for multiple dependent variables by one or more factor variables or covariates.

z The factor variables divide the population into groups.

z Using this general linear model procedure, you can test null hypotheses about the effects of factor variables on the means of various groupings of a joint distribution of dependent variables.

GLM Multivariate Analysis

z Both balanced and unbalanced models can be tested. A design is balanced if each cell in the model contains the same number of cases.

z In a multivariate model, the sums of squares due to the effects in the model and error sums of squares are in matrix form rather than the scalar form found in univariate analysis. These matrices are called SSCP(sums-of-squares and cross-products) matrices.

GLM Multivariate Analysis

z If more than one dependent variable is specified, the multivariate analysis of variance using Pillai's trace, Wilks' lambda, Hotelling's trace, and Roy's largest root criterion with approximate F statistic are provided as well as the univariate analysis of variance for each dependent variable.

四个统计量的含义：

z Pillai’s轨迹：恒为正数，值越大，表明该效应项对模型的贡献越大；

z Wilks’Lambda：取值范围在0～1之间，值越小，说明该效应项对模型的贡献越大；

z Hotelling轨迹：为检验矩阵特征根之和，值总比Pillai’s轨迹的值大。与Pillai’s轨迹相似，值越大贡献越大；

z Roy最大根统计量：为检验矩阵特征根中最大值，因此它总是小于或等于Hotelling轨迹。

当模型建立的前提条件不满足时，Pillai’s轨迹最为稳健。