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manova1

One-way multivariate analysis of variance

Syntax

d = manova1(X,group)
d = manova1（x，group，alpha）
[d,p] = manova1(...)
[d,p,stats] = manova1(...)

描述

d = manova1(X,group)进行单向多变量分析（MANOVA），以比较列的多元均值X, grouped by团体。Xis anm-经过-n数据值的矩阵，每一行都是测量的向量nvariables for a single observation.团体is a grouping variable defined as a categorical variable, vector, character array, string array, or cell array of character vectors. Two observations are in the same group if they have the same value in the团体大批。每个组中的观察结果代表来自人群的样本。

功能返回d, an estimate of the dimension of the space containing the group means.manova1测试每个组的平均值相同的零假设n- 维数载体，并且在样品中观察到的任何差异Xis due to random chance. Ifd=0，没有证据可以拒绝这一假设。如果d=1, then you can reject the null hypothesis at the 5% level, but you cannot reject the hypothesis that the multivariate means lie on the same line. Similarly, ifd=2多元均值可能位于同一平面上n-dimensional space, but not on the same line.

d = manova1（x，group，alpha）gives control of the significance level,alpha。The return valued将是最小的维度p>alpha, wherepis ap-value for testing whether the means lie in a space of that dimension.

[d,p] = manova1(...)也返回ap，一个向量p-values for testing whether the means lie in a space of dimension 0, 1, and so on. The largest possible dimension is either the dimension of the space, or one less than the number of groups. There is one element ofpfor each dimension up to, but not including, the largest.

如果theithp- 价值接近零，这对群体的含义躺在一个空间中的假设产生了怀疑i-1维度。批判的选择p-value to determine whether the result is judged statistically significant is left to the researcher and is specified by the value of the input argumentalpha。如果p-value is less than 0.05 or 0.01.

[d,p,stats] = manova1(...)also returnsstats，一种包含其他MANOVA结果的结构。该结构包含以下字段。

Field Contents
W

集体内和跨产品矩阵的总和下载188bet金宝搏
B

集体间和跨产品矩阵的总和下载188bet金宝搏
T

Total sum of squares and cross-products matrix
dfW

Degrees of freedom forW
足协

Degrees of freedom forB
dfT

Degrees of freedom forT
lambda

Vector of values of Wilks' lambda test statistic for testing whether the means have dimension 0, 1, etc.
chisq

Transformation oflambdato an approximate chi-square distribution
chisqdf

Degrees of freedom forchisq
eigenval

Eigenvalues ofW-1B
eigenvec

Eigenvectors ofW-1B; these are the coefficients for the canonical variablesC, and they are scaled so the within-group variance of the canonical variables is 1
canon

Canonical variablesC， 等于xc*eigenvec, whereXCisX通过减去手段以中心的列
MDIST

从每个点到其组平均值的Mahalanobis距离向量
gmdist

A matrix of Mahalanobis distances between each pair of group means

The canonical variablesCare linear combinations of the original variables, chosen to maximize the separation between groups. Specifically,C(:,1)是线性的组合Xcolumns that has the maximum separation between groups. This means that among all possible linear combinations, it is the one with the most significantF单向方差分析中的统计量。C(:,2)has the maximum separation subject to it being orthogonal toC(:,1), and so on.

You may find it useful to use the outputs frommanova1along with other functions to supplement your analysis. For example, you may want to start with a grouped scatter plot matrix of the original variables usinggplotmatrix。您可以使用GSCATTER使用前两个规范变量可视化组分离。您可以使用manovacluster绘制一个模拟图，显示组平均值之间的簇。

Assumptions

The MANOVA test makes the following assumptions about the data inX:

  • The populations for each group are normally distributed.

  • The variance-covariance matrix is the same for each population.

  • All observations are mutually independent.

Examples

you can usemanova1to determine whether there are differences in the averages of four car characteristics, among groups defined by the country where the cars were made.

负载Carbig [D，P] = Manova1（[MPG加速度位移]，...原点）d = 3 P = 0 0.0000 0.0000 0.0075 0.1934

There are four dimensions in the input matrix, so the group means must lie in a four-dimensional space.manova1表明您不能拒绝3D子空间中的手段的假设。

参考

[1] Krzanowski，W。J.多变量分析的原则:用户的Perspective。New York: Oxford University Press, 1988.

Version History

在R2006a之前引入

See Also

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