fx911
用minitab作正交数据分析用到Stat→ANOVA→General Linear Model一般线性模型,结果是
X2 的方差分析,在检验中使用调整的 SS
来源 自由度 Seq SS Adj SS Adj MS F P
A 2 0.03582 0.03582 0.01791 9.54 0.095
B 2 0.03902 0.03902 0.01951 10.39 0.088
C 2 0.82149 0.82149 0.41074 218.74 0.005
误差 2 0.00376 0.00376 0.00188
合计 8 0.90009
S = 0.0433333 R-Sq = 99.58% R-Sq(调整) = 98.33%,
这其中seq ss和adj ss分别是连续平方和和校正平方和,具体这两者有什么区别?分别是用于什么场合?请大侠赐教,或者推荐一本教材。多谢了。
liuerbai
The sequential (sometimes called type I) sums of squares measure the reduction in the residual sums of squares provided by each additional term in the model. For example, if your model contains the terms A, B, and C (in that order), then the sequential sums of squares for B represents the reduction in the residual sum of squares that occurs when B is added to a model containing only A.
The adjusted (sometimes called type III) sums of squares measure the reduction in the residual sums of squares provided by each term relative to a model containing all the other terms. For example, if your model contains the terms A, B, and C (in that order), then the adjusted sums of squares for B represents the reduction in the residual sum of squares that occurs when B is added to a model containing both A and C.
The sequential and adjusted sums of squares are always the same for the last term in the model. For example, if your model contains the terms A, B, and C (in that order), then both sums of squares for C represent the reduction in the residual sum of squares that occurs when C is added to a model containing both A and B.
The sequential and adjusted sums of squares will be the same for all terms if the design matrix is orthogonal. The most common case where this occurs is with factorial and fractional factorial designs (with no covariates) when analyzed in coded units. In these designs, the columns in the design matrix for all main effects and interactions are orthogonal to each other. Plackett-Burman designs have orthogonal columns for main effects (usually the only terms in the model) but interactions terms, if any, may be partially confounded with other terms (i.e. not orthogonal). In response surface designs, the columns for squared terms are not orthogonal to each other.