加载中…问题9、如何用SPSS作方差分析比较？（转）
(2010-12-11 10:23:41)
标签：
方差自变量因素显著性分析 |
分类： 统计 |
问题9、如何用SPSS作方差分析比较？
我们的实例是Kirk (1968, 第一版)的数据库crf24。
get file 'd:\crf24.sav'.
这些数据来源于2因素4水平的析因设计，不过仍可以作为单因素方差分析的实例。变量y是因变量。变量a是2水平的自变量，b是4水平的自变量。
用单因素方差分析的比较命令
glm y by b.
|
Between-Subjects Factors |
||
|
|
N |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
194.500(a) |
3 |
64.833 |
44.276 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
631.366 |
.000 |
|
B |
194.500 |
3 |
64.833 |
44.276 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .826 (Adjusted R Squared = .807) |
|||||
means tables = y by b
/ cells mean.
|
Case Processing Summary |
||||||
|
|
Cases |
|||||
|
Included |
Excluded |
Total |
||||
|
N |
Percent |
N |
Percent |
N |
Percent |
|
|
Y * B |
32 |
100.0% |
0 |
.0% |
32 |
100.0% |
|
Report |
|
|
B |
Y |
|
1 |
2.75 |
|
2 |
3.50 |
|
3 |
6.25 |
|
4 |
9.00 |
|
Total |
5.38 |
显而易见，自变量b的全部F检验都有显著性。现在，设计一些能够进行检验的比较：
（1）第3组与第4组比较
（2）第1，2组的均数与第3，4组的均数比较
（3）第1，2，3组的均数与第4组比较
glm y by b /contrast(b)=special (0 0 1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
194.500(a) |
3 |
64.833 |
44.276 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
631.366 |
.000 |
|
B |
194.500 |
3 |
64.833 |
44.276 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .826 (Adjusted R Squared = .807) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.605 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.989 |
|
|
Upper Bound |
-1.511 |
||
Test Results Dependent Variable: Y |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
30.250 |
1 |
30.250 |
20.659 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
glm y by b /contrast(b)=special (1 1 -1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
194.500(a) |
3 |
64.833 |
44.276 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
631.366 |
.000 |
|
B |
194.500 |
3 |
64.833 |
44.276 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .826 (Adjusted R Squared = .807) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-9.000 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-9.000 |
||
|
Std. Error |
.856 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-10.753 |
|
|
Upper Bound |
-7.247 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
162.000 |
1 |
162.000 |
110.634 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
glm y by b /contrast(b)=special (1 1 1 -3).
|
Between-Subjects Factors |
||
|
|
N |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
194.500(a) |
3 |
64.833 |
44.276 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
631.366 |
.000 |
|
B |
194.500 |
3 |
64.833 |
44.276 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .826 (Adjusted R Squared = .807) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-14.500 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-14.500 |
||
|
Std. Error |
1.482 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-17.536 |
|
|
Upper Bound |
-11.464 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
140.167 |
1 |
140.167 |
95.724 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
注意到可对每一因素作多重比较，如下所示。每次比较必须用逗号隔开。当每次检验的差异有显著性时，便不输出t值。若想获得t值，就不得不在比较结果表（K 矩阵）中按标准误将比较的估计值分开。
glm y by b ?/contrast(b)=special (0 0 1 -1, 1 1 -1 -1,? 1 1 1 -3).
Between-Subjects Factors |
||
|
|
N |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
194.500(a) |
3 |
64.833 |
44.276 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
631.366 |
.000 |
|
B |
194.500 |
3 |
64.833 |
44.276 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .826 (Adjusted R Squared = .807) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.605 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.989 |
|
|
Upper Bound |
-1.511 |
||
|
L2 |
Contrast Estimate |
-9.000 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-9.000 |
||
|
Std. Error |
.856 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-10.753 |
|
|
Upper Bound |
-7.247 |
||
|
L3 |
Contrast Estimate |
-14.500 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-14.500 |
||
|
Std. Error |
1.482 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-17.536 |
|
|
Upper Bound |
-11.464 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
192.250 |
2 |
96.125 |
65.646 |
.000 |
|
Error |
41.000 |
28 |
1.464 |
|
|
用双因素方差分析的比较命令： 我们用双因素方差分析对变量b作同样的比较。
glm y by a b.
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
glm y by a b /contrast(b)=special (0 0 1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
30.250 |
1 |
30.250 |
39.243 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
glm y by a b /contrast(b)=special (1 1 -1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-9.000 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-9.000 |
||
|
Std. Error |
.621 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-10.281 |
|
|
Upper Bound |
-7.719 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
162.000 |
1 |
162.000 |
210.162 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
glm y by a b /contrast(b)=special (1 1 1 -3).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-14.500 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-14.500 |
||
|
Std. Error |
1.075 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-16.719 |
|
|
Upper Bound |
-12.281 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
140.167 |
1 |
140.167 |
181.838 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
注意到双因素方差分析的F值要比单因素方差分析的F值大。是因为均方残差变小的缘故。
SPSS有许多可用的内置比较方法，每一种都是仅有的（如上例)。下面给出带有解释的比较结果列表以及语句如何执行的实例。比较第1和第2组，第2和第3组，第3和第4组，见比较结果表（K矩阵）。
Name of contrast |
Comparison made |
|
Simple |
Compares each level of a variable to the last level (or whichever level is specified). |
|
Deviation |
Compares deviations from the grand mean. |
|
Difference |
Compares levels of a variable with the mean of the previous levels of the variable. |
|
Helmert |
Compare levels of a variable with the mean of the subsequent levels of the variable. |
|
Polynomial |
Orthogonal polynomial contrasts. |
|
Repeated |
Adjacent levels of a variable. |
|
Special |
User-defined contrast. |
glm y by a b /contrast(b)=repeated.
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Repeated Contrast |
Y |
||
|
Level 1 vs. Level 2 |
Contrast Estimate |
-.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.100 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-1.656 |
|
|
Upper Bound |
.156 |
||
|
Level 2 vs. Level 3 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Level 3 vs. Level 4 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
用双因素方差分析的比较命令： 我们用双因素方差分析对变量b作同样的比较。
glm y by a b.
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
glm y by a b /contrast(b)=special (0 0 1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
30.250 |
1 |
30.250 |
39.243 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
glm y by a b /contrast(b)=special (1 1 -1 -1).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-9.000 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-9.000 |
||
|
Std. Error |
.621 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-10.281 |
|
|
Upper Bound |
-7.719 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
162.000 |
1 |
162.000 |
210.162 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
glm y by a b /contrast(b)=special (1 1 1 -3).
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Special Contrast |
Y |
||
|
L1 |
Contrast Estimate |
-14.500 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-14.500 |
||
|
Std. Error |
1.075 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-16.719 |
|
|
Upper Bound |
-12.281 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
140.167 |
1 |
140.167 |
181.838 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
注意到双因素方差分析的 F值要比单因素方差分析的F值大。这是因为均方残差变小的缘故。
SPSS有许多可用的内置比较方法，每一种都是仅有的（如上例)。下面给出带有解释的比较结果列表以及语句如何执行的实例。比较第1和第2组，第2和第3组，第3和第4组，见比较结果表（K矩阵）。
Name of contrast |
Comparison made |
|
Simple |
Compares each level of a variable to the last level (or whichever level is specified). |
|
Deviation |
Compares deviations from the grand mean. |
|
Difference |
Compares levels of a variable with the mean of the previous levels of the variable. |
|
Helmert |
Compare levels of a variable with the mean of the subsequent levels of the variable. |
|
Polynomial |
Orthogonal polynomial contrasts. |
|
Repeated |
Adjacent levels of a variable. |
|
Special |
User-defined contrast. |
glm y by a b /contrast(b)=repeated.
|
Between-Subjects Factors |
||
|
|
N |
|
|
A |
1 |
16 |
|
2 |
16 |
|
|
B |
1 |
8 |
|
2 |
8 |
|
|
3 |
8 |
|
|
4 |
8 |
|
|
Tests of Between-Subjects
Effects |
|||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Corrected Model |
217.000(a) |
7 |
31.000 |
40.216 |
.000 |
|
Intercept |
924.500 |
1 |
924.500 |
1199.351 |
.000 |
|
A |
3.125 |
1 |
3.125 |
4.054 |
.055 |
|
B |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
A * B |
19.375 |
3 |
6.458 |
8.378 |
.001 |
|
Error |
18.500 |
24 |
.771 |
|
|
|
Total |
1160.000 |
32 |
|
|
|
|
Corrected Total |
235.500 |
31 |
|
|
|
|
a R Squared = .921 (Adjusted R Squared = .899) |
|||||
|
Contrast Results (K Matrix) |
|||
|
|
Dependent Variable |
||
|
B Repeated Contrast |
Y |
||
|
Level 1 vs. Level 2 |
Contrast Estimate |
-.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.100 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-1.656 |
|
|
Upper Bound |
.156 |
||
|
Level 2 vs. Level 3 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Level 3 vs. Level 4 |
Contrast Estimate |
-2.750 |
|
|
Hypothesized Value |
0 |
||
|
Difference (Estimate - Hypothesized) |
-2.750 |
||
|
Std. Error |
.439 |
||
|
Sig. |
.000 |
||
|
95% Confidence Interval for Difference |
Lower Bound |
-3.656 |
|
|
Upper Bound |
-1.844 |
||
|
Test Results |
|||||
|
Source |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Contrast |
194.500 |
3 |
64.833 |
84.108 |
.000 |
|
Error |
18.500 |
24 |
.771 |
|
|
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