These data are from a 2x4 factorial design but the same data can also be used for one-way ANOVA examples. The variable y is the dependent variable. The variable a is an independent variable with two levels while b is an independent variable with four levels.use http://www.ats.ucla.edu/stat/stata/faq/crf24
anova y b
Number of obs = 32 R-squared = 0.8259
Root MSE = 1.21008 Adj R-squared = 0.8072
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 194.50 3 64.8333333 44.28 0.0000
|
b | 194.50 3 64.8333333 44.28 0.0000
|
Residual | 41.00 28 1.46428571
-----------+----------------------------------------------------
Total | 235.50 31 7.59677419
table b, contents(mean y)
----------+-----------
b | mean(y)
----------+-----------
1 | 2.75
2 | 3.5
3 | 6.25
4 | 9
----------+-----------
It is quite clear that there is a significant overall F for the
independent variable b. Now, let's devise some contrasts that we can test:anovacontrast b, values(0 0 1 -1) Contrast variable b (0 0 1 -1) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 20.66 contrast | 30.25 1 30.2500 Prob > F = 0.0001 error | 41 28 1.4643 ---------+--------------------------------- anovacontrast b, values(1 1 -1 -1) Contrast variable b (1 1 -1 -1) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 110.63 contrast | 162 1 162.0000 Prob > F = 0.0000 error | 41 28 1.4643 ---------+--------------------------------- anovacontrast b, values(1 1 1 -3) Contrast variable b (1 1 1 -3) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 95.72 contrast | 140.166667 1 140.1667 Prob > F = 0.0000 error | 41 28 1.4643 ---------+---------------------------------
anova y a b a*b
Number of obs = 32 R-squared = 0.9214
Root MSE = .877971 Adj R-squared = 0.8985
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 217.00 7 31.00 40.22 0.0000
|
a | 3.125 1 3.125 4.05 0.0554
b | 194.50 3 64.8333333 84.11 0.0000
a*b | 19.375 3 6.45833333 8.38 0.0006
|
Residual | 18.50 24 .770833333
-----------+----------------------------------------------------
Total | 235.50 31 7.59677419
anovacontrast b, values(0 0 1 -1)
Contrast variable b (0 0 1 -1) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 39.24
contrast | 30.25 1 30.2500 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
anovacontrast b, values(1 1 -1 -1)
Contrast variable b (1 1 -1 -1) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 210.16
contrast | 162 1 162.0000 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
anovacontrast b, values(1 1 1 -3)
Contrast variable b (1 1 1 -3) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 181.84
contrast | 140.166667 1 140.1667 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
Note that the F-ratios in these contrasts are larger than the F-ratios in the one-way ANOVA example. This is
because the two-way ANOVA has a smaller mean square residual than the one-way ANOVA.
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