Stata FAQ: How can I test for nonadditivity in a randomized block ANOVA in Stata?
Randomized block ANOVA models assume additive block and treatment effects, that is, that there is no treatment by block interaction. Tukey’s test for nonadditivity is a one degree of freedom test of the hypothesis that there is a linear treatment by linear block interaction. The nonadd command can be added to your Stata system by installing the nonadd.ado program written by ATS. You can download the nonadd command by typing search nonadd (see How can I use the search command to search for programs and get additional help? for more information about using search).
Now, let’s read in an example dataset, rb4a, which is adapted from Kirk (1982, 2nd Edition). This example has eight subjects with four repeated measures on each subject.
use https://stats.idre.ucla.edu/stat/stata/faq/rb4a, clear
Let’s look at a table of the data.
table s a, contents(mean y)
----------+-----------------------
| a
s | 1 2 3 4
----------+-----------------------
1 | 3 4 7 7
2 | 6 5 8 8
3 | 3 4 7 9
4 | 3 3 6 8
5 | 1 2 5 10
6 | 2 3 6 10
7 | 2 4 5 9
8 | 2 3 6 11
----------+-----------------------
Now let’s compute the randomized block ANOVA.
anova y a s
Number of obs = 32 R-squared = 0.8790
Root MSE = 1.16496 Adj R-squared = 0.8214
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 207.00 10 20.70 15.25 0.0000
|
a | 194.50 3 64.8333333 47.77 0.0000
s | 12.50 7 1.78571429 1.32 0.2914
|
Residual | 28.50 21 1.35714286
-----------+----------------------------------------------------
Total | 235.50 31 7.59677419
Next, we’ll do the test for nonadditivity. Note that the variables are entered the same way as for the randomized block analysis.
nonadd y a s Tukey's test of nonadditivity for randomized block designs F (1,20) = 7.8345468 Pr > F: .01108091
In this case the test for nonadditivity was statistically significant, the data are nonadditive.
Here is a second example, rb4b, this time from Kirk’s 3rd edition. Again, it has eight subjects with four repeated measures on each subject.
use https://stats.idre.ucla.edu/stat/stata/faq/rb4b, clear table s a, contents(mean y) ----------+----------------------- | a s | 1 2 3 4 ----------+----------------------- 1 | 3 4 4 3 2 | 2 4 4 5 3 | 2 3 3 6 4 | 3 3 3 5 5 | 1 2 4 7 6 | 3 3 6 6 7 | 4 4 5 10 8 | 6 5 5 8 ----------+-----------------------anova y a s Number of obs = 32 R-squared = 0.7318 Root MSE = 1.18523 Adj R-squared = 0.6041 Source | Partial SS df MS F Prob > F -----------+---------------------------------------------------- Model | 80.50 10 8.05 5.73 0.0004 | a | 49.00 3 16.3333333 11.63 0.0001 s | 31.50 7 4.50 3.20 0.0180 | Residual | 29.50 21 1.4047619 -----------+---------------------------------------------------- Total | 110.00 31 3.5483871 nonadd y a s Tukey's test of nonadditivity for randomized block designs F (1,20) = 1.2795813 Pr > F: .27135918
This time the test for nonadditivity was not significant, that is, there is no indication of a treatment by block interaction.
References:
- Kirk, R. (1982).Experimental Design: Procedures for the Behavioral Sciences. 2nd edition.
- Kirk, R. (1995).Experimental Design: Procedures for the Behavioral Sciences. 3rd edition.