# Re: st: syntax for nested two-factor ANOVA

 From David Airey <[email protected]> To [email protected] Subject Re: st: syntax for nested two-factor ANOVA Date Mon, 10 Apr 2006 21:45:39 -0500

I admit remaining confused about the design and think I may have sent you down the wrong path. It is hard to suggest over the listserv, without much thought, and without seeing the data.

In looking at the data I see you have replication in the table cells, e.g., you have 4 cases for brand 7 and company 1 with a 0 keep status. This is making the repeated measures request fail (I think). I also see that you sometimes have a company with only one brand for sale, so there is no variance in those cases that is separate between company and brand.

Also I now imagine the experiment as you obtaining a continuous DV measure on each box of cereal that was sold or discarded, and that you have more than one box measured per brand, cereal combination.

/*

use http://www.ats.ucla.edu/stat/stata/examples/kirk/spf2-4, clear

// I remembered this example and made a suggestion, not really understanding what you were doing

anova y a / s|a b a*b /, repeated(b) // a is between subject, b is within subject, a and b are fixed, s is random

anova y a / s|a b / a*b /, repeated(b) // here, a is fixed, b and s are random

// both compute without issue and I think are correct when making the second factor b random

// looking at some of the data

list in 1/9

+----------------+
| a b s y |
|----------------|
1. | 1 1 1 3 |
2. | 1 2 1 4 |
3. | 1 3 1 7 |
4. | 1 4 1 7 |
|----------------|
5. | 1 1 2 6 |
6. | 1 2 2 5 |
7. | 1 3 2 8 |
8. | 1 4 2 8 |
|----------------|
9. | 1 1 3 3 |

// you see the explicit subject factor listed above
*/

(s) (a) (b) (y)
brand company keep testresult
1 1 1 .839
1 1 0 .605
2 1 1 .798
2 1 0 .567
3 2 1 .855
3 2 0 .650
etc etc etc etc

but you really have data like:

+------------------------------------+
| y keep brand company |
|------------------------------------|
1. | -.0800775 0 7 1 |
2. | .071272 0 7 1 |
3. | .1124799 0 7 1 |
4. | .3309362 0 7 1 |
5. | .0646274 1 7 1 |
6. | .1491636 1 7 1 |
7. | .3802552 1 7 1 |
8. | .3819582 1 7 1 |
9. | .4677568 1 7 1 |

which is really like:

+------------------------------------------+
| y keep brand company box |
|------------------------------------------|
1. | -.0800775 0 7 1 1 |
2. | .071272 0 7 1 2 |
3. | .1124799 0 7 1 3 |
4. | .3309362 0 7 1 4 |
5. | .0646274 1 7 1 5 |
6. | .1491636 1 7 1 6 |
7. | .3802552 1 7 1 7 |
8. | .3819582 1 7 1 8 |
9. | .4677568 1 7 1 9 |

where we have a three factor nested design, with brand nested in company and crossed with keep, and keep is between subjects.

Since you don't have brand separable from company for half your companies, why not simplify and just control for brand, in which case you have a two factor ANOVA with unequal replication with one of your factors a random (blocking) effect. Usually you don't interact that blocking effect, so:

anova y brand keep

gives the test to look at for keep:

. anova y brand keep

Number of obs = 89 R-squared = 0.3444
Root MSE = .199951 Adj R-squared = 0.2409

Source | Partial SS df MS F Prob > F
----------- +----------------------------------------------------
Model | 1.59643837 12 .133036531 3.33 0.0007
|
brand | .504996573 11 .045908779 1.15 0.3373
keep | .905309904 1 .905309904 22.64 0.0000
|
Residual | 3.03851904 76 .039980514
----------- +----------------------------------------------------
Total | 4.63495741 88 .052669971

In the case for a two factor ANOVA with one random factor, you might allow interactions (unlike the randomized block model above that assumes no interactions).

Say A is fixed and B is random, then the test for A is MSA/MSAB, for B is MSB/MSE, and for MSAB/MSE.

So you can try also, if you allow interactions,

quietly anova y brand keep / brand*keep /

Number of obs = 89 R-squared = 0.3971
Root MSE = .204223 Adj R-squared = 0.2081

Source | Partial SS df MS F Prob > F
----------- +----------------------------------------------------
Model | 1.84058059 21 .087646695 2.10 0.0116
|
brand | .361996382 11 .032908762 1.21 0.3921
keep | .595857339 1 .595857339 21.97 0.0011
brand*keep | .244142211 9 .027126912
----------- +----------------------------------------------------
brand*keep | .244142211 9 .027126912 0.65 0.7500
|
Residual | 2.79437683 67 .041707117
----------- +----------------------------------------------------
Total | 4.63495741 88 .052669971

-Dave

*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/