ANOVA with Covariate = slope test

jacob_warren — Sat, 22 Oct 2011 15:02:05 GMT

I'm an applied statistics student trying to get help understanding some SAS output and how to correct a problem I'm having. This is based on a hw problem I'm answering, but I promise if you answer I promise this doesn't violate any academic dishonesty policy or anything, the hw is not graded I just need to turn it in, but I want to try and get it correct and understand it before I do. Anyhow...

This is based on based on Design and Analysis of Experiments by Angela Dean and Daniel Voss. In an example in that text they describe how an equality of slopes test can be run on a covariate using the code:

Proc GLM;

CLASS COLOR;

MODEL INFTIME=COLOR X COLOR*X;

RUN;

and the results:

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	7	273.2067301	39.0295329	5.97	0.0004
Error	24	157.0320199	6.5430008
Corrected Total	31	430.2387500

R-Square	Coeff Var	Root MSE	INFTIME Mean
0.635012	12.63565	2.557929	20.24375

Source	DF	Type I SS	Mean Square	F Value	Pr > F
COLOR	3	127.6612500	42.5537500	6.50	0.0022
X	1	120.8353249	120.8353249	18.47	0.0002
X*COLOR	3	24.7101552	8.2367184	1.26	0.3108

Source	DF	Type III SS	Mean Square	F Value	Pr > F
COLOR	3	119.5483312	39.8494437	6.09	0.0031
X	1	132.2254691	132.2254691	20.21	0.0001
X*COLOR	3	24.7101552	8.2367184	1.26	0.3108

and that

/*The interaction term X*COLOR will be significantly different from zero if the

linear run order trends are not the same for each TRTMT. (X is for run order)*/

Now, since the p-value for X*COLOR is 0.3108, the interpretation is that interaction is not significantly different from zero so the run order trends are the same for each TRTMT, meaning the equal slopes model can be used.

My main problem is that I'm trying to run this same test on a different data set but when I run the test I have no error df and thus I get no F or p-values. My code is:

Proc GLM;

class TRTMT;

model ABSORB=TRTMT RATE TRTMT*RATE;

run;

my results are:

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	11	0.38463976	0.03496725	.	.
Error	0	0.00000000	.
Corrected Total	11	0.38463976

R-Square	Coeff Var	Root MSE	ABSORB Mean
1.000000	.	.	0.466583

Source	DF	Type I SS	Mean Square	F Value	Pr > F
TRTMT	5	0.31614510	0.06322902	.	.
RATE	1	0.04055338	0.04055338	.	.
RATE*TRTMT	5	0.02794128	0.00558826	.	.

Source	DF	Type III SS	Mean Square	F Value	Pr > F
TRTMT	5	0.03317064	0.00663413	.	.
RATE	1	0.00221343	0.00221343	.	.
RATE*TRTMT	5	0.02794128	0.00558826	.	.

and then I can't make any conclusion. How do I adjust in order to have error df. My only thought is to also assign TRTMT as a covariate and then I get:

Proc GLM;

class ;

model ABSORB=TRTMT RATE TRTMT*RATE;

run;

and

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	0.17898819	0.05966273	2.32	0.1517
Error	8	0.20565157	0.02570645
Corrected Total	11	0.38463976

R-Square	Coeff Var	Root MSE	ABSORB Mean
0.465340	34.36306	0.160332	0.466583

Source	DF	Type I SS	Mean Square	F Value	Pr > F
TRTMT	1	0.00551384	0.00551384	0.21	0.6556
RATE	1	0.11543332	0.11543332	4.49	0.0669
TRTMT*RATE	1	0.05804103	0.05804103	2.26	0.1713

Source	DF	Type III SS	Mean Square	F Value	Pr > F
TRTMT	1	0.05991067	0.05991067	2.33	0.1654
RATE	1	0.11460643	0.11460643	4.46	0.0677
TRTMT*RATE	1	0.05804103	0.05804103	2.26	0.1713

Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	4.348758487	1.81291361	2.40	0.0433
TRTMT	-0.780015644	0.51094274	-1.53	0.1654
RATE	-1.915624580	0.90724987	-2.11	0.0677
TRTMT*RATE	0.385052917	0.25625591	1.50	0.1713

and I can interpret that again in this data set interaction is not significant and thus the equal slopes model would be correct to use. But, I don't think this is correct because TRTMT isn't supposed to be a covariate and by assigning it as such I think I'm completely changing the model.

Thanks for any help you can give!

ANOVA with Covariate = slope test

Reeza — Mon, 24 Oct 2011 16:40:34 GMT

TRT is a covariate in both models, but in the first it is treated as a categorical variable and in the second it is treated as a continuous variable.

Two things to check:

1) Run a proc freq of your data for trt*rate such as

proc freq data=have;

table trtmt*rate;

run;

2) a Proc means on the rate variable and see the output

proc means data=have;

class trtmt;

var rate;

run;

I'm guessing one of those will show what's wrong with your model.

ANOVA with Covariate = slope test

Doc_Duke — Mon, 24 Oct 2011 16:59:38 GMT

Jacob,

The problem here

Proc GLM;

class TRTMT;

model ABSORB=TRTMT RATE TRTMT*RATE;

run;

is that TRTMT has 6 levels and you only have twelve observations. Therefore your model is overparameterized to check for equality of slopes across all treatments. I would generally consider the first model to be overparameterized as well, just not so much as to be mathematically degenerate (You fail to reject the equal slopes assumption, but you have so little power that you really can't accept it either). Harrell, in his regression modelling strategies book, recommends at least 15 observations per degree of freedom tested in a linear model to have a chance to obtain stable results.

Doc Muhlbaier

Duke

ANOVA with Covariate = slope test

jacob_warren — Tue, 25 Oct 2011 16:40:06 GMT

Thank you, that was a very helpful explanation.

topic ANOVA with Covariate = slope test in Statistical Procedures

ANOVA with Covariate = slope test

ANOVA with Covariate = slope test

ANOVA with Covariate = slope test

ANOVA with Covariate = slope test