You can create a new TRT variable that takes on the values 0 11 12 12 13 21 22 23 31 32 33 41 42 43 where 0 represents the Control and ij represents the ith row variable and the jth column variable. You can then use CONTRAST options to test various hypotheses.

PROC GLM;

CLASS TRT;

MODEL Y = TRT;

CONTRAST 'C VS REST' TRT 12 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1;

CONTRAST 'ROW MAIN EFFECT' TRT 0 1 1 1 -1 -1 -1 0 0 0 0 0 0,

TRT 0 1 1 1 0 0 0 -1 -1 -1 0 0 0, TRT 1 1 1 0 0 0 0 0 0 -1 -1 -1;

CONTRAST 'COL MAIN EFFECT' TRT 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0,

TRT 0 1 0 -1 1 0 -1 1 0 -1 1 0 -1;

CONTRAST 'ROW*COL INTERACTION' TRT 0 1 -1 0 -1 1 0 0 0 0 0 0 0, ETC.

YOU CAN ALSO USE VARIOUS ESTIMATE OPTIONS AND/OR CONTRAST OPTIONS TO TEST OTHER HYPOTHESES OF INTEREST.

The usual approach is treat the design as a one-way design, with 13 treatments, and then use post-hoc contrasts that would mimic the comparisons for Control vs. Treatment, across N treatments, N x time interaction, and so on.

This example gives you a start:

https://stats.oarc.ucla.edu/sas/faq/how-can-i-do-anova-contrasts/

Thank you very much all of you for the answers.

Dr Sal Mangaiafico sorry If I type your name wrongly! , I used RCBD for all the 13 treatments as you said.

My main objective is to evaluate the best combination of the factorial 4*3, and then compare them all to the control to suggest the most suitable alternative fertilization using.

Dr Dallas E.Johnson's Sorry if I spell your name wrongly.Thank you very much for your suggestion. I planned to do 2-way ANOVA for the factorial 4*3 to evaluate the main effects or interactions there, before one-way ANOVA for 13 treatments to compare the 12 with the control.Now I have copleted sowing and I have problem on anlysis.

I just wonder if only one-way ANOVA is enough as said by Dr Sal Mangaiafico .To help me more Iam happy if you allow me to communicate by email.Than I I will send you original arrangement on excel too.

My email: abdeta.alex [email protected] just for both of you Dr Dr Sal Mangaiafico and Dr Dallas E.Johnson's.

Thank you all very much.

It's not that the experiment is analyzed as a one-way design. It's that you feed it to SAS as if it were a one-way design, and then use the contrast statement to test e.g. each main effect, the interaction effect, all treatments vs. control, or whichever contrasts you want to test. You can include the block effect also in the model.

See also the example in the question here: https://www.researchgate.net/post/Is_this_how_to_analyse_a_2_X_3_factorial_plus_control_experiment .

I didn't look at it very carefully, so I'm not sure what the poster suggests is correct, but that should be a good starting point for you.

Thank you Dr Sal Mangiafico for you gave me direction. Example you gave me look similar with mine (https://www.researchgate.net/post/Is_this_how_to_analyse_a_2_X_3_factorial_plus_control_experiment). May be the difference is I will see Treated mean Vs Control mean . My data is 4 x 3 factorial plus control arrangement of treatments. The study investigated the effects of N rates and time of N application time to bread wheat. First I want to analyze the data as a factorial (omitting the control) and Second I want to to compare specific treatments (e.g., control Mean vs treated mean ( all treatments). Is am I correct?

Yes, but using contrasts, you don't need to omit the control, per se. The control just isn't included in the contrasts that test the main and interaction effects. (That is, it's 0 in the contrast). You can also compare any treatment to the control.

Unfortunately I don't have a good article that explains this. But this approach is common in agricultural experiments, and there should be good examples in SAS. You might look for "orthogonal contrasts".

For example, there is also the consideration that contrasts shouldn't "use up" all the degrees of freedom in the larger model. But there's nothing mathematically preventing this. (And I might argue that this is okay.)

WOW thank you very much Dr Sal Mangiafico for you gave me more explanation and am very happy to the way you said.Dr am more happy if I get you with email.Thank more!

Dr Sal Mangiafico,

To speak the truth Iam a beginner with the use of SAS specially Orthogonal contrast. Your contributions above has really helped me create a contrast command for my analysis and wish to seek your opinion on it. Will this be effective to interpret the results of my data???

My experiment involve the use of 4 N rates at 3 time of N application of inclusion plus a control.The responses are labeled as variables 1-39 as depicted in the SAS command I just prepared. I used Proc IML to get the coefficients for the polynomial effects of N-level. Here is what I have:

N-rates= 4

N-time of application =3

Control=1

Total treatments= 13

I am happy if you give my SAS command in my case.

Thanks in anticipation of your kind suggestions and advise

Dear Alemayehu,

It is so simple! You should NOT be supposed to run an analysis of variance with the control! You must run the ANOVA with the treatments that are factorial combined without the control treatment. But still, the control treatment is very important for various analyses. For example, what is the trend of productivity over the years and locations without any input? What are the net benefits of each treatment compared to the control etc?

Thank you dear My brother DrTadele! Dr Tade, I have already started my experiment. When I collected data and Come to analysis I faced with this problem. My major objective is to see Treated mean Vs Control mean . My data is 4 x 3 factorial plus control arrangement of treatments. The study investigated the effects of N rates and time of N application time to bread wheat. First I want to analyze the data as a factorial (omitting the control) and Second I want to to compare specific treatments (e.g., control Mean vs treated mean ( all treatments). Is am I correct? Other difficulty is am beginner of Orthogan contrset in SAS.Now if any Sytax for analsis please.Thank you for you help me more!

Dear Alemayehu,

I understand you very well and it is very common! We usually add (0,0) or control as a pilot treatment for the reason I mentioned earlier. You can call me at 0918766289 if there are any points I can help you with! For the midlands (Woina Dega) and highlands (Dega) of Ethiopia, we know that factorial combination of 0 N and 0 P is already not recommended as it needs high rates of these nutrients as you reasonably set your experiment!

For four nitrogen levels, the orthogonal polynomial contrasts are:

Linear -3 -1 1 3

Quadratic 1 -1 -1 1

Cubic -1 3 -3 1

For five levels which includes the 0 control, the orthogonal polynomial contrasts are:

Linear -2 -1 0 1 2

Quadratic 2 -1 -2 -1 2

Cubic -1 2 0 -2 1

Quartic 1 -4 6 -4 1

You should be able to find coefficients for other levels of treatment factors by googling "Orthogonal Polynomials"

Thank you All!

Dr Dallas E.Johnason thank for you Advice me more!

Dr Tadele thank you for your openness! I will call you and I hope as I get more information from me.Thank very much.