# What statistical model to be used?

#### Abubakar sufyan

##### New Member
Anybody guide me ..... I am stuck in Factorial design ...

For my experiment, I ve wheat straw to feed dairy cows. Before feeding I need to process it in two way to improve its nutritional value. Firstly I need to sterilize it (I want to apply 4 methods to sterilization) and then addition of good bacteria (I want to inoculate the sterilized straw with 3 types of bacteria). So, in my understanding, my study has two factors; 1. sterilization method (with 4 levels) and 2) type of bacteria (with 3 levels). These will become 4x3 = 12 treatments with 3 replicates each. I want to compare the effect of these 12 treatments against the plain straw as Control (without sterilization and without addition of bacteria). This Control group actually, is not the part of 4x3 factorial. I am confused here ...

Kindly guide me what design and model be applied.

#### GretaGarbo

##### Human
Kindly guide me what design and model be applied.
You have just described your design. In addition you need to randomize the straws to the 12 treatment and run them in random order.

But are you ready to do the main experiment? Remember Box Hunter Hunters advice to not spend more that 25% of your research budget on a preliminary experiment. Sometimes "things happen" and it turns your experiment to a preliminary one.

Have you done a power calculation or is the 3 replicates just based on convention?

Since all treatment will be compared to the control, it is good to take more samples in the control. Take sqrt(12) so about 3.5 more samples in the control than in the treatments, so about 10 samples in the control while 3 samples in the treatments.

What is your response variable? Will it be normally distributed?

#### j58

##### Active Member
Your contol condition seems to be of limited usefulness, because all you can do with it is compare specific sterilization–inoculation treatment conbinations to it. It seems to me that you should either eliminate the "control," so that you have a real 4x3 factorial design, or change the design to either a 5x4, 4x4, or 4x3 factorial by including a 0-level of inoccuation at each level of sterilzation, a 0-level of sterilization at each level of inocculation, or both.

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#### Abubakar sufyan

##### New Member
You have just described your design. In addition you need to randomize the straws to the 12 treatment and run them in random order.

But are you ready to do the main experiment? Remember Box Hunter Hunters advice to not spend more that 25% of your research budget on a preliminary experiment. Sometimes "things happen" and it turns your experiment to a preliminary one.

Have you done a power calculation or is the 3 replicates just based on convention?

Since all treatment will be compared to the control, it is good to take more samples in the control. Take sqrt(12) so about 3.5 more samples in the control than in the treatments, so about 10 samples in the control while 3 samples in the treatments.

What is your response variable? Will it be normally distributed?
Thank you for your kind and prompt reply. I got your advice. Response variable is Protein contents in wheat straw which is supposed to increase after bacterial inoculation.

#### Abubakar sufyan

##### New Member
Your contol condition seems to be of limited usefulness, because all you can do with it is compare specific sterilization–inoculation treatment conbinations to it. It seems to me that you should either eliminate the "control," so that you have a real 4x3 factorial design, or change the design to either a 5x4, 4x4, or 4x3 factorial by including a 0-level of inoccuation at each level of sterilzation, a 0-level of sterilization at each level of inocculation, or both.
You really got my point. Thank you very much for understanding. As per your suggestion, I intend to go with 4x4. For detail and further guidance plz see the attachment, please. I will be really grateful for your kind courtesy.

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#### j58

##### Active Member
The design you present in the pdf is a full 4x4 factorial. If you eliminate the no-inoculation condition as you propose, you will not be able to ascertain the effects of inoculation versus no inoculation. If those comparisons are not of interest, it is fine to eliminate the no-inoculation condition. You will then have a full 4x3 factorial, which would be analyzed the same way as a 4x4 factorial, only a little simpler, because there wil be fewer comparisons to make. Make sense?

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#### GretaGarbo

##### Human
I would suggest that you combine your bacteria. It is more interesting to see the combined effekt of two or three bacteria.

Let your bacteria be f= florida, e= eryngii, o=osteatus. 0 is without the bacteria and 1 is with the bacteria.
Like this:

f e o
0 0 0
1 0 0
0 1 0
1 1 0
0 0 1
1 0 1
0 1 1
1 1 1

Each row is one experimental run. Now it is a factorial design. There is one combination completely without bacteria and there is one with all combinations and so on. You can estimate main effects and interaction effect. Much better!

This part is 8 runs.

Let s1 be one factor and s2 another factor. You can express your four sterilization levels with four combinations of s1 and s2.

Like this

s1 s2 name
0 0 water
1 0 steam
0 1 lime
1 1fumigation

With the previous 8 runs time the 4 runs of s1 and s2 would make 8*4 = 32. But you don't have to run a full factorial. You can run a fractional factorial, just half of the 32 combination, ie 16 runs.

Like this:

f e o s1 s2
0 0 0 0 1
1 0 0 0 0
0 1 0 0 0
1 1 0 0 1
0 0 1 0 0
1 0 1 0 1
0 1 1 0 1
1 1 1 0 0
0 0 0 1 0
1 0 0 1 1
0 1 0 1 1
1 1 0 1 0
0 0 1 1 1
1 0 1 1 0
0 1 1 1 0
1 1 1 1 1

Randomize the raw material to the 16 runs and run them in random order.

Again, you can estimate the main effects and many interaction effects. Much better.

#### Abubakar sufyan

##### New Member
The design you present in the pdf is a full 4x4 factorial. If you eliminate the no-inoculation condition as you propose, you will not be able to ascertain the effects of inoculation versus no inoculation. If those comparisons are not of interest, it is fine to eliminate the no-inoculation condition. You will then have a full 4x3 factorial, which would be analyzed the same way as a 4x4 factorial, only a little simpler, because there wil be fewer comparisons to make. Make sense?
Once again Thank you very much. I want to keep just one no-inoculation with cold water method (in treatment no. 1 as Control). With other three methods of sterilization there is no use of no-inoculation. So is that OK if I omit three treatments of my will from the design ?? If it is feasible then guide me is that 4x3 or 4x4. Thank you

#### GretaGarbo

##### Human
So is that OK if I omit three treatments of my will from the design ?? If it is feasible then guide me is that 4x3 or 4x4.
What design were you thinking of here?