# Experimental Design

#### ZS0020

##### New Member
Hi everyone

I am trying to figure out the best possible way to design an experiment I am interested in. I want to investigate the effect of three factors (A,B,C) and A has 3-levels, B has 2-level and C has 2-level and we will have 2 runs. I want to investigate these factors before a treatment and after a treatment. The treatment is the factor C.

What do you think of my suggestion. Would it give robust and reliable results?

Thanks!

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#### Karabiner

##### TS Contributor
Could you please describe the topic and reserach questions, the study design; the variables included, and their measuerement; and the sample size which you expect?

With kind regards

Karabiner

#### ZS0020

##### New Member
Could you please describe the topic and reserach questions, the study design; the variables included, and their measuerement; and the sample size which you expect?

With kind regards

Karabiner
I want to investigate if some of these factors (A,B,C) can optimize the warming process in terms of time and nutritional content of some food when using different material of a container A (material1, material2, material3), different thickness of container B (thickness1, thickness2) and different machines to heat the container C (machine1, machine2) on the food inside the container in terms of time and nutritional content. Therefor I will measure the time and nutritional content before the heating process and after the heating process and want to perform 2 runs for each.

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#### Karabiner

##### TS Contributor
If I understand your design correctely, then you could consider a mixed analysis
of variance, with 2 repeated-measures factors (pre/post and runs 1/2) and
3 between-subjects factors (material, machine, and thickness).

With kind regards

Karabiner

#### ZS0020

##### New Member
If I understand your design correctely, then you could consider a mixed analysis
of variance, with 2 repeated-measures factors (pre/post and runs 1/2) and
3 between-subjects factors (material, machine, and thickness).

With kind regards

Karabiner
I want to investigate the effect of material 1 on all levels of thickness and machine before the treatment and after and the same for material 2 and material 3. So it is only the material that change, but the other factors will be inside each level of material and this will be repeated 2 times (post and pre). So I was therefor wondering how the two other factors could be between subject factors?

#### Karabiner

##### TS Contributor
The table from you initial post describes a full factorial 3 (material) * 2 (machine) * 2 (thickness) * 2 (run) design, consequently there are 24 groups. In addition, you have a pre-post measure (repeated measures factor). The pre-post * material interaction from the mixed ANOVA would tell you whether the preservation was different for the 3 materials, across all levels of the other factors (as long as there are no higher order interactions present).

With kind regards

Karabiner

#### ZS0020

##### New Member
The table from you initial post describes a full factorial 3 (material) * 2 (machine) * 2 (thickness) * 2 (run) design, consequently there are 24 groups. In addition, you have a pre-post measure (repeated measures factor). The pre-post * material interaction from the mixed ANOVA would tell you whether the preservation was different for the 3 materials, across all levels of the other factors (as long as there are no higher order interactions present).

With kind regards

Karabiner
That make sense! Thank you.

I have another question

I choose that the factor A is fixed as the material will origin from only 3 different composition (A1,A2,A3), B will also be fixed as I will only investigate three thicknesses of each material and also the machine will be fixed. However, the food that I choose to test will be random as I know that the composition of the food will vary in terms of nutrients, but I will not choose specific food in terms of its nutritional content; this will give me more representative samples.

Do I understand the definition fixed and random effect correct?
Does it make sense to obtain a representative sample in the way I do it? And how can I decide the number of food samples I would need to not violate the representation if I would work with 24 groups?

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#### Karabiner

##### TS Contributor
I am not completely sure what your question is, but depending on how large your groups will
be, it could make sense to perform block randomization. I.e. if your groups are small,
there's is a risk that by chance some food items are clustered in certain groups which
react much more/react much less than ususal. Block randomization can decrease such
a risk. Regarding group size, I have no idea what is practically possible to achieve in
the context of your study. As a rule of thump, n=8 is often considered as absolute
minimum, but the more the better.

With kind regards

Karabiner

#### ZS0020

##### New Member
I am not completely sure what your question is, but depending on how large your groups will
be, it could make sense to perform block randomization. I.e. if your groups are small,
there's is a risk that by chance some food items are clustered in certain groups which
react much more/react much less than ususal. Block randomization can decrease such
a risk. Regarding group size, I have no idea what is practically possible to achieve in
the context of your study. As a rule of thump, n=8 is often considered as absolute
minimum, but the more the better.

With kind regards

Karabiner
I only have n= 2 in this design so I should actually consider increasing it?

#### Karabiner

##### TS Contributor
At least you won't be able to perform meaningful statistical tests of
significance, as far as I can see. So "run" is not a factor, but indicates
that one item is used for the experiment? I am not familiar with your field
of research, maybe there are special procedures for such experiments.

With kind regards

Karabiner