# how to analyze data with 3 samples with factorial experimental design

#### alibina1997

##### New Member
I am trying to analyze data for my thesis so a factorial experimental design has been suggested. The problem is I have done the collecting data process before designing such an experiment. I have just 3 samples with 6 factors (velocity, time, depth, humidity of soil, humidity of environment) and one response value (efficiency). I am a bit confused about how to analyze these datasets. Should I run the experiment again or is there a solution?

#### GretaGarbo

##### Human
(velocity, time, depth, humidity of soil, humidity of environment)
I can only see five factors in there.

Does this mean that you have high and low on each factor and that you in total have 2*2*2*2*2 =32 experimental conditions?
(If you had only velocity and time you would have 2*2 = 4 experimental conditions.)

Does it also means that for each experimental condition you have run the experiment 3 times, så that you have 32*3 = 96 experimental runs?

If you write an example of a few lines it will be much easier to understand.

Did you randomize the experiment?

#### fed2

##### Active Member
try using a bayesian sampler to estimate the factorial hyper parameters.

#### alibina1997

##### New Member
thank you for your response, as I mentioned above l have 6 variable ( time, depth, environment temp, soil temp, velocity, efficiency) I decided to assign 5 variable as independent variable and "efficiency" as dependent variable without considering which one of the independent variables is control variable or covariance . Each of the Theses factors have 3 different values. Before I design factorial experiment l have been collected data. Now I should considering analyzing data with factorial، I think I should have 3^5 data but I have just 3 also no replication. I will be appropriate for your advice whether this consideration is true or not? And is it possible to analyze this data with factorial experiment?

#### GretaGarbo

##### Human
Please write a few example lines of the design matrix. Then it will be easier to understand what you have done.
Do you have 3 levels on each factor? Do you have 3^5 = 243 experimental conditions?

#### alibina1997

##### New Member
again thank you, I attached my experiment below. no, I just have 3 samples. the main problem is instead of 243 I have 3 experiment conditions.
( my adviser said to use factorial after running the experiments)

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#### GretaGarbo

##### Human
With only 3 experimental runs and when several of the factors vary, then it will be impossible estimate which factors that have an influence.
It is a very good idea to do experiments as factorials.

If you choose to run the experiment with each factor on only two levels, high and low, then you can do the following:

If you choose 3 factors then you can run 2^3 = 8 experimental runs and evaluate it as a full factorial design (with linear regression).
If you choose 4 factors then you can run 2^4 = 16 experimental runs and evaluate it as a full factorial.
If you choose 5 factors then you can run 2^5 = 32 experimental runs and evaluate it as a full factorial.
If you choose 5 factors then you can run 2^(5-1) = 16 experimental runs and evaluate it as a fractional factorial.

But if the experimental variance is high then it might be that you need many more experimental runs to get good enough statistical precision.

#### alibina1997

##### New Member
Alright I got it. Thanks a lot

#### Miner

##### TS Contributor
again thank you, I attached my experiment below. no, I just have 3 samples. the main problem is instead of 243 I have 3 experiment conditions.
( my adviser said to use factorial after running the experiments)
This is very problematic because these three factors are 100% confounded (aliased) with each other. You cannot separate the effects of one from the others.