# Finding the CRD factorial on a experiment data

I am about to finish my thesis . But i am stuck in a problem. I have researched on two varieties of strawberry one is chandler and the other is camarosa. I have found the phenol content of both the varieties. There are three samples for each variety and three replications. Now, my work is to compare the two species of strawberry and i decided to use completely randomized design factorial. My teacher said its not possible. But i doubt it because he is known to avoid the queries of students. So can you please tell me if it is possible to use crd factorial on this data and how? I have attached the screenshot of my excel file.

To be clear, you have 3 samples A,B,C of Chandler strawberries and you make 3 phenol determinations on each sample, altogether making a total of 9 phenol determinations on Chandler strawberries. (And similarly for Camarosa.)

If that is true, then--generally inattentive, or not--your teacher is right that this is not a completely randomized design. The 3 numbers for sample A may be more alike than than the 3 for B, etc.

You have a hierarchical design: e.g., A,B,C within Chandler, then reps 1,2,3 within A. You do not have 9 independent phenol values for Chandler. So you can't do 2-sample t test of 9 val's for Chandler vs 9 for Camarosa. Your ANOVA table would have $$1$$ degree of freedom for 'Variety', $$4$$ degrees of freedom for 'Samples within Variety', and $$12$$ degrees of freedom for 'Error'. 'Samples(Variety)' would be random factor.

Note: If you absolutely can't figure out how to analyze a hierarchical design in whatever software you are using, you might consider a one-factor ANOVA with 6 levels of the factor ChA, ChB, ChC, CaA, CaB, CaC. There would be 3 replications for each factor. Your ANOVA table would have $$5$$ degrees of freedom for Factor (Between), and $$6(2) = 12$$ degrees of freedom for Error (Within).

Finally, if the overall F-test for the ANOVA finds that not all six 'levels' are alike, you can use a pre-defined linear contrast to compare ChA, ChB, ChC with CaA, CaB, CaC. That would tell you whether there is a significant difference between Chandler and Camarosa. [Theoretically, this would not be exactly the same as doing the hierarchical design, but the results would be numerically the same.]