This experiment would be conducted with,
1) Two varieties of a crop at nursery stage
2) control (no fertilizer), Fertilizer A, Fertilizer B
3) 4 levels of fertilizer A, 4 levels of fertilizer B
*What would be the most siutable design?
* CRD with Three factors or
* CRD with Two Factors - - - Can I consider variety as factor one (two levels) and combinations of ferlizer type and Conentration (9 levels) as factor two.o
It's been a while since I've run experiments like this, but your design might depend on whether you want to know the crop response at all combinations of Fertilizers A and B, or whether you want to know if yield (or whatever criterion you are interested in maximising) is highest at a particular combination of A and B.
If it is all combinations, then you'll probably have to run 2 varieties * 5 levels of A * 5 levels of B * N replications. The 5 levels of fertilizer are the 4 levels + Zero, allowing you to see what A does without B and vice versa.
If it is just a particular combination of A and B, then perhaps a Box-Behnken Design might reduce the amount of combinations you need to run.
I haven't tried this myself, so perhaps consulting a statistician before you set anything up would be the best course of action. This is always a good idea, as turning up at their door with a handful of data and asking for help to analyse it will invariably result in a polite refusal.
Since the topic of design and analysis of experiments is vast, the book has been divided into two parts; first part covering fundamentals of design and analysis of experiments related to, by and large, single factor experiments and the second part focusing mostly on multifactor experiments and advanced topics. Fertilizer comes in a few different forms. There is liquid, powder, and granular. Liquid fertilizers are often diluted with water. Spreading them is similar to watering your garden, usually done with a hose attachment. Powdered fertilizers also need water to be productive. Usually they are spread by hand and watered to complete absorption. Granular lawn fertilizers can easily be spread on top of soil. These nutrient pack granules will be soaked into your garden over time as you water it.
Fertilizer recommendations contain several important factors, including fertilizer form, source, application timing, placement, and irrigation management. Another important part of a fertilizer recommendation is the amount of a particular nutrient to apply.
Though, a number of statistical books on designing and analysis of experiments are available, most of these books are intended for statisticians because the subject is treated through rigorous algebraic theories
https://notionpress.com/read/fertilizers-technology
Regards
You have two factors, one is varieties or genotypes and the other is Fertilizer. You can use Two factorial Completely randomized designs. Then for analysis you will have two way ANOVA test.
I prefer that your experience with three factors, the first is the varieties, the second is the first type of fertilizer with its different levels, and the third factor is the second type of fertilizer with different concentrations as well. As for the appropriate design, if your experiment is taking place in controlled conditions, the appropriate design is the Factorial experiment in complete randomized design(CRD), and if The conditions of the experiment could not be controlled, as the appropriate design is the factorial one in a complete randomized Block design(RCBD), or any other suitable factorial one.
you can use two possible design
Factorial CRD if Controlled or RCBD if under field
split plot design where genotypes as main plot and the two types of fertilizer as sub plots
split
You can use split plot design in field conditions..
And factorial CRD in controlled conditions
Consider three factors: Two cultivars (first factor), fertilizande A (second factor) and fertilizer B (third factor). With fertilizers A and B will be distributed in 4 levels each, apply a 2x4x4 factorial. Working in the field, consider system in randomized blocks.
Two varieties and three fertilizer treatments can be combined using factorial RCBD with three or four replications and you will have 2X3= six treatments in each replication
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