I am new to experimental design and would like to perform the following experiment but I am not sure if my setup is correct or not so far. My idea is below.
Let's say you want to optimise the growth conditions for the small fish. You have been using a standard type of food that has worked reasonably well. But now, three new brands of fish food have become available and you want to conduct an experiment to test which food works best and whether it is worth changing to one of the new food types. Based on previous experiments, you reckon that you will need 10 replicates to have a good chance of finding meaningful differences. There are aquaria and tanks of different sizes available so you are not constrained by the equipment.
For this experiment, I assume there will three treatments (the three new brands of fish food). I will call them A, B and C. Since we are testing three different brands of fish food, I will replicate the brands of fish food three times so there will be nine tanks used in this experiment in total. I will label them from 1 to 9. Each tank will randomly receive different food brands of food every day.
But now, how will I find meaningful differences in the growth of the fish if I apply different treatments randomly on the tanks? Also, how many fish do you recommend I use for this experiment and how often should I monitor the growth of the fish? Or do you have another suggestion of how I could set up this experiment, help. Your help will be much appreciated. Thanks in advance.