this question is not being answered with one sentence. First of all: What trait do you have in mind? What is the expected mean and standard deviation of the trait(s)? What do you consider a significant difference? What should be the power of your analysis (0,8 or 0,99)? How many groups do you want to compare? What should be the error for alpha and beta (0,05 and 0,2 for example?). I always use the free software GPower (http://www.gpower.hhu.de/) in order to calculate the sample size required for my (simple) studies.
this question is not being answered with one sentence. First of all: What trait do you have in mind? What is the expected mean and standard deviation of the trait(s)? What do you consider a significant difference? What should be the power of your analysis (0,8 or 0,99)? How many groups do you want to compare? What should be the error for alpha and beta (0,05 and 0,2 for example?). I always use the free software GPower (http://www.gpower.hhu.de/) in order to calculate the sample size required for my (simple) studies.
Bear also in mind that statistical differences as observed in your trials will not always be relevant in practice or detected by consumers. Also the other way around relevant differences might not be found to be statistically different if the design is inadequate.
One more point on statistics: are animals within an experimental unit (eg pen) considered to yield dependent or independent data? There are conflicting opinions on this and it will greatly influence the number of degrees of freedom and thus statistical power of your experiment.
in my humble opinion, you will have two possibilities, a) There is some variance data in the literature about the experiment do you want to perform, or b) there is no information about variance. In a) case you can use the file that I have attached you, in the b case, you have to guess.
Also it should be considered the type of analysis that you are thinking about.
For example in sensory, it is not the same consumers that panel test. It is not the same a question of global acceptability (in mouth) that visual acceptability, our senses have different sensibility and different training. Even it is not the same on visual acceptability evaluate a global that a specific point (discoloration or fatness in meat).
See for statistics: Food Quality and Preference 17 (2006) 522–526 and Food Quality and Preference 31 (2014) 124–128
Arim was spot on. Also read the literature and see what differences people have reported for the traits of interest and the sample size used. Whatever you do MAKE sure you include replication!
Still be aware that if you take meat from different animals that, although they might have a common genetical background and treatment before slaughter, they still will differ despite identical treatments afterwards. So replicates are always essential in carrying out studies with animals.
You should also consider your experimental design in terms of the capacity to effectively perform the study. Its also about scale. Simply having more animals/samples/treatment groups for statistical purpose may not be feasible if your limited by time, $$, and personnel. Essentially, bigger is not always better, particularly when dealing with live animals. IMO, more replicates with fewer treatments outweighs more treatments with fewer replicates