So I have have been conducting an experiment of an interesting feed on livestock. So essentially what I have done is, divided the total livestock $N$ in two different sized groups $n_1 $ and $ n_2$. I am not going to name them control or intervention, because of reasons you will see below.
I've conducted baselining, that is for 14 days sampled $N$, that is both $n_1$ as well as $n_2$ twice everyday to get their volume and fat % data points without any sorts of intervention for each livestock.
I fed the $n_1$ group the new food, by replacing a fixed portion of their regular food. I didn't change anything with the $n_2$ group and fed it the regular food. For 14 days I sampled $N$, that is both $n_1$ as well as $n_2$ twice everyday to get their volume and fat % data points with this setup for each livestock.
I reverted back to completely regular food for the $n_1$ group. I now fed the $n_2$ group the new food, by replacing the same fixed portion of their regular food. For 14 days I sampled $N$, that is both $n_1$ as well as $n_2$ twice everyday to get their volume and fat % data points with this setup.
How do I go ahead with understanding statistically whether there was an impact of my new feed on livestock on the fat and/or volume or just total fat production $ Total\ fat = Volume *fat \ \% $ ?
A good point to mention would be that typical values of each livestock are different than other: for example one member of $n_1$ would have volumes somewhere around 800 ml per sampling whereas as another from $n_1$ would have volumes somewhere around 2000 ml. So I guess its random in a way.
Right of the mind I can think of applying Student's T paired test for each group individually between two stages. But how ? Should it be between baselining and stage 1 for group $n_1$ for example ? Or between stage 1 and stage 2 for $n_1$ ? Similarly what about $n_2$ ? And how do I compare between the groups ?
I just need to (dis)prove the hypothesis that my new food increases the volume or fat % or total fat. I've seen the best practices post but couldnt find much whether the methods there apply to my trials.