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I have two questions that tie into one another (for context). I've been told to always check my data to see if it's normally distributed before doing any analysis, but if the data are associated with a variable that has more than 1 group/level (or multiple variables with many groups) then am I testing every single group for normality or the whole dataset altogether as one sample?

This brings me to my second question. I understand that a sample is a subset of a population, but at what point does 1 sample become many?

I know count data isn't normally distributed, but just as an example, if I went fishing in a pond, would the fish I catch be 1 sample of the fish in that pond for that 1 day, or could I call them multiple samples if I defined one group of fish my morning sample and another group of fish my afternoon sample? Would I test both groups for normality? Can samples be infinitely divisible into their own groups?

One non-technical conceptual answer to tie these together would be really helpful!

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This answer comes from re-discovered notes from my entry-level statistics course (so, please correct me if I'm wrong):

  1. Each group (all fish caught in the morning in this pond) is it's own sample. *Not sure if each sample is independent though...
  2. Each group would need to be tested for normality (if testing for normality was your thing).
  3. If groups of individuals are tested for differences (different means, etc.) and found to be similar (i.e. t-test) these groups can be combined into a single group. *Mean count of morning group is similar to afternoon mean count, so these become 1 sample of day 1.
  4. Individuals can be sub-divided into their own groups, but it depends on the question being asked. If the level of analysis asks "do you catch more fish in the morning or afternoon?", then that's as far as the group divisions need to go. However, a model with only 1 variable and 2 levels (time of day = morning/afternoon) may not describe count data very well -> a.k.a you might not predict the correct number of fish one would catch if you only considered the time of day, because the day of time also carries with it many other "sub-factors" (temp., salinity, time of day, etc.). So, with more variables a sample could be broken up into many -> all the fish caught in 15°C freshwater between 9am - 10am could now be 1 sample among the other "morning time" samples.
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