I have a dataset consisting of 12 subsets, each subset contains between 10 and 15 temperature observations from one person.
I would like to determine whether or not it is reasonable to assume that, within each subset (person), the temperature observations are normally distributed. That is, I would like to be able to say "the data supports the assumption that temperature observations for an individual person follow a normal distribution".
Mean temperature and variance varies considerably from subset to subset (person to person). Therefore, my proposed analysis is to qualitatively test for normality using a QQ plot as follows:
- For each subset, standardize data (for each observation within a subset, subtract the mean of that subset, and divide by the standard deviation of that subset)
- Pool this standardized data for all subsets
- Plot pooled data against theoretical quantiles for N(0,1)
Is this an appropriate analysis?
I'm concerned that pooling in this way may not be valid since subsets are unequal sample size (more weight is given to larger subsets). Would interpolating the larger subsets make sense here?
Is there a better way to test the assumption of normality?
My reason for wanting to assume normality of temperature observations:
Firstly, it would be helpful to make predictions about future temperature observations. For example, it would be useful to be able to say "based on the average standard deviation found in this study, a 95% prediction interval can be calculated for future temperature observations, in other words, based on an average person in this study, 95% of the time we can reasonably expect someone's temperature to be within ±X° of their mean temperature". My understanding is that I can only make such a prediction if the assumption of normality is reasonable.
Secondly, it would be interesting to know if temperature observations are (or at least appear to be) normally distributed (given the conditions of my study), from a 'basic science' understanding of body temperature.
Edit: Researching this issue further, I have come to learn what I am proposing might be described as the equivalent of generating a QQ plot of the studentized residuals. From my non-technical viewpoint, this suggests it is a valid approach to checking the assumption of normality: