I have read other posts before raising this question. I understood the mechanics behind Anova but I have not fully grasped its essence in logical terms. What I mean is that if I calculate the mean difference between two treatments I fully understand the concept and can visually see it in a plot.
What remains not fully understood is the concept of confidence intervals (lwr and upr in aov function using R). If for instance I have a dataset of 5382 observations of 2 treatments or variables I will obviously have 1 as degree of freedom within and 5380 in residuals.
Are the upper/lower confidence telling me the min/max value the mean difference between these 2 groups can vary assuming those degree of freedom and a p-val (say) of 5%?
Or should we also take in consideration the sum/mean of squares and F-value to get to that conclusion?
My question is what in essence lower and upper confidence intervals are telling us (possibly without falling in the standard definition of min and max values of the difference of mean within treatments)?