I am unsure how to interpret the significance of a paired test.
I have data for six days of the week; for each day I have relevant data for 11 hours minutewise. I want to determine, whether a trait 'A' is more common on different days.
Both, the total number of observations N as well as the number of observations of trait 'A' vary with the time of day in a very similar fashion on the different days.
I proceed as follows: For every minute, I compute A/N. I then perform a series of paired t-Tests (or Wilcoxon-signed-rank tests) to compare the ratios A/N of different days with the time as pairing factor.
I intepret a p-value below a given threshold (taking into account a Bonferroni correction) as A/N being significantly different on the days I compared.
What puzzles me is that if I look at the ratios A/N aggregated over the entire day, I find Tue > Fri > Sat. But while the differences between Tue and Fri as well as Fri and Sat are significant, the difference between Tue and Sat is not significant.
Is the interpretation that a significant paired test signals a difference in means correct?
Is it too naive to expect the significance of paired tests to be transitive when looking at aggregated values?
Edit: I have a nominal variable and trait 'A' is one level. I want to compare the frequency, with which 'A' occurs in the total number of observations. The sampling times are the same for all days and are known precisely, I binned them into minutes. I have one data point per minute per day.
Here is a plot of the data, all figures are per minute: I want to test, whether there are difference in the relative number of occurences on the different days. Since the total number of occurences also varies on the different days, I form the ratio A/N and analyse that.