I recently decided to investigate whether or not some days of the week are better predictors of spam outbreaks than others.  If we get a big increase on Sunday, for example, does it mean that the rest of the week is going to to see a big increase?

To calculate this, I took all of our data for spam volume on each individual day of the week (N=43).  I then added up all of the spam for the week (ie, calculated the weekly spam volume).  I then found the % change in spam volume, both for the week and for the the day of the week as compared to the previous week.  Next, I calculated the correlation between the % change in daily spam, week-over-week, to the % change in weekly spam.  Below are the results:

Sunday Correlation       0.64153
Monday Correlation       0.78755
Tuesday Correlation      0.80776
Wednesday Correlation    0.81024
Thursday Correlation     0.88218
Friday Correlation       0.32781
Saturday Correlation     0.70321

From the above table, Thursday is most closely associated with changes in spam volume, followed closely by Wednesday and Tuesday.  In other words, a change in spam volume on those particular days is most closely associated with a change in overall volume of spam seen during the week (in retrospect, I should have calculated the spam volume using the days of the week as mid-points or starting points - my current experiment always had Sunday as the starting point).  Monday is next.  The relationship on Saturday and Sunday is not as strong but still statistically significant.

What surprises me is how weak the Friday correlation is.  Changes in spam volume on Friday do correspond to changes in weekly volume but the relationship is no where near as strong for the rest of the week.  It is not consistent with randomness but I wouldn't pick Friday to be my bellweather, either.