Is VTSAX really cheaper on Mondays?

On my last blog post I looked at which day of the week is better to buy VTSAX over time. On that post I showed that over the time period ranging from 11/13/2000 thru 10/5/2018, the median price difference between the daily price and the weekly average was the lowest on Monday. The plot showing this result is once again shared below

Box Plot for daily price difference from weekly average:

Since this post, I have received a few comments asking if the difference is “really real” meaning is this difference statistically significant? One way to answer this question is through hypothesis testing. For those asking a similar question, I decided to share my findings here: Looking at the price variation from the weekly average, the Kruskal-Wallis test rejects the null hypothesis that all days come from the same distribution at a 1% significance level. The Wilcoxon rank sum test also rejects the null hypothesis of equal medians at the 1% significance level between Monday and any other day except for Tuesday. So basically, I would say yes, this difference is statistically significant. Now, while these results help answer this question, I am more of a graphical person. Therefore, I decided to plot the 95% confidence intervals for the median daily price deviation from weekly average. This plot is shown below with blue circles indicating the Median Value and Red Circles indicading the +/- 95% Confidence Intervals (CI). Once again, since the Monday CI does not overlap with the CI of any of the other days except Tuesday, I would say that this difference is significant. Even with Tuesday, the tails of the CI are just barely overlaping.

+/- 95% Confidence Intervals for Median Daily Price Difference:

By the way, I have decided the use the median and not the mean here since there are a number of outliers in the data, as seen on the box plot above. The median value would be less affected by these points.