Methodology to determine if "end-of-month" production increases in a statistically significant way to meet quota I am trying to determine if an "end-of-month" phenomenon is happening at my workplace.  The hypothesis is that more units of work are being performed in the latter part of the month compared to earlier in the month as a rush to meet a work quota.
I have units of work per day for a year and am trying to think of how to structure the problem.  One thought is group events into quarters of the month and to set up a hypothesis test such that 
$$H_0: μ_{lastquarter} = μ_{all}, H_A : μ_{lastquarter} > μ_{all}$$
I don't like the approach because I'm making an assumption that testing the last quarter of the month is correct, whereas it might actually be true that the rush to complete work happens in the last sixth of the month.  I'd appreciate any recommended approaches!
 A: Okay, I'm just repeating to ensure I have understood you correctly:


*

*You have 365 (Jan 1 until Dec 31) data points

*For each data point you have


*

*a "date" variable

*a numeric "units of work" variable



Right?
I would be more straight forward here and do classic DATA EXPLORATION first.


*

*Create a "day of month" (1-31) variable. You can derive this from your date variable.

*Boxplot it (e.g., with Python/matplotlib). The boxplot should have "days until end of month" on the x-axis and "units of work" on the y-axis.


If there is a difference of amount of work over the course of the month, it should show up in the visualization (e.g., through outliers, higher median/mean of units of work in the lower x-values).
If nothing shows up: Use "days until end of month" as your x-axis variable. By doing that you take into account that the months have a different number of days (max. 28-31) and your anecdotal observation specifically mentions a rush in the last days. Therefore, just taking "day of month" could be too imprecise if the effect is weak.
If there is still nothing: Try to correct for weekends and holidays that fall on the last days of the month. Therefore you will have a variable "working days until end of month". Plot that on the x-axis.
