I have calculated what the average salary of a archaeology Field/Lab technician in the US based off of the inflation and job postings from the website shovelbums.org (see figure). The purpose of which was to compare were salaries are now to what they should have been if they followed inflation.
As you can see in my table there is great variability between those results following wages from 1999 (field tech pay is well behind) and 2000 (behind but not bad). Now, ideally I would go with 1999 as I would want to see as far back as possible but that only has a sample of 17 (first year website was founded so fewer results) compared to a N of 41 for 2000 (the website became more established). Does that mean that 1999 is a less accurate number?
That is a real kicker as there is no way I can statistically determine this. I do not now the size of population, in this case all job postings for field technicians. I also do not have any proxy variables that could stand in to help determine this which means I do not know if 1999 is an accurate representation of the average starting salary for a field tech in that year.
It is at this point numbers fail me and I must then make a judgment call on which set of numbers to use. This allows for politics and biases to enter into the equation. For example, if I was a field tech I would use the 1999 numbers as they show that I should be paid more and there is no mathematical way to prove me wrong. The same could go for bosses and the need to use the numbers from 2000.
This happens all to often in archaeology and in the real world. It is how politicians can look at the same set of numbers and get different results and archaeologists as well. Mathematics is rarely corruptible but the interpretations are almost always fair game. If only more people realized that.