I am trying to calculate average wait time for one of the projects that I am working on. The way the project works is that there are pathways that students follow and each pathway has several steps. At each step students get a challenge, or challenge sets or they earn a badge. Students can earn multiple badges (at different steps) within the same pathway.
My task is to calculate the average time the students have to wait in a pathway to earn a badge, and to find out whether it has some effect on the success of the pathway or not.
Below is the example that will help understand my question.
PathwayID TotalSteps BadgeEarned@Step 1 4 2 4 2 7 3 5 7 3 5 2 4 4 9 4 6 8
They way I am calculating the average wait time right now, is by dividing the average of BadgeEarned@Step by total number of steps in that pathway. So according to these calculations, Average Wait time for the pathways will be below.
PathwayID AvgWaitTime 1 0.75 2 0.71 3 0.60 4 0.67
Wait Time for Pathway 4 appears to be smaller than wait time for Pathway 1, which is not actually the case, as in pathway 4, students have to wait longer until they even earn their first badge. Right now the way I am calculating the average wait time, there is some bias toward the pathways with more number of steps. I will appreciate if someone can give me an idea to calculate average wait time, that is not biased by the length of the pathway.