More of a maths question but... how do I analyse this?

[Nightlytic]

Hi,

So this is pretty embarrassing, I don't even know if a mathematical method exists around this... And please do tell if excel can solve this!

Suppose I have a list of staff members who work tills, how many transactions they served and in how many of these transactions an error was made (I'll attach a simple example of what I mean). Normally, in a scenario like this, I would calculate the error rate, visualise it a little, draft a chart, add context like 'Raul and Zack are new, they're doing fine considering that fact. Steve might require further training'. Happy days, it's something.

But is there a mathematical way in which to express how confident I am that these numbers are not caused just by pure chance? I can clearly see as a person with some sense, that if a cashier that does 50 transactions and makes 2 errors, that could be just them being unlucky, but if one does 500 and makes 50 errors, that's probably not just bad luck at play here. I presume that I need to calculate the expected errors, based on averages multiplied by how many transactions each person had, and compare the 'expected' against the actual numbers of errors? Is that regression, or am I entirely in the woods now?

Bottom line is, when I calculate rates of error, pull fancy charts and tables, I dread the moment my manager asks "so does that mean Steve is a bad cashier?"
-"Sorry, I have no clue"

 

[NARAYANK991]

Hi ,

My questions to you would be :

1. Do you have any past data (historical data) on expert cashiers , which can serve as a benchmark ? Similar historical data on beginner cashiers would also be helpful.

2. What would be the maximum number of transactions that you would consider for these rates ?

3. Would you have any more data on different types of errors , or is it all clubbed under one type ?

4. Would you have data on the severity of errors ? Errors which cost the organization in cents or a few dollars , would be easier to forgive than a single error which has cost the organization 10,000 dollars.

Narayan