Data transformation and kruskal-wallis

It's the first time I'm posting in your forum!
I'm using statistics in a university project about operations research, and I'm having some doubts...hope you can help me out...

I measured the time a given worker takes to perform a task (50 times), then I measured the same worker performing a similar task, the difference is that this task is longer (larger average time). The time distributions do not follow a normal distribution.
How can I compare if the worker is performing the same way in both tasks, even if I know before hand they are just different in terms of average time?
Or, in other words, how I can I know that the worker time distribution not being affected by the task, besides changing the average. Should I scale/transform the data? Would it be OK to divide each time observation by the average in each set of observations and then perform a Kruskal-Wallis procedure to check for significant differences?

Thank you!!!Looking foward for your replies!


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So you want to test if the only difference a treatment (in this case a different task) makes in the response distribution is a change in location (ie the mean value)?
Yes, basically that's it... for instance, if there would be significant changes in terms of the dispersion then the treatments/tasks had to be considered different (or I wasn't controlling some other variable affecting the outcome)...?