And please keep in mind that measuring response time outside of a controlled environment is not really measuring only response time, but also internet connection, browser speed, server stability, etc. So if for your experiment response time really is key, you might rethink the idea of running this experiment over the internet.
Issues that I see:
1. People will access your experiment with different setups (computer vs. smartphone, Wifi vs Lan vs 3/4/5g connection, different OS and browser combinations) all of which can have an impact on "response time"
2. People will access your experiment at different times and you have no control on how the server behaved during this time. E.g. some might respond during a time where there is very little server load, while others will be responding during a time where a lot of other respondents are also responding. As the installation is hosted by your university, there might be several other surveys running at the same time that can also have an impact on the general server load.
This has nothing to do with Limesurvey itself, but is rather a general issue of running experiments that measure response time and are not run in a controlled environment (e.g. same time, same setup, same connection, etc).
I answer at the LimeSurvey forum in my spare time, I'm not a LimeSurvey GmbH employee.
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