I've created an anonymous survey and I'm currently testing it.
after I answer the survey, the responses don't show up anywhere in the "response and statistics" tab but I can see from the survey summary that the survey has been completed by one user.
Please see the attached screenshots
note that I'm using the free cloud version which is 3.15.1
If you are using the LimeSurvey Pro hosting "Free" package? Get in touch with Limesurvey GmbH then via the "Support" link in the top navigation and create a support ticket with them, as they are responsible for the hosted version.
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Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.