Is there a study about a user's reaction to a browser request of a geolocation?
What is the percentage of acceptation? In which case? What triggers acceptance and what triggers denial?
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As always, it depends of type of user and service. For example,
Users will accept if you explain the benefit, and it is worth it.
Younger users will be less reticent to accept than older ones.
And so on.
I have been working on a responsive website for a clothing store franchise, and the smartphone version asks geolocation when you are looking for the nearest store. That is pertinent and useful, and users will usually accept.
However, a service that asks for your geolocation without a clear purpose (i.e. when you turn on the app), or for sending you unspecified (i.e. "local offers"), will probably have more refusals.
My experience running studies was that about 25-30% of study participants using Chrome didn't even notice the request.
Some participants quickly scanned content on the site and ignored everything else. They hadn't considered whether they wanted to 'allow' or 'deny' geolocation -- they hadn't even noticed that a decision was being requested.
A little point to be aware of: Some users might decline to provide their location or just ignore the request because they know it won't be accurate.
If their location information is derived from their IP address, it can be off by a long shot. In my case when using the Internet from home, it shows up hundreds of kilometres away on the central coast of New South Wales. I live inland in north-east NSW. As far as I can tell, this is down to some quirk of how Telstra runs things on their side. This will also happen by design if your users are using a VPN to connect to your site, too.
If you want to provide some location-based service, like finding local branches of your store, provide your users with an option to manually specify a location. Don't just rely on automated means of getting it.