Apple - How do I prevent other wifi networks from showing up on my computer?

You can’t really prevent other networks from announcing themselves so until and unless Apple adds a filter, you can just join the networks you care about and save them in the keychain and try to avoid looking at the list.

The filter would be a check mark or other item to only show “trusted” networks so you can choose amongst them and not all of the networks.

To learn more why these are showing - go grab the lite version of WiFi Explorer - - I use the paid versions for work, but most of what you need to understand how far from these devices you’d need to move to not see their advertisements is in the free version (or using the airport command line interface)

  • What OS X signal strength test apps exist to measure Wi-Fi networking?

You can’t because the functionality you are using is actually a scanner for available networks. So if you’re clicking it you are scanning for networks and you’re going to get a list of networks as a result.

You can't set which wifi's are shown but you can set it up so that you automatically connect to your network by using the Network panel in the System Preferences. If you open the Network panel in System Preferences you get the option shown below.

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Be sure to unlock the panel if you wish to make changes.