Speaker Polarity Testing


Is it possible to correctly connect cables as marked between
speakers and amp yet still not have correct speaker polarity? Is it necessary to test polarity, and is it incorrect often?

I have read some places about reversing the wire connections
on one speaker and listening to see if sound is improved.
Is this safe? Has anyone tried this?

I would like to make sure this is safe and causes no damage before trying on my system.
128x128megasam
Let me reiterate that about half of the CDs out there have the absolute phase reversed. Everyone needs a component in their system with a phase reversing switch as the difference can be startling. There are some previous threads on this subject.
I do not intend to plug an item I have for sale on the site...but if you REALLY want to be sure, the best way is to use the Sheffield Labs/LAX polarity tester and test track CD. Not only will it measure relative polarity, but it will also tell you if the absolute polarity of your system (or a given recording) is off. Fun and useful if you do a lot of component swapping..and very useful if you amp and/or DAC/CD Plate allow you to switch absolute polarity. Alas, my preamp don't do that, and i just sold my Muse 296, so it don't do it for me anymore.
What about if you have a test CD tell you to reverse the leads on one of your speakers - i.e. that one speaker came from the factory out of phase?
Could there be any other problem?