Is it a good practice to prompt user to fill field 'Confirm password' on registration screen in mobile application?
Could you tell pros/cons?
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There are many arguments against using confirm password, well summarised here: http://uxmovement.com/forms/why-the-confirm-password-field-must-die/
The general consensus these days is that a single field works best, with a toggle to unmask the password. Since you're designing specifically for mobile you could leave the password unmasked by default, but some users will find this disconcerting.
As long as your reset password process is painless, one field is the way to go.
I assuming you are masking whatever the user types in the password fields?
If a human being cannot see what they type, because the field is masked, there is actually a high risk they will make a typo, especially on a mobile device where the virtual keyboard is tiny and is not physically tactile like a mechanical computer keyboard.
So the only reason why you will use a second password field is because the chance of someone making the same identical typo twice is actual quite low.
As you asked for pros and cons:
Single password field
Two password fields
I have seen the arguments stating a confirm password field is slower, but this is far too simplistic conclusion - its only one extra field.
However, the actual solution to this problem is to fix the root problem - you are masking the password! You now see many solutions allowing you to display what you type.
I have worked with a few Apps and websites, and tested a couple of things, including the registration flow.
Requiring users to confirm their passwords (or not), hasn't typically been dramatically affecting the registration event. Or too much drop off.
BUT, people are getting lazier and lazier and so, need simple ways to do things... so, I foresee this affecting the registration user experience more and more. This is why more and more websites are now incorporating the Show/Hide password toggle.