Clean install of android

Yes and no. I'll explain:

TL;DR Simple method at end of post

Using your example...
Formatting a hard drive on a desktop computer (depending on quick or full format) effectively writes 0s to all (or at least enough) memory addresses to where the drive will assume it's been wiped clean. Any data recovery specialist will claim otherwise though, since data can most always be recovered.

If your goal is complete eradication of all data on your phone (though I'd wonder why lol), then you absolutely have to have root permissions, and I'd recommend a full partition map for your device. Then just open up an ADB terminal on the device and issue the following command as root:

WARNING, DO NOT ATTEMPT THIS COMMAND UNLESS YOU KNOW ABSOLUTELY WHAT IT MEANS

dd if=/dev/null of=/dev/block/mmcblk0

This command will assuredly destroy all data on the phone and prevent all but the most technically savvy recovery specialist from being able to find any usable data.

TL;DR

But if all your looking to do is to start fresh with a clean OS and you're not concerned about data recovery then you can simply do a factory reset via settings menu (remove Google account first!), via recovery menu (remove Google account first!), or if you have/are able to have an unlocked bootloader then you can manually flash the stock firmware via fastboot.