The claim has been repeatedly made on the internet (example: 1, 2, 3* )that when a mobile phone is connected to WiFi, disabling cellular data can extend battery life, as it stops the phone from looking for 3G signals. Equally, there are several counterclaims to this idea (example), which basically claim that when on WiFi, many phones automatically turn off their 3G radios, making this pointless.
Is there evidence to support this, for some or all models of smartphone (or for some or all types of popular smartphone software)?
*Yes this is an SE answer, but no sources are cited, so I'm treating it as a claim