Why does the LEDs affect Analog Input?
I think it is because of power consumption.
If the LEDs consume lots of power, the LED on Arduino(typically mini red LED) will be off or faded.
So before you connect the  LEDs, check the  mini red LED which is on Arduino and after connection the LEDs, check ones again.
If the red LED is faded or off, the problem must be power consumption.
Connect 12v or 5v to vin to powering the Arduino, and also to LEDs
The important thing is you should not connect LEDs to Arduino 5v.