How to scale object positions? The answer sadly used an image - how does that work our days?

https://blenderartists.org/forum/archive/index.php/t-246537.html
Click the button to the left of the object origin button. This should make it so the objects move away from each other without affecting the size.

For Blender 2.8.x it can be found under the Options popover above the 3D View: