Just to clear things up.... as far as "floating" the scope goes.... this can be a dangerous practice. It is much better to float the DUT than to float the scope, from a safety viewpoint. The fact that the scope probe reference leads are connected by the Mains connection to an Earth ground can be a valid concern when testing devices that have unknown, maybe "OU" characteristics. In cases where that issue has been raised, I have sometimes used an isolation transformer that doesn't have a straight-through ground connections as many do, or a "ground-lift" adapter that simply removes the ground prong from the mains connection, or I've used scopes that are actually ground-isolated themselves such as the Fluke 123 or 199 ScopeMeters. This is not my normal practice though.
The "switch" that Farmhand remembers is probably the one on my old Interstate (Racal-Dana) F43 FG, which has a built-in ground isolation switch that floats the signal "ground" or Black, BNC shield, output connection. This switch is normally on the rear panel of the instrument which is hard to get to in my "stack" so I installed a parallel switch on the front panel. Not too many more modern FGs seem to have this feature, I think. Their "black" or BNC Shield outputs are connected permanently to chassis and Mains ground. For instruments that can be isolated, of course whenever the BNC connections are used to connect the FG to another, grounded instrument, this isolation goes away, so one has to be careful using it. The same is true when "floating" the scope itself: as soon as a probe reference lead is connected to something else like another instrument's ground that isn't floated, the isolation is removed.
I've taught myself to be very conscious of inadvertent groundloops of this kind; that is one reason why I'm an advocate of clean, simple layouts so that the chances of making wiring mistakes are minimized. And I do this because of costly mistakes I've made, myself! Fortunately only instruments have suffered, I haven't electrocuted myself (yet)!

@Smudge: Unfortunately TinMan's scope has a little weirdness concerning the Math trace. While it does the usual Math functions, like trace multiplication of a voltage and a current trace to obtain an instantaneous power curve, it _does not_ do any automatic Measurements on the resulting Math trace. SO it can't even take the "mean" or average value of the Math trace or p-p or any other measurements of it. This may be a flaw in the old firmware or it may just be a peculiarity of the particular model of the scope. The User's Manual for the 1000 series Atten scopes gives instructions for getting measurements from the Math trace but TinMan's scope doesn't seem to have the necessary options in its Menus, so he can't do it. We've gone over this several times and it doesn't seem to be "user error", it's a flaw in the scope itself. It may be possible to download the channel trace data to a CSV file for a spreadsheet and use the spreadsheet to generate and then get measurements on the Math trace but as far as I can tell he hasn't tried to do this yet. It seems very strange to me that a scope with Math capability can't do measurements on the resulting Math trace, but there it is.
As far as TinMan's experimental setup where the bulb got brighter but the "average" or mean current through it was less... I did repeat and reproduce that effect using a simple pulsed circuit and did some measurements on it. We had a big discussion on OU about it, where we showed that using "average" values of voltage and current gave wrong results when computing average power. My scope, fortunately, does do Measurements on its Math trace, so I was able to show that the bulb brightness in the experiment follows the power, as it should. Less brightness, less power dissipated in the bulb according to the properly obtained and computed measurements, and more brightness = more power dissipated in the bulb. The Red Herring was only using the mean current instead of doing the instantaneous multiplication of current x voltage and then taking the mean of the resulting Instantaneous Power trace.