Play back both test videos side by side. See how the brightness compares visually, and see which one dims first and which bulb dies first.
The magic of video editing, I really like this idea. The effect of the Batteroo sleeve would be obvious if you can see the lamp still glowing without the sleeve for half of the video while the Batteroo side is dark. Don't forget to place a timer (I will use my iPhone) in the test setup as well.
Good one. As Dave mentioned, the fixed exposure is important, as usually the iPhone will normally adjust it's exposure so you won't be able to tell the actual relative brightness of the bulb. And to have the same ambient brightness and exposure/iso/frame rate/shutter speed/aperture in each time lapse. There are pro photog apps which you can get for the iPhone which will allow you to do this. But don't use the built in iPhone camera time lapse app. Sorry if this is all obvious to you, don't mean to tell you how to suck eggs. Look forward to seeing what you come up with.
(As was also suggested, having two bulbs and two battery holders side by side in the same shot - and starting both at the same time one with and one without a Batteroo sleeve - would save some time, but I was just afraid of detractors claiming that the two bulbs have slightly different resistance values which could make a difference to the outcome.)
Having a stopwatch, clock, or timer in the shot is important, as you mentioned.
[edit, oh I just misread the iPhone bit, that you're using the iPhone as the timer, not the video camera. Never mind, the fixed exposure stuff obviously still applies
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