That tells me your 'clamps' are no better than the QC-15 with the ANR off - aka, not very good.

As 'Foxy' said, ANR samples the sound and creates an out of phase sound to cancel it. If anything, your kids should be louder with the QC-15's than they are with the 'clamps'. The 'clamps' reduce all sound equally. The QC-15's (and all ANR) reduce all sound equally the same way the 'clamps' do, passively (though usually not very much), and then reduce 'constant' noise through the ANR as a 'bonus', if you will.

Since no one has independently tested the various headsets (Bose won't put a NRR on any of their headsets) against each other, it's hard to prove one way or the other. If you go to UFlyMike's website you can see they have a pilot survey of various headsets. Now, maybe the data is skewed b/c this survey was likely done by UFlyMike users, but it captures the sentiments of most pilots pretty well. The 'clamps' are unsafe b/c they are uncomfortable, the fancy Bose headset is super expensive, and any non-over the ear headset lets in too much noise, whether it's got ANR or not. Most every pilot who has tried the UFlyMike prefers it to any other set-up.

The biggest downside of the UFM is that you have to turn your overhead speaker on if the battery dies and you don't have a spare, as the headphones stop putting out audio entirely if the battery dies (see the paragraph below for a detailed TSO discussion). The 'low battery' light blinks to tell you it is low about 5 hours before it dies, so you really have to be an idiot or penny pincher to let it die. As UFM points out, airplanes run off batteries and fuel, which are both expendable power sources. As a pilot, it is your job to monitor expendable energy sources already, so you can handle the battery issue.

For the TSO'd forum nerds (if you don't know what I'm talking about, skip this paragraph): No discussion of the UFlyMike would be complete without the question - is it TSO'd? The FAA does not require you to use a TSO'd headset, only some airlines do. All TSO'd headsets require that you be able to hear ATC passively, and the Bose QC2 and QC15 don't do this (that's why Bose makes you pay over $1000 for their 'aviation' headset, so that it makes noise when the battery dies, and why Bose pushed the TSO angle, as UFM undercut their huge profit machine). If you fly for an airline that demands TSO approved headsets, you must also use the Westone UM1 earbuds (you can't just use any iPod ear buds, you have to use Westone UM1 earbuds, as they were the ones used for the TSO certification). So you have to buy the UFM A100T (the microphone), the Westone UM1 earbuds, and a QC2 (the QC-15 is not yet TSO approved with the UFM as of this writing). That's $225 for the UFM, $5 for shipping, $79 for the ear buds, and $299.95 for the Bose (or whatever the price is for the QC2, since Bose doesn't sell them anymore). You also have to get a special sticker put on your QC2's and UFM. Yes, seriously. All this is to have a TSO'd headset b/c a certain airline in the 'southwest' get a burr under their saddle about all their pilots using non-TSO'd headsets, and then it spread like wildfire. Of course, if you have modified your headset at all (custom ear molds, new mic muff, added ANR, ANYTHING but totally, 100% stock) your headset isn't TSO'd either - it has to be in the same EXACT configuration that it got certified as TSO'd in. So, essentially, 95% of guys don't bother with all this, and 5% of guys have the fancy ear buds and stickers so that when their Chief Pilot or FAA POI mouths off to them about their non-TSO'd headset, they can put them in their place.

It's not coincidence that the new Bose QC15's came out, and then the Bose A20 aviation headset came out. Both claim to have better ANR than their predecessors (the QC2 and X) b/c they have a second microphone on the exterior of the ear cup and redesigned ear cushions. As far as your ears are concerned, they're the exact same . . . except one of them costs $796 more than the other one b/c it has a microphone and still lets the sound come through after the battery dies, but is unusable as a non-aviation headset.

I just tried to find this research. Reference please? Sound waves, like all waves, cancel each other out if 180 degrees out of phase. In the same way that you can make water flat by canceling out waves by creating 'opposite waves' (try it in a sink or bathtub), you can make sound 'flat' - ie, quiet. If ANR doesn't reduce sound amplitude (what leads to hearing loss), than that would possibly have major implications in many areas of physics, not just ear phones.

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Sorry for the length.