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Correlation does not equal causation, of course. And we lack information on the conditions of the pedestrian accidents (e.g. were the drivers not paying attention, and did each pedestrian specifically say "didn't hear the car coming" as the reason for the accident?).
8,387 were hybrids, of which 77 had struck a pedestrian — this works out to a 0.9 percent incidence rate

559,703 vehicles were traditional gas-burners, which struck 3,578 pedestrians, which works out to a 0.6 percent incidence rate

The article says "nearly twice as likely", which is not even really close at all. Also, the sample size is much smaller for the hybrids.

I understand that cars which are running on electricity are harder to hear coming. For the blind, I can see that as being troubling. That being said, I can hear a hybrid or a full electric fairly easily. I might have trouble hearing one coming if it were going over 20mph, since I'd have less time to react. The point is moot, though, since I actually look both ways when I'm crossing a street, like you are told when you're a child.

I would also expect hybrid cars to be used more in cities and less outside them, which could also add to a chance to hit someone, because there are more pedestrians in the cities. And so on. The conclusion should rather say, that there is no significant difference in this matter, as it isn't. (0.6 to 0.9…)
There actually is a statistically significant difference between .6 and .9 with those sample sizes. So the conclusion should in fact say that there is a statistical significance.
They may have edited the article, but it reads, "up to twice as likely" and that observation is based on the incidents of bicyclists hit by hybrids vs standards (.6 to .3 percent respectively).

Also, to say that one can avoid being hit by a car by simply looking both ways when crossing a street is a little crass. I'm sure the thousands of pedestrians actually injured and killed by cars every year never thought to "look both ways".

I'm sure they are. But I suspect the difference between a gas engine and a hybrid one would not have made a difference in cases like those.
Why not?

I don't think the initial hypothesis is so bad: If you can't hear something coming, you're more likely to get hit by it. A gas engine is significantly noisier than a hybrid one.

It's just a hypothesis. The burden of proof rests on gathering evidence. So far, I don't think there is any.
I think the study is likely detecting "hybrids are disproportionately used in big cities and blue states", where pedestrian/bicycle traffic is disproportionately likely to be close to cars and thus gets hit more often (versus, say, rural Kansas where cars generally hit stationary objects or each other).

You would probably also find that hybrids strike proportionately more vegetarians than non-hybrid cars. This does not mean meat scares Priuses away.

There's also the possibility that hybrid drivers simply drive more often because their cost per mile is cheaper.
I suppose that is possible, but consumer gas consumption is mostly non-elastic (i.e. does not change with the price). We saw this during the price spikes a few years ago. It doesn't strike me as likely that it would suddenly get elastic when moving downwards.

This is assuming for the sake of argument that hybrids are cheaper per mile. The thing that makes that claim difficult to evaluate is "Cheaper than what". There are several plausible candidates for a yardstick which make the claim catastrophically false. (Gas is a fraction of the cost per mile. People notice it because they don't remember ever not having a $350 car payment and don't consider the cost-per-mile that was rolled into that.)

Modern gasoline compacts with small engines are very quiet at city speeds. Even on an empty street you wouldn't hear a huge difference. Tires on pavement would be an audible constant for both. On a busy street with other background noise it would be nearly impossible to distinguish the two. Certainly there's an audible difference between a hybrid and a diesel truck but you'd assume people stopped relying on audible warnings with the advent of quiet gasoline cars.

I think it's more likely that hybrids change the way some people drive. The peppy stop & go performance, combined with good braking performance, might make people more daring, more likely to accelerate quickly, more likely to rely on short stopping. This is exactly why insurance rates on sporty or high performance cars is higher than an under powered station wagon. Your choice of car changes the way you drive. If this is true it's likely that quiet gasoline compacts with good acceleration would also cause a higher number of accidents involving pedestrians.