Why don't experimental physics groups have statisticians in it?

Perhaps someone can clear up a bit a cognitive dissonance I am experiencing. Pollsters are under constant scrutiny of statisticians for even the most mundane of survey topics. With so much riding on the results of fundamental physics experiments, why don't we *need* statisticians to do the data analysis for us (or at least be looking over our shoulders)?

Because physicists learn the math and do it themselves. Why do you need a special expert class of people nowadays?

EDIT: Deconstructing statistics

In response to comments that "statisiticians go through years of study", I would like to say why I think all this studying is counterproductive. The theory of statistics (when it isn't about statistical mechanics or pure mathematical measure theoretic things) is usually concerned with the inference problem--- what is the likelyhood of a parameter to be x when a measured quantity correlated with the parameter is measured to be $y_1,y_2,...,y_n$ in a sequence of trials.

The complete solution to this problem is given by Bayes's theorem: the probability that the underlying parameter has value x is given by the probability that this value x will produce the experimental results $y_1,y_2,..,y_n$ conditioned by the prior knowledge which gives you some distribution on x to begin with.

Because Bayes's theorem solves the problem of inference so simply and naturally, the field of statistics is almost entirely built on rejecting it. Most of the field is based on the idea that one should not do Bayesian inference for one cockamamie reason or another, usually based on some silly philosphy which rejects priors or rejects the notion of a fundamental a-priori notion of probability. Because of this, physicists never learn Baysian inference from a class, they have to rediscover it for themselves (I certainly did, and most other people who do inference do too).

This means that if you hire a statistician, they will most often find lousy workarounds for Baysian methods, which will be useless to the experimental physicist. The issue is deeply ingrained--- many famous topics in statistics, like the sufficient statistics or the t-test, are born of the quest for a non-Baysian inference This quest is misguided, and will waste the experimental physicist's time. Within statistics, however, anti-Baysianism is a useful motivation for new results, so the field is dominated by anti-Bayesians.

It is also true in Biology. There, the Baysian method is (with difficulty) replacing statistician's pet inference methodologies. This diatribe is based on experience from about a decade ago, and might be out of date.