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# Run-11 Transverse Jets: Statistical Cross-checks (Run List Part 1)

It was obvious that I had some wrong intuition about the χ^{2} distributions in my last post. Carl set me straight, pointing out that the average of the χ^{2} distribution should equal the number of degrees of freedom, rather than peak at the number of degrees of freedom. After some homework, I have redone the χ^{2} studies. First, I have rebinned the χ^{2} histograms to even out some of the fluctuations. I then coded up the exact distribution (as seen in Bevington Appendix C-4) and fit the histograms with the χ^{2} function for the appropriate degrees of freedom. I let an over-all scale factor float for the fit. The results are shown below.

# χ^{2} Distributions

## Figure 1

Now, the distributions actually look pretty good to my eyes. As Carl points out, the expected distribution is quite asymmetric for small values of ν.

## Figure 2

The previous distributions showed rather sizable fluctuations, so I have rebinned these distributions considerably. The result is, again, quite good.

## Figure 3

As with the Collins fits as a function of z, the fits as a function of j_{T} are entirely sensible.

## Figure 4

The high-z asymmetries have very few statistics, however, rebinning sufficiently removes the flutuations that one gets a decent picture of the χ^{2}. Again, it's completely sane.

## Figure 5

The story is much the same for Collins-like.

## Figure 6

## Figure 7

Finally, the x_{F} < 0 high-z Collins-like looks nuts, but I suspect it's a result of fewer statistics. Perhaps, it's just an outlier in what appears to be an otherwise perfectly sane statistical cross-check.

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