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

It was obvious that I had some wrong intuition about the χ2 distributions in my last post. Carl set me straight, pointing out that the average of the χ2 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 χ2 studies. First, I have rebinned the χ2 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 χ2 function for the appropriate degrees of freedom. I let an over-all scale factor float for the fit. The results are shown below.

χ2 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 jT 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 χ2. Again, it's completely sane.

Figure 5

The story is much the same for Collins-like.

Figure 6

Figure 7

Finally, the xF < 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.