Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chi-squared Test for Binned, Gaussian Samples   We examine the $\chi^2$ test for binned, Gaussian samples, including effects
due to the fact that the experimentally available sample standard deviation and
the unavailable true standard deviation have different statistical properties.
For data formed by binning Gaussian samples with bin size $n$, we find that the
expected value and standard deviation of the reduced $\chi^2$ statistic is
\begin{equation} \frac{n-1}{n-3}\pm
\frac{n-1}{n-3}\sqrt{\frac{n-2}{n-5}}\sqrt{\frac{2}{N-1}}, \end{equation} where
$N$ is the total number of binned values. This is strictly larger in both mean
and standard deviation than the value of $1\pm (2/(N-1))^{1/2}$ reported in
standard treatments, which ignore the distinction between true and sample
standard deviation.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph