Determining whether a group of spatially extensive data is centered around one point in space Consider a single x axis representing points along a line in space. I've got a set of data (in this case the receptive fields of hippocampal place cells recorded as a rat runs along a linear track), which are themselves spatially extensive, ie. if displayed graphically against the axis they would look like a series of horizontal bars, distributed at different points along the axis.

  ____   
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           ____ fields

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What I want to do is to define a point of interest on the line, and determine whether there are significantly more fields overlapping this point than elsewhere. I've achieved a simpler version of this by finding the centre of the fields and then measuring distances from this point and another arbitrarily defined point, but this approach loses all of the information that comes from the fact that they are spatially extensive.
Can anyone point me in the right general direction? Even knowing the broad class of statistical test I should use for this kind of situation would be a big help!
Thanks!
 A: A null hypothesis of your significance test could be that the number of fields overlapping an $x$ point of the axis ($fields(x)$) comes from the same $k$ distribution no matter which point of the axis we take, i.e. $fields(x) \sim K$, where $K$ may take the values $0, 1, 2, ... \infty$. The alternative hypothesis could be that the number of fields at the point of interest ($fields(x_A)$) comes from an other distribution. You have already defined the test statistic: the number of fields overlapping ($fields(x)$), and the wording “significantly more” suggests you are thinking in terms of a one tailed test.
When you say “elsewhere” does it mean anywhere along this continuous axis? Or does it mean a number of points along the axis? I will assume the second, and that you have an $(x_1, fields(x_1)), (x_2, fields(x_2)), ... (x_N, fields(x_N))$ sample. I will also assume that the $x_1, x_2, ... X_N$ points are “not too close to each other” - your above figure suggests that the width of the fields is not negligible, thus $fields(x_1) = fields(x_2)$ if $x_1$ and $x_2$ are close to each other.
The significance value of the test is the probability of observing a number of fields equal to or more than $fields(x_A)$ under the null hypothesis. Under the above assumptions this is $p \approx 1 - ECDF_K(fields(x_A)-1))$, where $ECDF_K$ is the empirical cumulative distribution function of $K$ estimated using the sample of $N$ points (not including $x_A$).
If you use R all you have to do is use the ecdf() function to perform this calculation.
