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The modeled matched filter search found an arrival difference of about $7\mathrm{ms}$, within the roughly $10\mathrm{ms}$ intersite light travel time. Background events were obtained by shifting one detector's timestamps far beyond that time and repeating the coincidence analysis. The binary search bounded the false alarm rate below one event per $203000$ years. That is an empirically estimated background rate, not a probability that the source interpretation is false.^[ref]

The logic is to destroy a common astronomical arrival while retaining each instrument's real glitches. A Poisson distribution approximation would turn a background rate $r$ into $1-e^{-rT}$ for at least one equally strong noise event during live time $T$, only after accounting for the search's ranking and trials. Repeated time slides reuse data; their accumulated background duration is not an equally long series of independent new observations. Correlated disturbances also require separate controls because shifting timestamps can erase them along with a true signal.

The dedicated noise study inspected auxiliary channels and deliberately applied magnetic, acoustic and mechanical disturbances to measure their coupling into strain. For GW150914, checks included environmental coincidences, instrument state, and exclusion of an intentional hardware injection. It also examined potentially correlated global magnetic disturbances, which time slides alone cannot exclude.^[ref] The point of an injection test is quantitative: a quiet environmental monitor is informative only if its sensitivity and coupling bound the disturbance needed to explain the candidate.

A noise-limited detection threshold is the decision boundary above which a measured statistic is declared to contain a signal, with the boundary chosen from a specified noise model and decision criterion. It belongs to a measurement procedure: filtering, observation time, baseline correction and the definition of a positive detection affect the result. A threshold in observed data is distinct from the true signal level required for a specified detection probability.

For an original one-sided Gaussian model, let $Y=A+N$, where $A\ge 0$ is the signal and $N\sim \mathcal{N}(0,{\sigma }^2)$. Declare a detection when $Y>T$ and choose $T=k\sigma$. If $\Phi$ is the cumulative distribution function of the standard normal distribution, thenHere $\alpha$ is the per-observation false alarm rate. The model assumes the same additive noise distribution with and without the signal.

With $k=5$, the noise-only crossing probability is approximately $2.87\times 10^{-7}$ for one independent observation. Yet a signal of size $A=5\sigma$ is detected only half the time: it puts the distribution's center exactly at the decision boundary. “Five times noise” therefore does not by itself mean reliable detection of a signal that large.

To require both a chosen false-positive probability $\alpha$ and a missed-detection probability $\beta$, this model givesFor $\alpha =\beta =0.05$, the two values are approximately $1.645\sigma$ and $3.290\sigma$. This distinction accords with the VIM definition of a limit of detection, which specifies both kinds of decision error rather than equating the limit with the observed threshold.^[ref]

The experiment should measure baseline fluctuations under the same bandwidth, loading and observation rule used for signal detection, then test known signal levels. Repeated searching also matters: for $M$ independent noise-only observations, the chance of at least one threshold crossing is $1-(1-\alpha {)}^M$. Correlated samples require a different calculation. Baseline drift, non-Gaussian fluctuations and signal-dependent noise likewise invalidate a threshold inferred from the simple model without further characterization.