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--- wiki:astronomy:observational_astronomy:snr [2024/11/04 21:06] – Roy Prouty
+++ wiki:astronomy:observational_astronomy:snr [2024/11/04 21:06] (current) – Roy Prouty
@@ Line 70: / Line 70: @@
 ==== Signal to Noise Ratio ====
-In returning to the ultimate goal of claiming one hypothesis true over another ... The Null Hypothesis is that the signal is indistinguishable from the noise. The Alternate Hypothesis is that the signal is distinguishable from the noise. We can construct the statistical model of the Alternate Hypothesis with $\mathcal{Norm}(\mu, \sqrt{\mu^2 + \mu_D^2 + \mu_U^2 + ... })$. And the Null Hypothesis with $\mathcal{Norm}(0, \sqrt{\mu_D^2 + \mu_U^2 + ... })$ -- where the uncertainties are just the sum of the uncertainties in quadrature.
+In returning to the ultimate goal of claiming one hypothesis true over another ... The Null Hypothesis is that the signal is indistinguishable from the noise. The Alternate Hypothesis is that the signal is distinguishable from the noise. We can construct the statistical model of the Alternate Hypothesis with $\mathcal{Norm}(\mu, \sqrt{\mu^2 + \mu_D^2 + \mu_U^2 + ... })$. And the Null Hypothesis with $\mathcal{Norm}(0, \sqrt{\mu_D^2 + \mu_U^2 + ... })$ -- where the uncertainties are just the sum of the uncertainties in quadrature. \\ \\
-So the figure of merit here is the Signal-to-Noise Ratio (SNR). In short, this quantity is the number of standard deviations the average calibrated signal is from the uncertainty in that average signal *collected*.
+So the figure of merit here is the Signal-to-Noise Ratio (SNR). In short, this quantity is the number of standard deviations the average calibrated signal is from the uncertainty in that average signal *collected*.\\ \\
-At the UMBC Observatory, we aim for an SNR > 10.
+**At the UMBC Observatory, we aim for an SNR > 10 to confidently reject the Null Hypothesis.**