File:P-value vs SN.gif
Summary
| Description |
English: If one wants to decide if there is a signal hidden in the noise, the p-value will drop sharply around S/N=1, and then keep decreasing exponentially.
In this example p=0.05 happens just before the curve tails to zero. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1183715504185397248 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
n = 5 10^3;
noise = RandomVariate[NormalDistribution[0, 1], {n}];
signal = Table[E^(-((x - n/2)^2/(2 (n/100)^2))), {x, 1, n}];
pvssn = Reap[For[a = 0, a <= 5, a = a + 0.05,
data = a signal + noise;
\[Chi]2 = Total[data^2];
p = NIntegrate[PDF[ChiSquareDistribution[n], x], {x, \[Chi]2, \[Infinity]}];
Sow[{a, p}];
];][[2, 1]]
p1 = Table[
GraphicsRow[{
ListPlot[pvssn[[j, 1]]*signal + noise, PlotRange -> All, Joined -> True, PlotStyle -> {Thick, Black}, LabelStyle -> {Black, Bold}, Axes -> False]
,
ListPlot[pvssn[[1 ;; j]], Joined -> True, PlotStyle -> {Thick, Black}, LabelStyle -> {Black, Bold}, AxesLabel -> {"S/N", "p-value"}, PlotRange -> {{0, 5}, {0, 1}}]
}, ImageSize -> Large, PlotLabel -> Style[StringForm["\!\(\*SubscriptBox[\(H\), \(0\)]\): the data is just Gaussian random noise.\nNull hypothesis rejected with p=``", ScientificForm[pvssn[[j, 2]], 3] ]],
LabelStyle -> {Black, Bold}]
, {j, 1, Dimensions[pvssn][[1]], 1}];
ListAnimate[p1]
Licensing
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