This example shows how to assess the significance of a sinusoidal component in white noise using Fisher's g-statistic. Fisher's g-statistic is the ratio of the largest periodogram value to the sum of all the periodogram values over 1/2 of the frequency interval, (0,Fs/2). A detailed description of the g-statistic and exact distribution can be found in  and .
Create a signal consisting of a 100-Hz sine wave in white Gaussian noise with zero mean and variance 1. The amplitude of the sine wave is 0.25. The sampling rate is 1 kHz. Set the random number generator to the default settings for reproducible results.
Fs = 1e3; t = 0:0.001:1-0.001; rng default; x = 0.25*cos(2*pi*100*t)+randn(size(t));
Obtain the periodogram of the signal using periodogram. Exclude 0 and the Nyquist frequency (Fs/2).
[Pxx,F] = periodogram(x,rectwin(length(x)),length(x),Fs); Pxx = Pxx(2:length(x)/2);
Find the maximum value of the periodogram. Fisher's g-statistic is the ratio of the maximum periodogram value to the sum of all periodogram values.
[maxval,index] = max(Pxx); fisher_g = Pxx(index)/sum(Pxx);
The maximum periodogram value occurs at 100 Hz, which you can verify by finding the frequency corresponding to the index of the maximum periodogram value.
F = F(2:end-1); F(index)
N = length(Pxx); upper = floor(1/fisher_g); for nn = 1:3 I(nn) = ... (-1)^(nn-1)*nchoosek(N,nn)*(1-nn*fisher_g)^(N-1); end pval = sum(I);
The p-value is less than 0.00001, which indicates a significant periodic component at 100 Hz. The interpretation of Fisher's g-statistic is complicated by the presence of other periodicities. See  for a modification when multiple periodicities may be present.
 Percival, Donald B. and Andrew T. Walden. Spectral Analysis for Physical Applications. Cambridge, UK: Cambridge University Press, 1993, p. 491.
 Wichert, Sofia, Konstantinos Fokianos, and Korbinian Strimmer. "Identifying Periodically Expressed Transcripts in Microarray Time Series Data." Bioinformatics. Vol. 20, 2004, pp. 5–20.