Table for Fisher's Test of Significance in Harmonic Analysis

Summary A table is calculated which facilitates the estimation of significant spectral peaks obtained by harmonic analysis which are above the 99, 98, 95, and 90% confidence level. The application of the test is also described. In the scheme of harmonic analysis for revealing the periodic structure of a time series, the inferences are based on the magnitude of the amplitude corresponding to each period. Yet, any set of random numbers subject to the harmonic analysis will yield harmonic amplitudes such that some are bigger than others by chance alone. The decision of reliability of these amplitudes, therefore, depends on comparison with the magnitude of the amplitudes which can be produced by harmonic analysis on the assumption that the time series are from a random fluctuation and do not have any physical meaning. 2. Fisher’s test and tables Fisher (1929) developed a test of significance in harmonic analysis from a series x(i), i= 1, 2, . .. , n constituting a random sample from a normally distributed population. The decomposition of x(i) into its harmonic constituents is