Another type of periodogram has been proposed by Legendre et al. (1981) to identify rhythms in series of qualitative ecological data. In this contingency periodogram, the Buys-Ballot table is replaced by a contingency table (Section 6.2). The columns of the table (Colwell, 1974) are the same as in a Buys-Ballot table, but the rows are the r states of the qualitative descriptor under study. Values in the table are frequencies fj of the states of the descriptor (rows i), observed at the various times (columns j) of period Tk. As in the periodogram of Whittaker & Robinson (above), a different table is constructed for each period Tk considered in the periodogram.
Information Information (H) as to the states of the qualitative variable of interest (S), which is statistic accounted for by a given period Tk, is the information in common between S and the sampling axis X (most often, time). This amount of information is computed as the intersection between S and X, for period Tk.
Equation 12.14 is the same as eq. 6.10, used for calculating the information shared by two descriptors (statistic B), so that H (S n X) = B.
The contingency periodogram is a graph of the values H (S n X) = B on the ordinate, as a function of periods Tk. Periodograms, as well as spatial correlograms (Section 13.1), are often read from left (shortest periods or lags) to right (larger periods or lags). This is the case when the process that may have generated the periodic or autocorrelated structure of the data, if any, is assumed to be stronger at small lags and to generate short periods before these are combined into long periods.
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