No abstract

(BrJ Ophthalmol 1995; 79: 225-228)

Tables are given for estimating the significance of spectral peaks obtained by harmonic analysis. These tables depend also on the rank order of the peak, thus allowing lower order peaks to be accepted where with other tests they were failed. The use of the tables is discussed.In studying the eigenvibrations of the Earth, one subjects seismic records to harmonic analysis of one form or another. Often there is sufficient noise on the records to render the results of the analysis uncertain.Even if there were no periodic components in a random time series of 2m + 1 (= n) points, some of the m amplitudes obtained by harmonic analysis would be greater than others, simply due to random fluctuation. One has, thus, to use significance tests in order to determine the plausability that a certain amplitude represents a real periodicity.Nowroozi (1965, 1966), in analysing the Alaskan and Rat Island earthquakes, applied a test developed by Fisher (1929). In a later study, Nowroozi (1967) described his use of Fisher's test and furthermore published tables to be used with that test. In applying Nowroozi's ideas to some actual records, Jarosch (1970 private communication) found that several amplitudes which seemed meaningful to him were rejected by a 95 per cent significance test suggested by Nowroozi. Nowroozi himself, in his 1965 and 1966 studies, labelled some periods as plausible although his significance test rejected them. It thus seemed that the test was perhaps too severe.Fisher's test determines the probability that the largest of the amplitudes ck(k = 1,2, ..., m) given in a normalized form with respect to the data is the result of the randomness of the data. Nowroozi, in his application of the test, rejects, at a certain level of significance, every amplitude below such a theoretical value, not taking into consideration that the test refers only to the largest amplitude.In the present work it is suggested that the proper application of Fisher's test would be in its extension for use with amplitudes other than the largest; thus, before deciding which amplitudes are meaningfd, we shall order them in decreasing order so that C, will be the r-th largest amplitude of those available. The significance tests used come from the ideas of order statistics. Grenander & Rosenblatt (1957) extended Fisher's test so that it refers also to Z, for values of r greater than one.I shall now briefly describe the ideas of Fisher, and of Grenander and Rosenblatt. Nowroozi's notation will be used, so that cross-reference will be easier.The 2m+ 1 (= n) terms of a time series x(i), i = 1,2, ..., n can be written as a sum of their harmonic constituents, as m k = l x(i) = a0/2 + C [ak cos (2nkiln) + bk sin (2nki/n)].(1) 373

No abstract

The effect of hemodialysis and of ultrafiltration on intraocular pressure (IOP) was studied in 30 non glaucomatous patients (58 eyes) with chronic renal failure. IOP and serum osmolality were measured before and after dialysis and every hour during the procedure. IOP showed a slight but non-significant rise when measured after hemodialysis and a significant drop for ultrafiltration. Serum osmolality decreased significantly when measured after hemodialysis, but remained stable for ultrafiltration. The variations in IOP were found to be significantly correlated with changes in osmolality during hemodialysis.