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Tests of significance in harmonic analysis
Open accessAbstract
If a series u1, u2,...u2n + 1 constitute a random sample from a normally distributed population, they any linear function A = S 12n + 1 (arur) will also be normally distributed; moreover its mean will be zero if S(ar) = 0, and its variance will be equal to that of the original population if S (ar2) = 1. Any other liner function B = S 12n + 1 (brur) will be distributed independently of the first if S(arbr) = 0, and in this case the sum of the squares, x = A2 + B2, will be distributed so that the chance of exceeding any particular value of x is e -x/e, where c is the mean value of x, equal to twice the variance of the population sampled.
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Cited by
Rey, G., Cesbron, F., Rougemont, J., Reinke, H., Brunner, M., & Naef, F. (2011) · PLoS Biology · doi:10.1371/journal.pbio.1000595 · Cited by 474
Shearer, W. T., Reuben, J. M., Mullington, J. M., Price, N. J., Lee, B.-N., Smith, E. O., Szuba, M. P., Van Dongen, H. P. A., & Dinges, D. F. (2001) · Journal of Allergy and Clinical Immunology · doi:10.1067/mai.2001.112270 · Cited by 455
THE DISTRIBUTION OF THE LARGEST OF A SET OF ESTIMATED VARIANCES AS A FRACTION OF THEIR TOTAL
COCHRAN, W. G. (1941) · Annals of Eugenics · doi:10.1111/j.1469-1809.1941.tb02271.x · Cited by 438
Circadian Clocks Are Resounding in Peripheral Tissues
Ptitsyn, A. A., Zvonic, S., Conrad, S. A., Scott, L. K., Mynatt, R. L., & Gimble, J. M. (2006) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020016 · Cited by 145
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Metadata
- Authors
- Fisher, R. A.
- Venue
- Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
- Publisher
- The Royal Society
- Published
- 1929-08-01
- Volume
- 125
- Issue
- 796
- Pages
- 54-59
- ISSN
- 0950-1207 (ISSN-L)
- 2053-9150
- OpenAlex
- W2135657996
- Cited by
- 672
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- diamond
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