Journal articles: 'Correlation (Statistics)'

1

McClure, Philip. "Correlation Statistics." Journal of Hand Therapy 18, no. 3 (July 2005): 378–80. http://dx.doi.org/10.1197/j.jht.2005.04.015.

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Curran-Everett, Douglas. "Explorations in statistics: correlation." Advances in Physiology Education 34, no. 4 (December 2010): 186–91. http://dx.doi.org/10.1152/advan.00068.2010.

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Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This sixth installment of Explorations in Statistics explores correlation, a familiar technique that estimates the magnitude of a straight-line relationship between two variables. Correlation is meaningful only when the two variables are true random variables: for example, if we restrict in some way the variability of one variable, then the magnitude of the correlation will decrease. Correlation cannot help us decide if changes in one variable result in changes in the second variable, if changes in the second variable result in changes in the first variable, or if changes in a third variable result in concurrent changes in the first two variables. Correlation can help provide us with evidence that study of the nature of the relationship between x and y may be warranted in an actual experiment in which one of them is controlled.

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Walizada, Sayeeda. "Significance of correlation in statistics." International Journal of Multidisciplinary Research and Growth Evaluation 2, no. 6 (2021): 317–18. http://dx.doi.org/10.54660/.ijmrge.2021.2.6.317-318.

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Correlation quantifies the degree and direction to which two variables are related. Correlation does not fit a line through the data points. The sign (+, -) of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association, e.g. A correlation of r = - 0.8 suggests a strong, negative association (reverse trend) between two variables, whereas a correlation of r = 0.4 suggest a weak, positive association. A correlation close to zero suggests no linear association between two continuous variables. Linear regression finds the best line that predicts dependent variable from independent variable. The decision of which variable calls dependent and which calls independent is an important matter in regression, as it'll get a different best-fit line if you swap the two. The line that best predicts independent variable from dependent variable is not the same as the line that predicts dependent variable from independent variable in spite of both those lines have the same value for R2. Linear regression quantifies goodness of fit with R2, if the same data put into correlation matrix the square of r degree from correlation will equal R2 degree from regression. The sign (+, -) of the regression coefficient indicates the direction of the effect of independent variable(s) into dependent variable, where the degree of the regression coefficient indicates the effect of the each independent variable into dependent variable.

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Gibbons, Steven J. "The optimal correlation detector?" Geophysical Journal International 228, no. 1 (August 23, 2021): 355–65. http://dx.doi.org/10.1093/gji/ggab344.

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SUMMARY Correlation detectors are now used routinely in seismology to detect occurrences of signals bearing close resemblance to a reference waveform. They facilitate the detection of low-amplitude signals in significant background noise that may elude detection using energy detectors, and they associate a detected signal with a source location. Many seismologists use the fully normalized correlation coefficient C between the template and incoming data to determine a detection. This is in contrast to other fields with a longer tradition for matched filter detection where the theoretically optimal statistic C2 is typical. We perform a systematic comparison between the detection statistics C and C|C|, the latter having the same dynamic range as C2 but differentiating between correlation and anticorrelation. Using a database of short waveform segments, each containing the signal on a 3-component seismometer from one of 51 closely spaced explosions, we attempt to detect P- and S-phase arrivals for all events using short waveform templates from each explosion as reference signals. We present empirical statistics of both C and C|C| traces and demonstrate that C|C| detects confidently a higher proportion of the signals than C without evidently increasing the likelihood of triggering erroneously. We recall from elementary statistics that C2, also called the coefficient of determination, represents the fraction of the variance of one variable which can be explained by another variable. This means that the fraction of a segment of our incoming data that could be explained by our signal template decreases almost linearly with C|C| but diminishes more rapidly as C decreases. In most situations, replacing C with C|C| in operational correlation detectors may improve the detection sensitivity without hurting the performance-gain obtained through network stacking. It may also allow a better comparison between single-template correlation detectors and higher order multiple-template subspace detectors which, by definition, already apply an optimal detection statistic.

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Joe, George W., and Jorge L. Mendoza. "The Internal Correlation: Its Applications in Statistics and Psychometrics." Journal of Educational Statistics 14, no. 3 (September 1989): 211–26. http://dx.doi.org/10.3102/10769986014003211.

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The internal correlation, a measure of dependency in a set of variables, is discussed and generalized. This coefficient is an upper bound to the product moment correlations, multiple correlations, and canonical correlations that can be defined in a set of variables. Applications of the internal correlation coefficient and its generalizations are given for a number of data-analytic situations. Where appropriate, we discuss tests of significance. We illustrate the internal correlation and expand the concept to a series of additional indices: local internal, up-internal, and down-internal correlations. Uses of these indices are illustrated in several areas: multicollinearity, ridge regression, factor analysis, principal components analysis, and test reliability.

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Zhuo, Bin, Duo Jiang, and Yanming Di. "Test-statistic correlation and data-row correlation." Statistics & Probability Letters 167 (December 2020): 108903. http://dx.doi.org/10.1016/j.spl.2020.108903.

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YAMAKI, Shunsuke, Masahide ABE, and Masayuki KAWAMATA. "Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A, no. 12 (2014): 2601–10. http://dx.doi.org/10.1587/transfun.e97.a.2601.

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Wang, Jinling, Ali Almagbile, Youlong Wu, and Toshiaki Tsujii. "Correlation Analysis for Fault Detection Statistics in Integrated GNSS/INS Systems." Journal of Global Positioning Systems 11, no. 2 (December 31, 2012): 89–99. http://dx.doi.org/10.5081/jgps.11.2.89.

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Zirmansyah, Zirmansyah. "Kualitas Skripsi Mahasiswa Universitas Al Azhar Indonesia: Pengaruh Hasil Belajar Metodologi Penelitian dan Statistik terhadap Kualitas Skripsi." JURNAL Al-AZHAR INDONESIA SERI HUMANIORA 1, no. 1 (April 4, 2011): 19. http://dx.doi.org/10.36722/sh.v1i1.20.

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The objective of the research is to study the relationship between learning outcome on statistic, learning outcome on research methodology and thesis quality. The research was carried out at the student Al Azhar University, with 53 samples of thesis which were selected randomly. The research concludes there is positive correlation between: (1) learning outcome on statistics and thesis quality; (2) knowledge on research methodology and thesis quality; (3) furthermore, there is a positive correlation between learning outcome on statistcs, learning outcome on research methodology, with thesis quality. Therefore thesis quality can be increased by improving learning outcome on statistic, and learning outcome on research metodhology.

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10

Schaff, D. P. "Semiempirical Statistics of Correlation-Detector Performance." Bulletin of the Seismological Society of America 98, no. 3 (June 1, 2008): 1495–507. http://dx.doi.org/10.1785/0120060263.

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11

Quinn, Robert J. "Exploring Correlation Coefficients with Golf Statistics." Teaching Statistics 28, no. 1 (February 2006): 10–13. http://dx.doi.org/10.1111/j.1467-9639.2006.00229.x.

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12

Gwinn, Carl. "Correlation Statistics of Quantized Noiselike Signals." Publications of the Astronomical Society of the Pacific 116, no. 815 (January 2004): 84–96. http://dx.doi.org/10.1086/381167.

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13

Wieneke, Bernhard. "PIV uncertainty quantification from correlation statistics." Measurement Science and Technology 26, no. 7 (June 5, 2015): 074002. http://dx.doi.org/10.1088/0957-0233/26/7/074002.

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14

Artuso, Roberto. "Correlation decay and return time statistics." Physica D: Nonlinear Phenomena 131, no. 1-4 (July 1999): 68–77. http://dx.doi.org/10.1016/s0167-2789(98)00219-x.

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15

Nikitina, M. A., and I. M. Chernukha. "Nonparametric statistics. Part 3. Correlation coefficients." Theory and practice of meat processing 8, no. 3 (October 10, 2023): 237–51. http://dx.doi.org/10.21323/2414-438x-2023-8-3-237-251.

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A measure of correlation or strength of association between random variables is the correlation coefficient. In scientific research, correlation analysis is most often carried out using various correlation coefficients without explaining why this particular coefficient was chosen and what the resulting value of this coefficient means. The article discusses Spearman correlation coefficient, Kendall correlation coefficient, phi (Yule) correlation coefficient, Cramér’s correlation coefficient, Matthews correlation coefficient, Fechner correlation coefficient, Tschuprow correlation coefficient, rank-biserial correlation coefficient, point-biserial correlation coefficient, as well as association coefficient and contingency coefficient. The criteria for applying each of the coefficients are given. It is shown how to establish the significance (insignificance) of the resulting correlation coefficient. The scales in which the correlated variables should be located for the coefficients under consideration are presented. Spearman rank correlation coefficient and other nonparametric indicators are independent of the distribution law, and that is why they are very useful. They make it possible to measure the contingency between such attributes that cannot be directly measured, but can be expressed by points or other conventional units that allow ranking the sample. The benefit of rank correlation coefficient also lies in the fact that it allows to quickly assess the relationship between attributes regardless of the distribution law. Examples are given and step-by-step application of each coefficient is described. When analyzing scientific research and evaluating the results obtained, the strength of association is most commonly assessed by the correlation coefficient. In this regard, a number of scales are given (Chaddock scale, Cohen scale, Rosenthal scale, Hinkle scale, Evans scale) grading the strength of association for correlation coefficient, both widely recognized and not so well known.

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16

Joe, Harry. "Generating random correlation matrices based on partial correlations." Journal of Multivariate Analysis 97, no. 10 (November 2006): 2177–89. http://dx.doi.org/10.1016/j.jmva.2005.05.010.

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17

YAMAKI, Shunsuke. "Statistical Properties of the Phase-Only Correlation Functions Clarified through Directional Statistics." IEICE ESS Fundamentals Review 13, no. 2 (October 1, 2019): 108–17. http://dx.doi.org/10.1587/essfr.13.2_108.

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18

Bland, J. Martin, Douglas G. Altman, and David S. Warner. "Agreed Statistics." Anesthesiology 116, no. 1 (January 1, 2012): 182–85. http://dx.doi.org/10.1097/aln.0b013e31823d7784.

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Statistical Methods for Assessing Agreement between Two Methods of Clinical Measurement. By J. Martin Bland, Douglas G. Altman. Lancet 1986; 1(8476):307-10. Abstract reprinted with permission of Elsevier, copyright 1986. In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analyzed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.

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19

Byrne, Gillian. "A Statistical Primer: Understanding Descriptive and Inferential Statistics." Evidence Based Library and Information Practice 2, no. 1 (March 14, 2007): 32. http://dx.doi.org/10.18438/b8fw2h.

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As libraries and librarians move more towards evidence-based decision making, the data being generated in libraries is growing. Understanding the basics of statistical analysis is crucial for evidence-based practice (EBP), in order to correctly design and analyze research as well as to evaluate the research of others. This article covers the fundamentals of descriptive and inferential statistics, from hypothesis construction to sampling to common statistical techniques including chi-square, correlation, and analysis of variance (ANOVA).

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20

Mestre, Xavier, and Pascal Vallet. "Correlation Tests and Linear Spectral Statistics of the Sample Correlation Matrix." IEEE Transactions on Information Theory 63, no. 7 (July 2017): 4585–618. http://dx.doi.org/10.1109/tit.2017.2689780.

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21

Biggs, James D. "An Analysis of Pulsar Nulling Statistics." International Astronomical Union Colloquium 128 (1992): 265–70. http://dx.doi.org/10.1017/s0002731600155301.

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AbstractWe have sought correlations between the fraction of null pulses with other pulsar parameters for an ensemble of 72 pulsars using survival analysis methods. The strongest correlation was found between the null fraction and pulse period. Correlations were also found between other parameters that typically have strong dependencies on pulse period, and this tends to indicate that the null fraction increases with age as was first suggested by Ritchings (1976). However, no explicit correlation was found between pulsar characteristic age and null fraction. A significant anti-correlation was found between the angle subtended by the magnetic and rotation axes and the null fraction.Many of the pulsars presented here were found to null. In particular, all pulse profile classes in the scheme devised by Rankin (1983a) have members that null. Differences in the mean age of these pulsar classes are not very pronounced, and the influence of class on pulse nulling statistics is probably less than that suggested by Rankin (1986), but cannot entirely be ruled out. Also, there is considerable variation in the fraction of null pulses from pulsars within each class, but generally class St pulsars null the least. Of special note is the fact that two pulsars PSR 0833-45 and PSR 1556-44 apparently do not null. The upper limit for PSR 0833–45 is quite low; no nulls were detected in observations of over 120,000 pulses.The similarity of the nulling parameters of pulsars observed at two frequencies near 400 MHz and 843 MHz suggests that the pulsar emission mechanism is wide band over this frequency range.

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22

Shen, Cencheng, Carey E. Priebe, and Joshua T. Vogelstein. "From Distance Correlation to Multiscale Graph Correlation." Journal of the American Statistical Association 115, no. 529 (April 11, 2019): 280–91. http://dx.doi.org/10.1080/01621459.2018.1543125.

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23

Lochstet, Gwenn, and Donna H. Lehman. "A Correlation Method for Collecting Reference Statistics." College & Research Libraries 60, no. 1 (January 1, 1999): 45–53. http://dx.doi.org/10.5860/crl.60.1.45.

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While studying a sampling technique for collecting reference statistics, a correlation method for calculating reference statistics using weekly door counts also was tested at the University of South Carolina. Reference statistics and door counts taken on the sample weeks of the test year were correlated, and the resulting correlation coefficient between the two variables was used to calculate weekly reference statistics for the nonsampled weeks. The sum of these calculated weekly values and the actual values of the sampled weeks yielded a yearly total of reference transactions that is comparable to the yearly total determined by using the sampling technique. Thus, the correlation method may offer libraries an accurate and less time-consuming procedure for keeping reference statistics.

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24

Gutynska, O., J. Šafránková, and Z. Němeček. "Correlation length of magnetosheath fluctuations: Cluster statistics." Annales Geophysicae 26, no. 9 (September 1, 2008): 2503–13. http://dx.doi.org/10.5194/angeo-26-2503-2008.

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Abstract. Magnetosheath parameters are usually described by gasdynamic or magnetohydrodynamic (MHD) models but these models cannot account for one of the most important sources of magnetosheath fluctuations – the foreshock. Earlier statistical processing of a large amount of magnetosheath observations has shown that the magnetosheath magnetic field and plasma flow fluctuations downstream of the quasiparallel shock are much larger than those at the opposite flank. These studies were based on the observations of a single spacecraft and thus they could not provide full information on propagation of the fluctuations through the magnetosheath. We present the results of a statistical survey of the magnetosheath magnetic field fluctuations using two years of Cluster observations. We discuss the dependence of the cross-correlation coefficients between different spacecraft pairs on the orientation of the separation vector with respect to the average magnetic field and plasma flow vectors and other parameters. We have found that the correlation length does not exceed ~1 RE in the analyzed frequency range (0.001–0.125 Hz) and does not depend significantly on the magnetic field or plasma flow direction. A close connection of cross-correlation coefficients computed in the magnetosheath with the cross-correlation coefficients between a solar wind monitor and a magnetosheath spacecraft suggests that solar wind structures persist on the background of magnetosheath fluctuations.

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25

Gwinn, Carl R. "Correlation Statistics of Spectrally Varying Quantized Noise." Publications of the Astronomical Society of the Pacific 118, no. 841 (March 2006): 461–77. http://dx.doi.org/10.1086/499388.

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26

Lee, Jounghun, and Ue‐Li Pen. "Galaxy Spin Statistics and Spin‐Density Correlation." Astrophysical Journal 555, no. 1 (July 2001): 106–24. http://dx.doi.org/10.1086/321472.

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27

Bitsanis, I., M. Tirrell, and H. Ted Davis. "Statistics of correlation functions from molecular dynamics." Physical Review A 36, no. 2 (July 1, 1987): 958–61. http://dx.doi.org/10.1103/physreva.36.958.

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Nagarajan, R., and M. Upreti. "Correlation Statistics for cDNA Microarray Image Analysis." IEEE/ACM Transactions on Computational Biology and Bioinformatics 3, no. 3 (July 2006): 232–38. http://dx.doi.org/10.1109/tcbb.2006.30.

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29

Sharp, W. D., and N. Shanks. "Fine's Prism Models for Quantum Correlation Statistics." Philosophy of Science 52, no. 4 (December 1985): 538–64. http://dx.doi.org/10.1086/289274.

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30

Balasubramanyam, Baskar, and Kaneenika Sinha. "Pair correlation statistics for Sato–Tate sequences." Journal of Number Theory 202 (September 2019): 107–40. http://dx.doi.org/10.1016/j.jnt.2019.01.015.

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31

Feng, Zhi-Hui, and Li-Yan Liu. "Energy fluctuation and correlation in Tsallis statistics." Physica A: Statistical Mechanics and its Applications 389, no. 2 (January 2010): 237–41. http://dx.doi.org/10.1016/j.physa.2009.09.005.

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32

Brown, Brielin C., Chun Jimmie Ye, Alkes L. Price, and Noah Zaitlen. "Transethnic Genetic-Correlation Estimates from Summary Statistics." American Journal of Human Genetics 99, no. 1 (July 2016): 76–88. http://dx.doi.org/10.1016/j.ajhg.2016.05.001.

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33

Bland, J. M., and D. G. Altman. "Statistics Notes: Correlation, regression, and repeated data." BMJ 308, no. 6933 (April 2, 1994): 896. http://dx.doi.org/10.1136/bmj.308.6933.896.

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34

Qian, Hong. "On the statistics of fluorescence correlation spectroscopy." Biophysical Chemistry 38, no. 1-2 (October 1990): 49–57. http://dx.doi.org/10.1016/0301-4622(90)80039-a.

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35

Bland, J. M., and D. G. Altman. "Statistics Notes: Measurement error and correlation coefficients." BMJ 313, no. 7048 (July 6, 1996): 41–42. http://dx.doi.org/10.1136/bmj.313.7048.41.

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36

Sukhanova, E. M. "Matrix Correlation." Theory of Probability & Its Applications 54, no. 2 (January 2010): 347–55. http://dx.doi.org/10.1137/s0040585x97984231.

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37

Maugis, Pierre-André G. "Correlation extrapolated." Statistics & Probability Letters 145 (February 2019): 89–95. http://dx.doi.org/10.1016/j.spl.2018.08.007.

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38

YAMAKI, Shunsuke, Masahide ABE, and Masayuki KAWAMATA. "Correlation Performance Measures for Phase-Only Correlation Functions Based on Directional Statistics." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E101.A, no. 6 (June 1, 2018): 967–70. http://dx.doi.org/10.1587/transfun.e101.a.967.

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39

Lesser, Lawrence M., and Dennis K. Pearl. "Statistical edutainment: Correlation recreation." Teaching Statistics 42, no. 3 (August 10, 2020): 126–31. http://dx.doi.org/10.1111/test.12228.

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40

Schechtman, Kenneth B. "Triserial correlation." Communications in Statistics - Theory and Methods 19, no. 8 (January 1990): 3011–22. http://dx.doi.org/10.1080/03610929008830361.

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41

Zhang, Zhengjun. "Quotient correlation: A sample based alternative to Pearson’s correlation." Annals of Statistics 36, no. 2 (April 2008): 1007–30. http://dx.doi.org/10.1214/009053607000000866.

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42

Barakat, H. M. "The maximal correlation for the generalized order statistics and dual generalized order statistics." Arabian Journal of Mathematics 1, no. 2 (April 11, 2012): 149–58. http://dx.doi.org/10.1007/s40065-012-0002-9.

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43

Tillett, H. E., J. Sellwood, N. F. Lightfoot, P. Boyd, and S. Eaton. "Correlations between microbial parameters from water samples: expectations and reality." Water Science and Technology 43, no. 12 (June 1, 2001): 19–22. http://dx.doi.org/10.2166/wst.2001.0705.

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Data which are collected in order to estimate the correlation between parameters must be analysed with caution. Classical statistics of correlation are often inappropriate. The “r” statistic is very easily distorted by non-Normal data. Non-parametric statistics can be helpful. The interpretation and usefulness of the estimates of correlation will depend on the study plan. If water samples come from disparate sources (e.g. upstream or downstream from sewage outlets) then parameters A and B may occur in their highest and lowest numbers according to how close the samples were to contamination sources thus correlating closely. However, if all samples come from sources with similar pollution levels then plots of A and B will show considerable scatter and apparently little correlation. So what is the relationship between A and B? An example of “perfect” correlation, as demonstrated by replicate counts of a single parameter from split samples, gave an r value of only 0.63 (ρ = 0.62) due to random variation in numbers of organisms between the two halves of the sample. Thus large amounts of data are needed for studying true correlation because relationships between parameters are embedded in the natural variation. This also illustrated that Standards for a single parameter can be “passed” or “failed” by two halves of the same sample. Study design is clearly of fundamental importance. Consideration must be given to the appropriate way of asking questions about correlation between different parameters.

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44

Urbano-Leon, Cristhian Leonardo, Manuel Escabias, Diana Paola Ovalle-Muñoz, and Javier Olaya-Ochoa. "Scalar Variance and Scalar Correlation for Functional Data." Mathematics 11, no. 6 (March 9, 2023): 1317. http://dx.doi.org/10.3390/math11061317.

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In Functional Data Analysis (FDA), the existing summary statistics so far are elements in the Hilbert space L2 of square-integrable functions. These elements do not constitute an ordered set; therefore, they are not sufficient to solve problems related to comparability such as obtaining a correlation measurement or comparing the variability between two sets of curves, determining the efficiency and consistency of a functional estimator, among other things. Consequently, we present an approach of coherent redefinition of some common summary statistics such as sample variance, sample covariance and correlation in Functional Data Analysis (FDA). Regarding variance, covariance and correlation between functional data, our summary statistics lead to numbers instead of functions which is helpful for solving the aforementioned problems. Furthermore, we briefly discuss the functional forms coherence of some statistics already present in the FDA. We formally enumerate and demonstrate some properties of our functional summary statistics. Then, a simulation study is presented briefly, with evidence of the consistency of the proposed variance. Finally, we present the implementation of our statistics through two application examples.

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45

Lai, Dejian. "Asymptotic distributions of the correlation integral based statistics." Journal of Nonparametric Statistics 10, no. 2 (January 1999): 127–35. http://dx.doi.org/10.1080/10485259908832757.

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46

Cheong, Hin-Fatt. "Correlation statistics of sediment motions and its dispersion." Journal of Hydraulic Research 31, no. 4 (July 1993): 495–507. http://dx.doi.org/10.1080/00221689309498872.

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47

Ma, Jian-Zhong. "Correlation Hole of Survival Probability and Level Statistics." Journal of the Physical Society of Japan 64, no. 11 (November 15, 1995): 4059–63. http://dx.doi.org/10.1143/jpsj.64.4059.

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48

Genack, A. Z., and N. Garcia. "Intensity Statistics and Correlation in Absorbing Random Media." Europhysics Letters (EPL) 21, no. 7 (March 1, 1993): 753–58. http://dx.doi.org/10.1209/0295-5075/21/7/007.

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Heuser, Cara C., Jessica Hunn, Michael Varner, Shaheen Hossain, Shiraz Vered, and Robert M. Silver. "Correlation Between Stillbirth Vital Statistics and Medical Records." Obstetrics & Gynecology 116, no. 6 (December 2010): 1296–301. http://dx.doi.org/10.1097/aog.0b013e3181fb8838.

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50

Healy, M. J. "Statistics from the inside. 7. Regression and correlation." Archives of Disease in Childhood 67, no. 10 (October 1, 1992): 1306–9. http://dx.doi.org/10.1136/adc.67.10.1306.

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Journal articles on the topic 'Correlation (Statistics)'

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