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	PA 765: Correlation
		Beside Pearsonian correlation (r), the most common type, there are other special types of correlation to handle the special characteristics of such types of variables as dichotomies, and there are other measures of association for nominal and ordinal variables.
		Correlation is the ratio of the observed covariance of two standardized variables, divided by the highest possible covariance when their values are arranged in the best possible match by order.
		Eta, the coefficient of nonlinear correlation, known as the correlation ratio, is discussed in the section on analysis of variance.
	www2.chass.ncsu.edu /garson/pa765/correl.htm (3727 words)

	Correlation
		In probability theory and statistics, the correlation, also called correlation coefficient, between two random variables is found by dividing their covariance by the product of their standard deviations.
		The correlation is 1 in the case of an increasing linear relationship, -1 in the case of a decreasing linear relationship, and some value in between in all other cases, indicating the degree of linear dependence between the variables.
		Pearson's correlation coefficient is a parametric statistic, and it is less useful if the underlying assumption of normality is violated.
	www.ebroadcast.com.au /lookup/encyclopedia/co/Correlation.html (299 words)

	Correlation - Wikipedia, the free encyclopedia
		The correlation coefficient can also be viewed as the cosine of the angle between the two vectors of samples drawn from the two random variables.
		This is because the interpretation of a correlation coefficient depends on the context and purposes.
		However, correlations are not presumed to be acausal, though the causes may not be known.
	en.wikipedia.org /wiki/Correlation (1834 words)

	PA 765: Canonical Correlation
		The canonical correlations are interpreted the same as Pearson's r: their square is the percent of variance in one set of variables explained by the other set along the dimension represented by the given canonical correlation (usually the first).
		The ratio of the eigenvalues is the ratio of explanatory importance of the canonical correlations (labeled "roots" in SPSS) which are extracted for the given data.
		Canonical correlation reflects the percent of variance in the dependent canonical variable explained by the independent canonical variable and is used when exploring relationships between the independent and the dependent set of variables.
	www2.chass.ncsu.edu /garson/pa765/canonic.htm (4752 words)

	History of Correlation and Association
		It is a measure of direction: a positive correlation indicates X, Y increase together; a negative correlation indicates one decreases as the other increases(4).
		Correlation is related to the slope of the regression line, but a particular correlation coefficient may translate into any slope depending on the units of the two variables.
		Finally, the calculation of the correlation coefficient depends upon a pair of continuous-valued variables (X,Y) measured in the same sample, with each specific observed value of X paired with a specific observed value of Y. This information may not available, or the format of the data may not meet this requirement.
	www.geocities.com /j_brutlag/corr.htm (4336 words)

	Classics in the History of Psychology -- Fisher (1925) Chapter 8
		To test if an observed value of the correlation ratio is significant is to test if the variation between arrays is significantly greater than is to be expected without correlation, from the variation within arrays, and this can be done from the analysis of variance (Table 52) by means of the table of z.
		then the correlation between y and Y is greater than the correlation of y with any other linear function of the independent variates, and thus measures, in a sense, the extent to which the value of y depends upon, or is related to, the combined variation of these variates.
		The case is in fact strictly comparable with that of the correlation ratio, and may be accurately treated by means of a table of the analysis of variance.
	psychclassics.yorku.ca /Fisher/Methods/chap8.htm (3157 words)

	THE CORRELATION COEFFICIENT
		This correlation squared is.45, which means that across the fourteen nations constituting the sample 45 percent of their variance on the two variables is in common (or 55 percent is not in common).
		Concerning positive correlation, this desire is clearly reflected in Figure 6.2c, for as the magnitude of a case on one variable is high, it is high on the other; as it is low on one, it is low on the other.
		The partial correlation of.13 is quite a drop from the original correlation of.61 between illiteracy and infant mortality, a sharp decrease from 37 percent to 2 percent covariation.
	www.hawaii.edu /powerkills/UC.HTM (11715 words)

	Effect of Ratio Correlation on Data Interpretation (Site not responding. Last check: 2007-10-20)
		Linear transformations of nonlinear models for estimating model parameters often suffer from ratio correlation, the replication of a common variable in the transformed model.
		Several models commonly used in environmental engineering were analyzed to show the effect of ratio correlation on the estimated model parameters.
		Since a casual reader often uses the correlation coefficient as a measure of the accuracy of a model, ratio correlation should be avoided in statistical data analysis.
	www.pubs.asce.org /WWWdisplay.cgi?8700224 (118 words)

	Glossary (Site not responding. Last check: 2007-10-20)
		The correlation between a continuous variable and a dichotomous variable, where we assume an underlying normality to the dichotomous variable.
		A correlation for ranked data which relies on the number of inversions of the rank order of one variable when the other variable is ranked in order.
		A variable whose correlation with the criterion is opposite in sign from its regression coefficient.
	www.uvm.edu /~dhowell/StatPages/Fundamentals/Glossary.html (5067 words)

	Appendix: Log-contrast principal components analysis and factor interpretation--a description of the method and tables ...
		The correlation matrix was solved for its latent roots (eigenvalues) and a new matrix specifying uncorrelated vectors (principal component axes) was calculated.
		Correlations are not free to range between -1 and +1.
		Centered log-ratio correlation coefficients are not comparable to correlation coefficients calculated from raw data, but the results of the principal components analyses (latent roots and vectors that specify factor loadings) can be inspected for similarities and differences.
	pubs.usgs.gov /of/2000/ofr-00-0474/HTML/Append.htm (1391 words)

	SHIVELA MIDDLE SCHOOL BAND - WHY MUSIC? (Site not responding. Last check: 2007-10-20)
		The lower the ratio of music teachers to pupils the higher the students' achievement on both the SAT and the ACT.
		The correlation between the pupil to music teacher ratio and ACT scores was -.47 and with SAT scores -.31 (the correlation between total pupil/teacher ratio and achievement was -.23).
		Although the same trend is observable in the overall pupil-teacher ratio, the correlation between music teacher ratio and the academic scores is even higher.
	www.murrieta.k12.ca.us /shivela/bdavidson/whyarch13.htm (180 words)

	The Sharpe Ratio
		While such a "return information ratio" may be useful as a descriptive statistic, it lacks a number of the key properties of what might be termed a "differential return information ratio" and may in some instances lead to wrong decisions.
		In the original applications of the ratio, where the benchmark is taken to be a one- period riskless asset, the differential return represents the payoff from a unit investment in the fund, financed by borrowing.
		Such lack of correlation is generally assumed for residual returns from an assumed factor model and hence applies to strategies in which long and short positions are combined to obtain zero exposures to all underlying factors in such a model.
	www.stanford.edu /~wfsharpe/art/sr/sr.htm (5543 words)

	Correlation (Site not responding. Last check: 2007-10-20)
		Correlation coefficients are statistics which can help to describe data sets which contain variables measured at the interval and ratio levels.
		Correlation coefficients are measures of association between two (or more) variables.
		Correlation is a measure of association that tests whether a relationship exists between two variables.
	www.csulb.edu /~msaintg/ppa696/696corrl.htm (476 words)

	Help-Analysis Programs in SDA
		Two interval-level statistics are given: R (the Pearson correlation coefficient), and Eta (the correlation ratio assuming the row variable to be the dependent variable).
		The standard error for the Pearson correlation is based on Fisher's Z, and it is calculated as the average distance of the upward and the downward confidence band for one standard error (based on the retransformation of Fisher's Z into Pearson's R).
		The t-statistic is calculated as the ratio of two quantities: The numerator is the difference between the correlation in the cell and the overall correlation.
	sda.berkeley.edu:7502 /HELPDOCS/helpan.htm (14564 words)

	Chapter 14 (Site not responding. Last check: 2007-10-20)
		In this case we should compute the correlation ratio rather than the coefficient of correlation.
		In this case, the coefficient of correlation is 0.
		The magnitude of the coefficient of determination indicates the proportion of variance in one variable, explained from knowledge of the second variable.The coefficient of determination is the primary information measure within the general linear model.
	www.public.asu.edu /~fmarti3/course/edp502/chap14.html (501 words)

	More Correlation Coeficients
		It is often the case that the data variables are not at the same level of measurement, or that the data might instead of being quantitative be catagorical (nominal or ordinal).
		In addition to correlation coefficients based on the product moment and thus related to the Pearson product moment correlation coefficient, there are coefficients which are instead measures of association which are also in common use.
		The cosine function, in its simpliest form, is the ratio of two side lengths in a right triangle, specifically, the side adjacent to the reference angle divided by the length of the hypotenuse.
	www.andrews.edu /~calkins/math/edrm611/edrm13.htm (1141 words)

	H Remote Sensing
		Zhang and colleagues proposed the Cross-Correlation Ratio method for improving wind estimates allowing the transverse wind to be determined with a single radar antenna.
		An advantage over current auto and cross- correlation techniques is a relative insensitivity to ground and point targets.
		Previously, wind estimates from SA measurements were obtained with the Full Correlation Analysis (FCA) method, which makes use of both cross-correlation and auto-correlation functions.
	www.rap.ucar.edu /asr2002/h-remote_sensing/h-remote_sensing.htm (1368 words)

	Performance of correlation estimators for spaced-antenna wind measurement in the presence of noise
		The theoretical accuracy of baseline winds, estimated using spaced antennas (SA) and a full correlation analysis (FCA) method to process signals in the presence of noise, is derived assuming horizontally isotropic refractive index perturbations with a horizontal scale small compared to the transmitting antenna diameter D.
		This performance of the FCA method is compared with the theoretical performance of another correlation-based approach (i.e., the cross-correlation ratio method, CCR).
		It is shown that the theoretical analysis is valid and the results can be applied to improve wind estimates obtained from SA signals contaminated with additive white noise.
	www.agu.org /pubs/crossref/2004/2003RS003022.shtml (303 words)

	SSRN-Hedge Ratio and Correlation between the Stock and the Futures Markets: Evidence from the Wavelet Analysis by ...
		Using this technique, we find that in the short- and long-run, there is a feedback relationship, while in the intermediate-run, the futures market leads the stock market.
		Furthermore, the magnitude of the correlation increases as the time scale increases, indicating that the stock market and the futures market of the All Ordinaries Index are found to be not fundamentally different.
		In, Francis and Kim, Sangbae, "Hedge Ratio and Correlation between the Stock and the Futures Markets: Evidence from the Wavelet Analysis".
	papers.ssrn.com /sol3/papers.cfm?abstract_id=393200 (329 words)

	Correlation ratio - Wikipedia, the free encyclopedia
		In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample.
		then the correlation ratio η (eta) is defined so as to satisfy
		is linear (which is certainly true when there are only two possibilities for x) this will give the same result as the square of the correlation coefficient; if not then the correlation ratio will be larger in magnitude, though still no more than 1 in magnitude.
	en.wikipedia.org /wiki/Correlation_ratio (186 words)

	The Correlation Coefficient (Site not responding. Last check: 2007-10-20)
		Correlation coefficient Regression line, image map (ps) grid
		Correlation coefficient Regression line, number of observations, image map (ps) grid
		Standard deviation of the sum of two correlated variables.
	noppa5.pc.helsinki.fi /koe/corr/index.html (52 words)

	Cross-correlation ratio method to estimate cross-beam wind and comparison with a full correlation analysis
		Cross-beam wind is usually estimated using a full correlation analysis (FCA) method applied to signals from spaced antennas.
		In this paper we present a cross-correlation ratio (CCR) method for wind measurements.
		The CCR method is illustrated using theory, and data obtained with the National Center for Atmospheric Research's multiple antenna profiling radar.
	www.agu.org /pubs/crossref/2003/2002RS002682.shtml (250 words)

	2001 Methodology for Total Population Estimates
		The estimates reported here for counties are the averages of estimates made using ratio-correlation, component-method II, and housing-unit methods.
		Ratio-correlation procedures utilize multiple regression techniques with the ratio of variable values for adjacent time periods rather than simply the variable values themselves being used as independent and dependent variables.
		After an extensive evaluation of the relative accuracy of alternative procedures (including difference-rate, ratio-correlation and rate-correlation methods) and an analysis of alternative variables, a simple ratio-correlation model was employed to complete the final estimates.
	txsdc.utsa.edu /tpepp/2001_txpopest_method.php (1596 words)

	RR-3378 : Multimodal Image Registration by Maximization of the Correlation Ratio
		In this paper, we address the determination of a new measure based on standard statistics from a theoretical point of view.
		We show that it naturally leads to a known concept of probability theory, the \textit{correlation ratio}.
		These results suggest that the correlation ratio provides a good trade-off between accuracy and robustness.
	www.inria.fr /rrrt/rr-3378.html (487 words)

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