Francis Galton's Account of the Invention of Correlation

Stigler, Stephen M.

doi:10.1214/ss/1177012580

Cited by 436 publications

(213 citation statements)

References 7 publications

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“…(1) correlation of the time series at a seasonal timescale using the Pearson product-moment method (Rodgers and Nicewander, 1988;Stigler, 1989); (2) gridpoint correlation of monthly T and T E with NDVI and subsequent comparison of the spatial patterns; (3) assignment of gridpoint correlation values to each vegetation type using Geographic Information Systems (GIS) overlay techniques and summary statistics of the resulting correlation coefficients for each set and (4) for each gridpoint, calculation of the mean difference between T and T E ; summary TEMPERATURE AND EQUIVALENT TEMPERATURE 2047 statistics of the resulting difference values are computed for each land cover type.…”

Section: Methodsmentioning

confidence: 99%

Temperature and equivalent temperature over the United States (1979–2005)

Fall

Diffenbaugh

Niyogi

et al. 2010

Intl Journal of Climatology

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Temperature (T ) and equivalent temperature (T E ) trends over the United States from 1979 to 2005 and their correlation to land cover types are investigated using National Centers for Environmental Prediction North American Regional Reanalysis data, the Advanced Very High Resolution Radiometer (AVHRR) land use/cover classification, the National Land Cover Database (NLCD) 1992-2001 Retrofit Land Cover Change and the Normalised Difference Vegetation Index (NDVI) derived from AVHRR. Even though most of the magnitude of T E is explained by T , the moisture component induces larger trends and variability of T E relative to T . The contrast between pronounced temporal and spatial differences between T and T E at the near-surface level (2 m) and minor-to-no differences at 300-200 mb is a consistent pattern. This study therefore demonstrates that in addition to temperature, atmospheric heat content may help to quantify the differences between surface and tropospheric heating trends, and hence the impact of land cover types on the surface temperature changes. Correlations of T and T E with NDVI reveal that T E shows a stronger relationship to vegetation cover than T , especially during the growing season, with values that are significantly different and of opposite signs (−0.31 for T vs NDVI; 0.49 for T E vs NDVI). Our results suggest that land cover types influence both moisture availability and temperature in the lower atmosphere and that T E is larger in areas with higher physical evaporation and transpiration rates. As a result, T E can be used as an additional metric for analysing near-surface heating trends with respect to land cover types. Moreover, T E can be tested as a complementary variable for assessing the impact of land surface and boundary layer processes in re-analysis and weather/climate model studies.

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Section: Methodsmentioning

confidence: 99%

Temperature and equivalent temperature over the United States (1979–2005)

Fall

Diffenbaugh

Niyogi

et al. 2010

Intl Journal of Climatology

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“…Such analysis is commonly used for correlation analysis as a measure of the degree of linear dependence between two variables. This calculated coefficient (r) ranges between +1 and −1, where +1, 0, and −1 represent total (perfect) positive correlation, no correlation, and total negative correlation, respectively (Stigler 1989). These r values varied over the course of the recovery periods and therefore were calculated separately at each indicated time point (points in x-axis of Figures 2 and 3).…”

Section: Discussionmentioning

confidence: 99%

Acute stress-induced changes in hormone and lipid levels in mouse plasma

Ahn¹,

Bae²,

Yun³

2016

Vet. Med.

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ABSTRACT:We evaluated the conventional acute stress model in mice and investigated the stress-induced changes in concentrations of plasma lipids and hormones such as corticosterone (CORT), insulin, glucagon, triiodothyronine (T 3 ), and thyroxine (T 4 ). Stress induction for 120 min using tape-immobilisation and restraint resulted in an increase in the plasma levels of CORT, insulin, glucose, total cholesterol (TC), and low density lipoprotein-cholesterol compared with unstressed mice. Stress also resulted in a decrease in the concentrations of T 3 , T 4 , triglycerides (TG), and high density lipoprotein-cholesterol. However, the amount of glucagon did not change. Moreover, the concentrations of T 3 , T 4 , TC, TG, and lipoprotein cholesterol were maintained at constant levels over the recovery periods after stress induction; however, CORT, glucose, and insulin concentrations decreased as a function of time. Statistical correlations between the parameters that changed in response to acute stress were also investigated. In contrast, stress induction for 30 or 60 min did not cause substantial changes in the lipid profiles, although there were fluctuations in the levels of some hormones. This study thus introduces an appropriate model for the study of the acute stress response of lipids and hormones and our data suggest that acute stress affects the levels of plasma lipids, especially cholesterol, in mice.

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“…The absolute value of Pearson's classical correlation ρ(X, Y ) satisfies axioms (i) -(iv). On the history of ρ see Pearson (1920) and Stigler (1989). We know that ρ = 0 if and only if X, Y are independent, and |ρ| = 1 if and only if there is a linear relationship between X and Y .…”

Section: Important Dependence Measuresmentioning

confidence: 99%

Four simple axioms of dependence measures

Móri

Székely

2018

Metrika

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Recently new methods for measuring and testing dependence have appeared in the literature. One way to evaluate and compare these measures with each other and with classical ones is to consider what are reasonable and natural axioms that should hold for any measure of dependence. We propose four natural axioms for dependence measures and establish which axioms hold or fail to hold for several widely applied methods. All of the proposed axioms are satisfied by distance correlation. We prove that if a dependence measure is defined for all bounded nonconstant real valued random variables and is invariant with respect to all one-to-one measurable transformations of the real line, then the dependence measure cannot be weakly continuous. This implies that the classical maximal correlation cannot be continuous and thus its application is problematic. The recently introduced maximal information coefficient has the same disadvantage. The lack of weak continuity means that as the sample size increases the empirical values of a dependence measure do not necessarily converge to the population value.

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Francis Galton's Account of the Invention of Correlation

Cited by 436 publications

References 7 publications

Temperature and equivalent temperature over the United States (1979–2005)

Temperature and equivalent temperature over the United States (1979–2005)

Acute stress-induced changes in hormone and lipid levels in mouse plasma

Four simple axioms of dependence measures

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