Statnote 14: the correlation of two variables (Pearson's 'r')

Pearson's correlation coefficient (‘r’) is one of the most widely used of all statistics. Nevertheless, care needs to be used in interpreting the results because with large numbers of observations, quite small values of ‘r’ become significant and the X variable may only account for a small proportion of the variance in Y. Hence, ‘r squared’ should always be calculated and included in a discussion of the significance of ‘r’. The use of ‘r’ also assumes that the data follow a bivariate normal distribution (see Statnote 17) and this assumption should be examined prior to the study. If the data do not conform to such a distribution, the use of a non-parametric correlation coefficient should be considered. A significant correlation should not be interpreted as indicating ‘causation’ especially in observational studies, in which the two variables may be correlated because of their mutual correlations with other confounding variables.

Activated polarization pulling and de-correlation of signal and pump states of polarization in fiber Raman amplifier

We report on a theoretical study of activated polarization pulling and de-correlation of signal and pump states of polarization based on an advanced vector model of a fiber Raman amplifier accounting for random birefringence and two-scale fiber spinning. As a result, we have found that it is possible to provide de-correlation and simultaneously suppress PDG and PMD to 1.2 dB and 0.035 ps/km1/2 respectively.

The correlation of indentation size effect experiments with pyramidal and spherical indenters

Experiments were conducted in annealed iridium using pyramidal and spherical indenters over a wide range of load. For a Berkovich pyramidal indenter, the hardness increased with decreasing depth of penetration. However, for spherical indenters, hardness increased with decreasing sphere radius. Based on the number of geometrically necessary dislocations generated during indentation, a theory that takes into account the work hardening differences between pyramidal and spherical indenters is developed to correlate the indentation size effects measured with the two indenters. The experimental results verify the theoretical correlation.

The correlation of the indentation size effect measured with indenters of various shapes

Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results. © 2002 Elsevier Science Ltd. All rights reserved.

Measurement and correlation of the solubility of telmisartan (form A) in nine different solvents from 277.85 to 338.35 K

The solubility of telmisartan (form A) in nine organic solvents (chloroform, dichloromethane, ethanol, toluene, benzene, 2-propanol, ethyl acetate, methanol and acetone) was determined by a laser monitoring technique at temperatures from 277.85 to 338.35 K. The solubility of telmisartan (form A) in all of the nine solvents increased with temperature as did the rates at which the solubility increased except in chloroform and dichloromethane. The mole fraction solubility in chloroform is higher than that in dichloromethane, which are both one order of magnitude higher than those in the other seven solvents at the experimental temperatures. The solubility data were correlated with the modified Apelblat equation and λh equations. The results show that the λh equation is in better agreement with the experimental data than the Apelblat equation. The relative root mean square deviations (σ) of the λh equation are in the range from 0.004 to 0.45 %. The dissolution enthalpies, entropies and Gibbs energies of telmisartan in these solvents were estimated by the Van’t Hoff equation and the Gibbs equation. The melting point and the fusion enthalpy of telmisartan were determined by differential scanning calorimetry.

Correlation of detector dog alerts to cocaine decomposition products found in illicit forensic specimens

The volatile chemicals which comprise the odor of the illicit drug cocaine have been analyzed by adsorption onto activated charcoal followed by solvent elution and GC/MS analysis. A series of field tests have been performed to determine the dominant odor compound to which dogs alert. All of our data to date indicate that the dominant odor is due to the presence of methyl benzoate which is associated with the cocaine, rather than the cocaine itself. When methyl benzoate and cocaine are spiked onto U.S. currency, the threshold level of methyl benzoate required for a canine to signal an alert is typically 1-10 $\mu$g. Humans have been shown to have a sensitivity similar to dogs for methyl benzoate but with poorer selectivity/reliability. The dominant decomposition pathway for cocaine has been evaluated at elevated temperatures (up to 280$\sp\circ$C). Benzoic acid, but no detectable methyl benzoate, is formed. Solvent extraction and SFE were used to study the recovery of cocaine from U.S. currency. The amount of cocaine which could be recovered was found to decrease with time. ^

The correlation of structure and electronic properties near the surface of transition metal oxides

The strong couplings between different degrees of freedom are believed to be responsible for novel and complex phenomena discovered in transition metal oxides (TMOs). The physical complexity is directly responsible for their tunability. Creating surfaces/interfaces add an additional ' man-made' twist, approaching the quantum phenomena of correlated materials. ^ The dissertation focused on the structural and electronic properties in proximity of surface of three prototype TMO compounds by using three complementary techniques: scanning tunneling microscopy, angle-resolved photoelectron spectroscopy and low energy electron diffraction, particularly emphasized the effects of broken symmetry and imperfections like defects on the coupling between charge and lattice degrees of freedom. ^ Ca1.5Sr0.5RuO4 is a layered ruthenate with square lattice and at the boundary of magnetic/orbital instability in Ca2-xSrxRuO4. That the substitution of Sr 2+ with Ca2+ causing RuO6 rotation narrows the dxy band width and changes the Fermi surface topology. Particularly, the γ(dxy) Fermi surface sheet exhibited hole-like in Ca1.5Sr0.5RuO4 in contrast to electron-like in Sr2RuO4, showing a strong charge-lattice coupling. ^ Na0.75CoO2 is a layered cobaltite with triangular lattice exhibiting extraordinary thermoelectric properties. The well-ordered CoO2-terminated surface with random Na distribution was observed. However, lattice constants of the surface are smaller than that in bulk. The surface density of states (DOS) showed strong temperature dependence. Especially, an unusual shift of the minimum DOS occurs below 230 K, clearly indicating a local charging effect on the surface. ^ Cd2Re2O7 is the first known pyrochlore oxide superconductor (Tc ∼ 1K). It exhibited an unusual second-order phase transition occurring at TS1 = 200 K and a controversial first-order transition at TS2 = 120 K. While bulk properties display large anomalies at TS1 but rather subtle and sample-dependent changes at TS2, the surface DOS near the EF show no change at T s1 but a substantial increase below TS2---a complete reversal as the signature for the transitions. We argued that crystal imperfections, mainly defects, which were considerably enhanced at the surface, resulted in the transition at TS2. ^

An investigation of the strategies used by organizations participating in the welfare-to-work network program and correlation of the strategies with the retention data to determine best practices for job retention among former welfare recipients

This ex post facto study (N = 209) examined the relationships between employer job strategies and job retention among organizations participating in Florida welfare-to-work network programs and associated the strategies with job retention data to determine best practices. ^ An internet-based self-report survey battery was administered to a heterogeneous sampling of organizations participating in the Florida welfare-to-work network program. Hypotheses were tested through correlational and hierarchical regression analytic procedures. The partial correlation results linked each of the job retention strategies to job retention. Wages, benefits, training and supervision, communication, job growth, work/life balance, fairness and respect were all significantly related to job retention. Hierarchical regression results indicated that the training and supervision variable was the best predictor of job retention in the regression equation. ^ The size of the organization was also a significant predictor of job retention. Large organizations reported higher job retention rates than small organizations. There was no statistical difference between the types of organizations (profit-making and non-profit) and job retention. The standardized betas ranged from to .26 to .41 in the regression equation. Twenty percent of the variance in job retention was explained by the combination of demographic and job retention strategy predictors, supporting the theoretical, empirical, and practical relevance of understanding the association between employer job strategies and job retention outcomes. Implications for adult education and human resource development theory, research, and practice are highlighted as possible strategic leverage points for creating conditions that facilitate the development of job strategies as a means for improving former welfare workers’ job retention.^

A preliminary analysis of the correlation of food-web characteristics with hydrology and nutrient gradients in the southern Everglades

We estimated trophic position and carbon source for three consumers (Florida gar, Lepisosteus platyrhincus; eastern mosquitofish, Gambusia holbrooki; and riverine grass shrimp, Palaemonetes paludosus) from 20 sites representing gradients of productivity and hydrological disturbance in the southern Florida Everglades, U.S.A. We characterized gross primary productivity at each site using light/dark bottle incubation and stem density of emergent vascular plants. We also documented nutrient availability as total phosphorus (TP) in floc and periphyton, and the density of small fishes. Hydrological disturbance was characterized as the time since a site was last dried and the average number of days per year the sites were inundated for the previous 10 years. Food-web attributes were estimated in both the wet and dry seasons by analysis of δ15N (trophic position) and δ13C (food-web carbon source) from 702 samples of aquatic consumers. An index of carbon source was derived from a two-member mixing model with Seminole ramshorn snails (Planorbella duryi) as a basal grazing consumer and scuds (amphipods Hyallela azteca) as a basal detritivore. Snails yielded carbon isotopic values similar to green algae and diatoms, while carbon values of scuds were similar to bulk periphyton and floc; carbon isotopic values of cyanobacteria were enriched in C13compared to all consumers examined. A carbon source similar to scuds dominated at all but one study site, and though the relative contribution of scud-like and snail-like carbon sources was variable, there was no evidence that these contributions were a function of abiotic factors or season. Gar consistently displayed the highest estimated trophic position of the consumers studied, with mosquitofish feeding at a slightly lower level, and grass shrimp feeding at the lowest level. Trophic position was not correlated with any nutrient or productivity parameter, but did increase for grass shrimp and mosquitofish as the time following droughts increased. Trophic position of Florida gar was positively correlated with emergent plant stem density.

U-Pb geochronology of the Santa Cruz Formation (early Miocene) at the Río Bote and Río Santa Cruz (southernmost Patagonia, Argentina): Implications for the correlation of fossil vertebrate localities

© 2016 Elsevier Ltd.The early Miocene Santa Cruz Formation (SCF) in southern Patagonia hosts the Santacrucian South American Land Mammal Age (SALMA), whose age is known mainly from exposures along the Atlantic coast. Zircon U-Pb ages were obtained from intercalated tuffs from four inland sections of the SCF: 17.36 ± 0.63 Ma for the westernmost Río Bote locality, and 17.04 ± 0.55 Ma-16.32 ± 0.62 Ma for central Río Santa Cruz localities. All ages agree with the bounding age of underlying marine units and with equivalent strata in coastal exposures. New ages and available sedimentation rates imply time spans for each section of ~18.2 to 17.36 Ma for Río Bote and 17.45-15.63 Ma for central Río Santa Cruz (Burdigalian). These estimates support the view that deposition of the SCF began at western localities ~1 Ma earlier than at eastern localities, and that the central Río Santa Cruz localities expose the youngest SCF in southern Santa Cruz Province. Associated vertebrate faunas are consistent with our geochronologic synthesis, showing older (Notohippidian) taxa in western localities and younger (Santacrucian) taxa in central localities. The Notohippidian fauna (19.0-18.0 Ma) of the western localities is synchronous with Pinturan faunas (19.0-18.0 Ma), but older than Santacrucian faunas of the Río Santa Cruz (17.2-15.6 Ma) and coastal localities (18.0-16.2 Ma). The Santacrucian faunas of the central Río Santa Cruz localities temporally overlap Colloncuran (15.7 Ma), Friasian (16.5 Ma), and eastern Santacrucian faunas.