Statnote 15: the non-parametric correlation coefficients

If in a correlation test, one or both variables are small whole numbers, scores based on a limited scale, or percentages, a non-parametric correlation coefficient should be considered as an alternative to Pearson’s ‘r’. Kendall’s t and Spearman’s rs are similar tests but the former should be considered if the analysis is to be extended to include partial correlations. If the data contain many tied values, then gamma should be considered as a suitable test.

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.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Volatility transmission between stock and bond markets

A two-factor no-arbitrage model is used to provide a theoretical link between stock and bond market volatility. While this model suggests that short-term interest rate volatility may, at least in part, drive both stock and bond market volatility, the empirical evidence suggests that past bond market volatility affects both markets and feeds back into short-term yield volatility. The empirical modelling goes on to examine the (time-varying) correlation structure between volatility in the stock and bond markets and finds that the sign of this correlation has reversed over the last 20 years. This has important implications far portfolio selection in financial markets. © 2005 Elsevier B.V. All rights reserved.

Correlates of depression in bipolar disorder

We analyse time series from 100 patients with bipolar disorder for correlates of depression symptoms. As the sampling interval is non-uniform, we quantify the extent of missing and irregular data using new measures of compliance and continuity. We find that uniformity of response is negatively correlated with the standard deviation of sleep ratings (ρ = -0.26, p = 0.01). To investigate the correlation structure of the time series themselves, we apply the Edelson-Krolik method for correlation estimation. We examine the correlation between depression symptoms for a subset of patients and find that self-reported measures of sleep and appetite/weight show a lower average correlation than other symptoms. Using surrogate time series as a reference dataset, we find no evidence that depression is correlated between patients, though we note a possible loss of information from sparse sampling. © 2013 The Author(s).

Lipoplexes formulation and optimisation:in vitro transfection studies reveal no correlation with in vivo vaccination studies

The aim of these studies was to compare the effect of liposome composition on physico-chemical characteristics and transfection efficacy of cationic liposomes both in vitro and in vivo. Comparison between 4 popularly used cationic lipids, showed 3b-N-(dimethylaminoethyl)carbamate (DC-Chol) to promote the highest transfect levels in cells in vitro with levels being at least 6 times higher than those of 1,2-di-O-octadecenyl-3-trimethylammonium propane (DOTMA). 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP), and dimethyldioctadecylammonium (DDA) and approximately twice as efficient as dipalmitoyl-trimethylammonium-propane (DPTAP). To establish the role of the helper lipid, DC-Chol liposomes were formulated in combination with either 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) or cholesterol (Chol) (1:1 molar ratio) with and without the addition of phosphatidyl choline. The choice of helper lipid incorporated within the bilayer was found to influence the formation of complexes, their resultant structure and their transfection efficiency in vitro, with SUV-DNA complexes containing optimum levels of DOPE giving higher transfection than those containing cholesterol. The inclusion of PC within the formulation also reduced transfection efficiency in vitro. However, when administered in vivo, SUV-DNA complexes composed of PC:Chol:DC-Chol at a molar ratio of 16:8:4 micromole/ml were the most effective at inducing splenocyte proliferation upon exposure to antigen in comparison to control spleens. These results demonstrate that there is no in vitro/in vivo correlation between the transfection efficacy of these liposome formulations and in vitro transfection in the above cell model cannot be taken as a reliable indicator for in vivo efficacy of DNA vaccines.

An Exploration of parametric software cost estimating models for Jackson Systems Development

Most parametric software cost estimation models used today evolved in the late 70's and early 80's. At that time, the dominant software development techniques being used were the early 'structured methods'. Since then, several new systems development paradigms and methods have emerged, one being Jackson Systems Development (JSD). As current cost estimating methods do not take account of these developments, their non-universality means they cannot provide adequate estimates of effort and hence cost. In order to address these shortcomings two new estimation methods have been developed for JSD projects. One of these methods JSD-FPA, is a top-down estimating method, based on the existing MKII function point method. The other method, JSD-COCOMO, is a sizing technique which sizes a project, in terms of lines of code, from the process structure diagrams and thus provides an input to the traditional COCOMO method.The JSD-FPA method allows JSD projects in both the real-time and scientific application areas to be costed, as well as the commercial information systems applications to which FPA is usually applied. The method is based upon a three-dimensional view of a system specification as opposed to the largely data-oriented view traditionally used by FPA. The method uses counts of various attributes of a JSD specification to develop a metric which provides an indication of the size of the system to be developed. This size metric is then transformed into an estimate of effort by calculating past project productivity and utilising this figure to predict the effort and hence cost of a future project. The effort estimates produced were validated by comparing them against the effort figures for six actual projects.The JSD-COCOMO method uses counts of the levels in a process structure chart as the input to an empirically derived model which transforms them into an estimate of delivered source code instructions.

A survey of some small firms in the rural areas of England: their structure and functions, with special reference to factors that affect their development

This study was concerned with the structure, functions and development, especially the performance, of some rural small firms associated with the Council for Small Industries in Rural Areas (C?SIRA) of England. Forty firms were used as the main basis of analysis. For some aspects of the investigation, however, data from another 54 firms, obtained indirectly through nine CoSIRA Organisers, were also used. For performance-analysis, the 40 firms were firstly ranked according to their growth and profitability rates which were calculated from their financial data. Then each of the variables hypothesised to be related to performance was tested to ascertain its relationship with performance, using the Spearman's Rank Correlation technique. The analysis indicated that each of the four factors .. the principal, the firm itself, its management, and the environment - had a bearing upon the performance of the firm. Within the first factor, the owner-manager's background and attitudes were found to be most important; in the second, the firm's size, age and scope of activities were also found to be correlated with performance; with respect to the third, it was revealed that firms which practised some forms of systems in planning, control and costing performed better than those which did not and, finally with respect to the fourth factor, it was found that some of the services provided by CoSIRA, especially credit finance, were facilitative to the firm's performance. Another significant facet of the firms highlighted by the study was their multifarious roles. These, meeting economic, psychological, sociological and political needs, were considered to be most useful to man and his society. Finally, the study has added light to the structural characteristics of the sampled firms, including various aspects of their development, orientation and organisation, as well as their various structural strengths and weakness. ' .

Atomic structure of the two intermediate phase glasses SiSe4 and GeSe4

The microscopic origin of the intermediate phase in two prototypical covalently bonded AxB1-x network glass forming systems, where A=Ge or Si, B=Se, and 0=x=1, was investigated by combining neutron diffraction with first-principles molecular-dynamics methods. Specifically, the structure of glassy GeSe4 and SiSe4 was examined, and the calculated total structure factor and total pair-correlation function for both materials are in good agreement with experiment. The structure of both glasses differs markedly from a simple model comprising undefective AB4 corner-sharing tetrahedra in which all A atoms are linked by B2 dimers. Instead, edge-sharing tetrahedra occur and the twofold coordinated Se atoms form three distinct structural motifs, namely, Se-Se2, Se-SeGe (or Se-SeSi), and Se-Ge2 (or Se-Si2). This identifies several of the conformations that are responsible for the structural variability in GexSe1-x and SixSe1-x glasses, a quantity that is linked to the finite width of the intermediate phase window.

The effect of zinc and titanium on the structure of calcium-sodium phosphate based glass

An array of different structural probes has been used to define the effect of adding Zn and Ti to a sodium-calcium phosphate glass. X-ray absorption spectroscopy at the Zn K-edge suggests that the Zn atoms occupy mixed (4- and 6-fold) sites within the glass matrix. X-ray diffraction reveals a feature at 2.03 angstrom that develops with the addition of Zn and Ti and is consistent with Zn-O and Ti-O near-neighbour distances. Neutron diffraction is used to resolve two distinct P-O distances and highlights the decrease in P center dot center dot center dot P coordination number from 2.0 to 1.7 as the Ti metal concentration rises, which is attributed to the O/P fraction moving away from the metaphosphate value of 3.0 to 3.1 with the addition of Ti. Other correlations, such as those associated with CaO(x) and NaO(x) polyhedra, remain largely unaffected. These results suggest that the network forming P center dot center dot center dot P correlation is most disrupted, with the disorder parameter rising from 0.07 to 0.10 angstrom with the additional modifiers. Zn appears to be introduced into the network as a direct replacement for Ca and causes no structural variation over the composition range studied.

True chemical shift correlation maps:a TOCSY experiment with pure shifts in both dimensions

Signal resolution in H NMR is limited primarily by multiplet structure. Recent advances in pure shift NMR, in which the effects of homonuclear couplings are suppressed, have allowed this limitation to be circumvented in 1D NMR, gaining almost an order of magnitude in spectral resolution. Here for the first time an experiment is demonstrated that suppresses multiplet structure in both domains of a homonuclear two-dimensional spectrum. The principle is demonstrated for the TOCSY experiment, generating a chemical shift correlation map in which a single peak is seen for each coupled relationship, but the principle is general and readily extensible to other homonuclear correlation experiments. Such spectra greatly simplify manual spectral analysis and should be well-suited to automated methods for structure elucidation. © 2010 American Chemical Society.

COOPER-framework:a unified process for non-parametric projects

Practitioners assess performance of entities in increasingly large and complicated datasets. If non-parametric models, such as Data Envelopment Analysis, were ever considered as simple push-button technologies, this is impossible when many variables are available or when data have to be compiled from several sources. This paper introduces by the 'COOPER-framework' a comprehensive model for carrying out non-parametric projects. The framework consists of six interrelated phases: Concepts and objectives, On structuring data, Operational models, Performance comparison model, Evaluation, and Result and deployment. Each of the phases describes some necessary steps a researcher should examine for a well defined and repeatable analysis. The COOPER-framework provides for the novice analyst guidance, structure and advice for a sound non-parametric analysis. The more experienced analyst benefits from a check list such that important issues are not forgotten. In addition, by the use of a standardized framework non-parametric assessments will be more reliable, more repeatable, more manageable, faster and less costly. © 2010 Elsevier B.V. All rights reserved.

The structure of the rare-earth phosphate glass(Sm2O3)0.205(P2O5)0.795 studied by anomalous dispersion neutron diffraction

The role of the Sm3+ ions in the structure of vitreous Sm2O3•4P2O5 has been investigated using the neutron diffraction anomalous dispersion technique, which employs the wavelength dependence of the real and imaginary parts of the neutron scattering length close to an absorption resonance. The data described here represent the first successful complete neutron anomalous dispersion study on an amorphous material. This experimental methodology permits one to determine exclusively the closest Sm• •• Sm separation. Knowledge of the R•••R (R = rare-earth) pairwise correlation is key to understanding the optical and magnetic properties of rare-earth phosphate glasses. The anomalous difference correlation function, ΔT''(r), shows a dominant feature pertaining to a Sm•••Sm separation, centred at 4.8 Å. The substantial width and marked asymmetry of this peak indicates that the minimum approach of Sm3+ ions could be as close as 4 Å. Information on other pairwise correlations is also revealed via analysis of T (r) and ΔT (r) correlation functions: Sm3+ ions display an average co-ordination number, n Sm(O), of 7, with a mean Sm–O bond length of 2.375(5) Å whilst the PO4 tetrahedra have a mean P–O bond length of 1.538(2) Å. Second- and third-neighbour correlations are also identified. These results corroborate previous findings. Such consistency lends support to the application of the anomalous dispersion technique to determine separations.

Network effects, network structure and consumer interaction in mobile telecommunications in Europe and Asia

This paper estimates the importance of (tariff-mediated) network effects and the impact of a consumer's social network on her choice of mobile phone provider. The study uses network data obtained from surveys of students in several European and Asian countries. We use the Quadratic Assignment Procedure, a non-parametric permutation test, to adjust for the particular error structure of network data. We find that respondents strongly coordinate their choice of mobile phone providers, but only if their provider induces network effects. This suggests that this coordination depends on network effects rather than on information contagion or pressure to conform to the social environment.

Correlation between p-GaN growth environment with electrical and optical properties of blue LEDs

Two blue (450 nm) light–emitting diodes (LED), which only differ in top p-GaN layer growth conditions, were comparatively investigated. I-V, C-V, TLM, Electroluminescence (EL) and Photoluminescence (PL) techniques were applied to clarify a correlation between MOCVD carrier gas and internal properties. The A-structure grown in the pure N2 environment demonstrated better parameters than the B-structure grown in the N2/H2 (1:1) gas mixture. The mixed growth atmosphere leaded to an increase of sheet resistances of p-GaN layer. EL and PL measurements confirmed the advantage of the pure N2 utilization, and C(VR) measurement pointed the increase of static charge concentration near the p-GaN interface in the B structure.