A cophenetic correlation coefficient for Tocher's method

The objective of this work was to propose a way of using the Tocher's method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices - one obtained with the generalized squared Mahalanobis distance and the other with the Euclidean distance - between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher's method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher's method were higher than those obtained with the hierarchical methods (Ward's algorithm and average linkage - UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher's method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

The electron antineutrino angular correlation coefficient a in free neutron decay: Testing the standard model with the aSPECT-spectrometer

The beta-decay of free neutrons is a strongly over-determined process in the Standard Model (SM) of Particle Physics and is described by a multitude of observables. Some of those observables are sensitive to physics beyond the SM. For example, the correlation coefficients of the involved particles belong to them. The spectrometer aSPECT was designed to measure precisely the shape of the proton energy spectrum and to extract from it the electron anti-neutrino angular correlation coefficient "a". A first test period (2005/ 2006) showed the “proof-of-principles”. The limiting influence of uncontrollable background conditions in the spectrometer made it impossible to extract a reliable value for the coefficient "a" (publication: Baessler et al., 2008, Europhys. Journ. A, 38, p.17-26). A second measurement cycle (2007/ 2008) aimed to under-run the relative accuracy of previous experiments (Stratowa et al. (1978), Byrne et al. (2002)) da/a =5%. I performed the analysis of the data taken there which is the emphasis of this doctoral thesis. A central point are background studies. The systematic impact of background on a was reduced to da/a(syst.)=0.61 %. The statistical accuracy of the analyzed measurements is da/a(stat.)=1.4 %. Besides, saturation effects of the detector electronics were investigated which were initially observed. These turned out not to be correctable on a sufficient level. An applicable idea how to avoid the saturation effects will be discussed in the last chapter.

A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

(Table 2) Similarity Indexes (Pearson's correlation coefficient) of the silicoflagellate assemblages of IODP Exp302

The silicoflagellate and ebridian assemblages in early middle Eocene Arctic cores obtained by IODP Expedition 302 (ACEX) were studied in order to decipher the paleoceanography of the upper water column. The assemblages in Lithologic Unit 2 (49.7-45.1 Ma), one of the biosiliceous intervals, were usually endemic as compared to the assemblages that occurred outside of the Arctic Ocean. The presence of these endemic assemblages is probably due to a unique environmental setting, controlled by the degree of mixing between the low-salinity Arctic waters and relatively high salinity waters supplied from outside the Arctic Ocean, such as the Atlantic and possibly the Western Siberian Sea. Using the basin-to-basin fractionation model, the early middle Eocene Arctic Ocean corresponds to an estuarine circulation type, which includes the modern-day Black Sea. The abundant down-core occurrence of ebridians strongly suggests the past presence of low-salinity waters, and may indicate that low oxygen concentrations prevailed in the euphotic layer, on the basis of the ecology of the modern ebridian Hermesinum adriaticum.

Statnote 32 : the partial correlation coefficient

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. The most important statistic used to measure the degree of correlation between two variables is Pearson’s ‘product moment correlation coefficient’ (‘r’). The correlation between two variables may be due to their common relation to other variables. Hence, investigators using correlation studies need to be alert to the possibilities of spurious correlation and the methods of ‘partial correlation’ are one method of taking this into account. This statnote applies the methods of partial correlation to three scenarios. First, to a fairly obvious example of a spurious correlation resulting from the ‘size effect’ involving the relationship between the number of general practitioners (GP) and the number of deaths of patients in a town. Second, to the relationship between the abundance of the nitrogen-fixing bacterium Azotobacter in soil and three soil variables, and finally, to a more complex scenario, first introduced in Statnote 24involving the relationship between the growth of lichens in the field and climate.

Statnote 33:the intra-class correlation coefficient

The intra-class correlation coefficient (ICC or ri) is a method of measuring correlation when the data are paired and therefore, should be used when experimental units are organised into groups. A useful analogy is with the unpaired or paired ‘t’ test to compare the differences between the means of two groups. In studies of reproducibility, there may actually be little difference between the ICC and Pearson’s ‘r’ for ‘true’ repeated measurements. If, however, there is a systematic change in the measurements made on the first compared with the second occasion, then the ICC will be significantly less than ‘r’, and less confidence would be placed in the reproducibility of the results.

Correlation Between Testosterone And Psa Kinetics In Metastatic Prostate Cancer Patients Treated With Diverse Chemical Castrations.

To assess total testosterone and prostatic-specific antigen (PSA) kinetics among diverse chemical castrations, advanced-stage prostate cancer patients were randomized into three groups of 20: Group 1, Leuprolide 3.75 mg; Group 2, Leuprolide 7.5 mg; and Group 3, Goserelin 3.6 mg. All groups were treated with monthly application of the respective drugs. The patients' levels of serum total testosterone and PSA were evaluated at two time periods: before the treatment and 3 months after the treatment. Spearman's rank correlation coefficient was utilized to verify the hypothesis of linear correlation between total testosterone and PSA levels. At the beginning the patients' age, stage, grade, PSA, and total testosterone were similar within the three groups, with median age 72, 70, and 70 years in Groups 1, 2, and 3, respectively. Three months after the treatment, patients who received Leuprolide 7.5 mg presented significantly lower median total testosterone levels compared with Goserelin 3.6 mg and Leuprolide 3.75 mg (9.5 ng/dL vs. 20.0 ng/dL vs. 30.0 ng/dL, respectively; p = .0072), while those who received Goserelin 3.6 mg presented significantly lower PSA levels compared with Leuprolide 7.5 mg and Leuprolide 3.75 mg (0.67 vs. 1.86 vs. 2.57, respectively; p = .0067). There was no linear correlation between total testosterone and PSA levels. Overall, regarding castration levels of total testosterone, 28.77% of patients did not obtain levels ≤50 ng/dL and 47.80% did not obtain levels ≤20 ng/dL. There was no correlation between total testosterone and PSA kinetics and no equivalence among different pharmacological castrations.

Correlation between margin fit and microleakage in complete crowns cemented with three luting agents

Microleakage can be related to margin misfit. Also, traditional microleakage techniques are time-consuming. This study evaluated the existence of correlation between in vitro margin fit and a new microleakage technique for complete crowns cemented with 3 different luting agents. Thirty human premolars were prepared for full-coverage crowns with a convergence angle of 6 degrees, chamfer margin of 1.2 mm circumferentially, and occlusal reduction of 1.5 mm. Ni-Cr cast crowns were cemented with either zinc phosphate (ZP) (S.S. White), resin-modified glass-ionomer (RMGI) (Rely X Luting Cement) or a resin-based luting agent (RC) (Enforce). Margin fit (seating discrepancy and margin gap) was evaluated according to criteria in the literature under microscope with 0.001 mm accuracy. After thermal cycling, crowns were longitudinally sectioned and microleakage scores at tooth-cement interface were obtained and recorded at ×100 magnification. Margin fit parameters were compared with the one-way ANOVA test and microleakage scores with Kruskal-Wallis and Dunn's tests (alpha=0.05). Correlation between margin fit and microleakage was analyzed with the Spearman's test (alpha=0.05). Seating discrepancy and marginal gap values ranged from 81.82 µm to 137.22 µm (p=0.117), and from 75.42 µm to 78.49 µm (p=0.940), respectively. Marginal microleakage scores were ZP=3.02, RMGI=0.35 and RC=0.12 (p<0.001), with no differences between RMGI and RC scores. The correlation coefficient values ranged from -0.27 to 0.30 (p>0.05). Conclusion: Margin fit parameters and microleakage showed no strong correlations; cast crowns cemented with RMGI and RC had lower microleakage scores than ZP cement.

A new correlation between electronic parameters and glass forming ability of metallic alloys

A quantitative correlation between the glass forming ability and the electronic parameters of metallic alloys is presented. It is found that the critical cooling rate for glass formation (R(c)) correlates well with the average work function difference (Delta phi) and the average electron density difference (Delta n(ws)(1/3)) among the constituent elements of the investigated alloys. A correlation coefficient (R(2)) of 0.77 was found for 68 alloys in 30 metallic systems, which is better than the previous proposed correlation between the glass forming ability and the average Pauling electronegativity difference.

Correlation between mastitis occurrence and the count of microorganisms in bulk raw milk of bovine dairy herds in four selective culture media

Milk is the normal secretion of the mammary gland, practically free of colostrum and obtained by the complete milking of oil(? or more healthy animals. Mastitis is all inflammatory process of the mammary gland and it may cause alterations in the milk. The present work aimed to verify whether it is possible, by means of the counts of microorganism in the bulk raw milk ill four selective culture media, to establish a correlation with the occurrence of mastitis and therefore, to monitor this disease in bovine dairy herds. The following selective culture media were Used: KF Streptococcus Agar, Edwards Agar, Baird-Parker Agar, Blood Agar plus potassium tellurite. Spearman`s correlation coefficient was calculated in order to compare the Occurrence of mastitis (percentage) in each herd with respective selective culture media counts of microorganisms in bulk raw milk. Thirty-six possibilities were analysed (Tamis and CMT-positive rates were compared with the log-transformed count in four selective Culture media) and there was a negative correlation between Tamis 3 and the Baird-Parker Agar plate count. The total results of microbiological tests showed that there were three correlations of the counts in selective culture media. Fifty-two possibilities were analysed and there was a negative correlation between no-bacteria I-growth mastitis rates and log(10) of KF Streptoccocus Agar plate Count and there were two positive correlations between coagulase-positive staphylococci and log(10) of Baird-Parker Agar plate count and Blood Agar plus potassium tellurite plate count.

Correlation between turbidimetric and nephelometric methods of measuring C-reactive protein in patients with unstable angina or non-ST elevation acute myocardial infarction

OBJECTIVE: To evaluate the performance of the turbidimetric method of C-reactive protein (CRP) as a measure of low-grade inflammation in patients admitted with non-ST elevation acute coronary syndromes (ACS). METHODS: Serum samples obtained at hospital arrival from 68 patients (66±11 years, 40 men), admitted with unstable angina or non-ST elevation acute myocardial infarction were used to measure CRP by the methods of nephelometry and turbidimetry. RESULTS: The medians of C-reactive protein by the turbidimetric and nephelometric methods were 0.5 mg/dL and 0.47 mg/dL, respectively. A strong linear association existed between the 2 methods, according to the regression coefficient (b=0.75; 95% C.I.=0.70-0.80) and correlation coefficient (r=0.96; P<0.001). The mean difference between the nephelometric and turbidimetric CRP was 0.02 ± 0.91 mg/dL, and 100% agreement between the methods in the detection of high CRP was observed. CONCLUSION: In patients with non-ST elevation ACS, CRP values obtained by turbidimetry show a strong linear association with the method of nephelometry and perfect agreement in the detection of high CRP.

Correlation of wear in vivo and six laboratory wear methods.

OBJECTIVE: We examined the correlation between clinical wear rates of restorative materials and enamel (TRAC Research Foundation, Provo, USA) and the results of six laboratory test methods (ACTA, Alabama (generalized, localized), Ivoclar (vertical, volumetric), Munich, OHSU (abrasion, attrition), Zurich). METHODS: Individual clinical wear data were available from clinical trials that were conducted by TRAC Research Foundation (formerly CRA) together with general practitioners. For each of the n=28 materials (21 composite resins for intra-coronal restorations [20 direct and 1 indirect], 5 resin materials for crowns, 1 amalgam, enamel) a minimum of 30 restorations had been placed in posterior teeth, mainly molars. The recall intervals were up to 5 years with the majority of materials (n=27) being monitored, however, only for up to 2 years. For the laboratory data, the databases MEDLINE and IADR abstracts were searched for wear data on materials which were also clinically tested by TRAC Research Foundation. Only those data for which the same test parameters (e.g. number of cycles, loading force, type of antagonist) had been published were included in the study. A different quantity of data was available for each laboratory method: Ivoclar (n=22), Zurich (n=20), Alabama (n=17), OHSU and ACTA (n=12), Munich (n=7). The clinical results were summed up in an index and a linear mixed model was fitted to the log wear measurements including the following factors: material, time (0.5, 1, 2 and 3 years), tooth (premolar/molar) and gender (male/female) as fixed effects, and patient as random effect. Relative ranks were created for each material and method; the same was performed with the clinical results. RESULTS: The mean age of the subjects was 40 (±12) years. The materials had been mostly applied in molars (81%) and 95% of the intracoronal restorations were Class II restorations. The mean number of individual wear data per material was 25 (range 14-42). The mean coefficient of variation of clinical wear data was 53%. The only significant correlation was reached by OHSU (abrasion) with a Spearman r of 0.86 (p=0.001). Zurich, ACTA, Alabama generalized wear and Ivoclar (volume) had correlation coefficients between 0.3 and 0.4. For Zurich, Alabama generalized wear and Munich, the correlation coefficient improved if only composites for direct use were taken into consideration. The combination of different laboratory methods did not significantly improve the correlation. SIGNIFICANCE: The clinical wear of composite resins is mainly dependent on differences between patients and less on the differences between materials. Laboratory methods to test conventional resins for wear are therefore less important, especially since most of them do not reflect the clinical wear.

Repeatability, correlation and path analysis of physical and chemical characteristics of peach fruits

This study aimed to determine the number of measurements necessary to evaluate physical and chemical characteristics of peach fruits, study the relationships between them and their direct and indirect effects on the content of ascorbic acid and total carotenoids. The characteristics skin and pulp color, fruit weight, suture, equatorial and polar diameters, firmness, soluble solids (SS), titratable acidity (TA), SS/TA ratio, ascorbic acid and total carotenoids were evaluated in 39 cultivars of peach and 3 cultivars of nectarine from the orchard of the Universidade Federal de Viçosa. The repeatability coefficient was estimated by ANOVA and CPCOR. Phenotypic correlation coefficients (rf) were estimated and, after the multicollinearity diagnostics, they were unfolded to direct and indirect effects of the explanatory variables on the response variable using path analysis. There was agreement on the magnitude of repeatability coefficients obtained by the two methods; however, they varied among the 14 characteristics. The highest correlations were found between FW, SD, ED and PD. Seven fruits are sufficient to evaluate the physical and chemical characteristics of peach with a correlation coefficient of 90%. The characteristics considered in the path diagrams (b* skin, hº skin, b* pulp, hº pulp, ED, PD, FIR, SS, SS/AT and TC) are not the main determinants of the ascorbic acid. The yellow hue of the pulp (hº pulp) has the potential to be used in indirect selection for total carotenoids.