The Unit-of-Analysis Problem in Applications of Simple Correlation Analysis to Educational Research

1977 ◽  
Vol 2 (3) ◽  
pp. 171-186 ◽  
Author(s):  
Thomas R. Knapp

This paper summarizes the interrelationships among within-aggregate, between-aggregate, and total-group correlation coefficients, with artificial and “real-data” examples. It also discusses the relevance of correlation analyses at various levels of aggregation and some of the difficulties encountered in cross-level inference.

2018 ◽  
Vol 21 (2) ◽  
pp. 125-137
Author(s):  
Jolanta Stasiak ◽  
Marcin Koba ◽  
Marcin Gackowski ◽  
Tomasz Baczek

Aim and Objective: In this study, chemometric methods as correlation analysis, cluster analysis (CA), principal component analysis (PCA), and factor analysis (FA) have been used to reduce the number of chromatographic parameters (logk/logkw) and various (e.g., 0D, 1D, 2D, 3D) structural descriptors for three different groups of drugs, such as 12 analgesic drugs, 11 cardiovascular drugs and 36 “other” compounds and especially to choose the most important data of them. Material and Methods: All chemometric analyses have been carried out, graphically presented and also discussed for each group of drugs. At first, compounds’ structural and chromatographic parameters were correlated. The best results of correlation analysis were as follows: correlation coefficients like R = 0.93, R = 0.88, R = 0.91 for cardiac medications, analgesic drugs, and 36 “other” compounds, respectively. Next, part of molecular and HPLC experimental data from each group of drugs were submitted to FA/PCA and CA techniques. Results: Almost all results obtained by FA or PCA, and total data variance, from all analyzed parameters (experimental and calculated) were explained by first two/three factors: 84.28%, 76.38 %, 69.71% for cardiovascular drugs, for analgesic drugs and for 36 “other” compounds, respectively. Compounds clustering by CA method had similar characteristic as those obtained by FA/PCA. In our paper, statistical classification of mentioned drugs performed has been widely characterized and discussed in case of their molecular structure and pharmacological activity. Conclusion: Proposed QSAR strategy of reduced number of parameters could be useful starting point for further statistical analysis as well as support for designing new drugs and predicting their possible activity.


2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bowen Guan ◽  
Jiayu Wu ◽  
Chao Xie ◽  
Jianhong Fang ◽  
Haile Zheng ◽  
...  

This article intends to study the influence of macrotexture and microtexture on the skid resistance of four types of aggregates. For this purpose, fractal dimension (D), root mean square height (Rq), and Polished Stone Value (PSV) were tested. The Pearson correlation coefficients between PSV and D or Rq in the interval of different polishing cycles were calculated and analyzed with correlation analysis. The relationships between PSV and Rq were also established. The results showed that the PSV development was approximately divided into 3 stages including accelerated attenuation stage, decelerated attenuation stage, and stabilization stage. There is a critical point of the entire polishing cycles. When the number of the polishing cycles exceeds this critical point, microtexture replaces macrotexture to play a major role in the skid resistance of aggregates. In the accelerated attenuation stage, macrotexture plays a major role in the skid resistance of aggregates. In the decelerated attenuation stage and stabilization stage, microtexture gradually plays a major role in the skid resistance of aggregates. Because of roughest microtexture in the stabilization stage, bauxite can provide the highest levels of skid resistance for high friction surface treatment over the long-term period.


1982 ◽  
Vol 62 (4) ◽  
pp. 1049-1055 ◽  
Author(s):  
A. K. SHARMA ◽  
R. T. BERG

Relationships of scrotal circumference (SC) with body weight (BW) and backfat thickness (FT) as measured from scanograms were studied. A total of 935 observations on growing multibreed synthetic beef bulls on a postweaning performance test were available from a commercial herd for this study. Significant breed group, period and group × period interaction effects were noted on SC, BW and FT. BW and SC increased significantly during the test in all breed groups, while FT showed no change in three breed groups. Repeatability pooled across groups for SC was estimated as 0.72; 0.66 after adjusting for BW. Significant correlations were noticed between SC and BW within each breed group. Partial correlations between SC and BW at constant FT were not different from gross correlations. Linear regression coefficients of SC on BW were significant in all groups and showed heterogeneity among groups but not between periods within groups. Adjustments of SC for BW should, therefore, be breed group specific. BW alone accounted for considerable variation in SC, from 38 to 76%. Simple correlation coefficients between SC and FT were low and significant in only two groups. A significant but low positive relationship was noted between SC and FT at constant BW in a group fed a high-concentrate diet during the postweaning gain period, but there was no relationship in four other groups. Results indicated that the method of adjusting SC for FT as an indirect way of adjusting for scrotal fat was not satisfactory. Key words: Bulls, scrotal circumference, growth


Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 22 ◽  
Author(s):  
Jordi Belda ◽  
Luis Vergara ◽  
Gonzalo Safont ◽  
Addisson Salazar

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.


Author(s):  
Javier García-Rubio ◽  
Daniel Carreras ◽  
Sebastian Feu ◽  
Antonio Antunez ◽  
Sergio J. Ibáñez

The NBA Draft Combine includes a series of standardized measurements and drills that provide NBA teams with an opportunity to evaluate players. The purpose of this research was to identify the Combine tests that explain draft position and future performance in the NBA rookie season. Variables were selected from the previous categories of anthropometric measurements and strength and agility tests. A regression analysis was carried out. Combine variables, anthropometric and agility/strength variables were analyzed to explore their effect on draft position. Moreover, correlation analyses were performed to identify relationships among: (i) Combine anthropometric and strength and agility measures and game performance through game related statistics; and (ii) the draft position and game performance using Pearson’s correlation coefficients. Results show that the Combine test does not predict draft position, with the exception of hand width and height in frontcourt players, and standard vertical jump and running vertical jump. Future performance indicators were explained by several Combine tests in all players.


1994 ◽  
Vol 58 (393) ◽  
pp. 533-541 ◽  
Author(s):  
J. T. Temple ◽  
J. N. Walsh

AbstractRelative concentrations of elements in the minerals of fine-grained sediments can be inferred from element-mineral correlation coefficients. The technique is applied to the distribution of REE in Middle Ordovician shales from South Wales analysed by ICPAES, Leco C/S125 and XRD. Phosphate and chlorite show mid-REE enrichment; muscovite + biotite shows mid-REE depletion. The complementarity of the chlorite and muscovite + biotite patterns may be due to fractionation during diagenetic recrystallisation. Partial correlation analysis is used to infer the presence of zircon.


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