The Weighted Rank Correlation Coefficient  $$r_W$$

2015 ◽  
pp. 9-27
Author(s):  
Joaquim Pinto da Costa
Keyword(s):  
Correlation Coefficient ◽  
Rank Correlation ◽  
Weighted Rank

The weighted rank correlation coefficient rW2 in the case of ties

2015 ◽  
Vol 99 ◽  
pp. 20-26 ◽  
Author(s):  
Joaquim Pinto Da Costa ◽  
Luís A.C. Roque ◽  
Carlos Soares
Keyword(s):  
Correlation Coefficient ◽  
Rank Correlation ◽  
Weighted Rank

scholarly journals Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings

2021 ◽  
Author(s):  
Antonella Plaia ◽  
Simona Buscemi ◽  
Mariangela Sciandra
Keyword(s):  
Correlation Coefficient ◽  
Real Life ◽  
Rank Correlation ◽  
Ranking Data ◽  
Weighted Distance ◽  
Preference Data ◽  
One To One ◽  
The One ◽  
Weighted Rank ◽  
Weighted Correlation

AbstractPreference data are a particular type of ranking data where some subjects (voters, judges,...) express their preferences over a set of alternatives (items). In most real life cases, some items receive the same preference by a judge, thus giving rise to a ranking with ties. An important issue involving rankings concerns the aggregation of the preferences into a “consensus”. The purpose of this paper is to investigate the consensus between rankings with ties, taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). By combining the structure of $$\tau _x$$ τ x proposed by Emond and Mason (J Multi-Criteria Decis Anal 11(1):17–28, 2002) with the class of weighted Kemeny-Snell distances, a position weighted rank correlation coefficient is proposed for comparing rankings with ties. The one-to-one correspondence between the weighted distance and the rank correlation coefficient is proved, analytically speaking, using both equal and decreasing weights.

Note on Use of phi as a Simplified Partial Rank Correlation Coefficient

1966 ◽  
Vol 18 (3) ◽  
pp. 973-974 ◽  
Author(s):  
Richard W. Johnson
Keyword(s):  
Correlation Coefficient ◽  
Rank Correlation ◽  
Partial Rank Correlation

Use of phi as a simplified partial rank correlation coefficient is described and illustrated.

scholarly journals An analysis of cloud overlap at a midlatitude atmospheric observation facility

2011 ◽  
Vol 11 (12) ◽  
pp. 5557-5567 ◽  
Author(s):  
L. Oreopoulos ◽  
P. M. Norris
Keyword(s):  
Correlation Coefficient ◽  
Seasonal Variations ◽  
Rank Correlation ◽  
Domain Size ◽  
Separation Distance ◽  
Cloud Fraction ◽  
Vertical Resolution ◽  
Clear Tendency ◽  
Systematic Relationships ◽  
Overlap Parameter

Abstract. An analysis of cloud overlap based on high temporal and vertical resolution retrievals of cloud condensate from a suite of ground instruments is performed at a mid-latitude atmospheric observation facility. Two facets of overlap are investigated: cloud fraction overlap, expressed in terms of a parameter "α" indicating the relative contributions of maximum and random overlap, and overlap of horizontal distributions of condensate, expressed in terms of the correlation coefficient of condensate ranks. The degree of proximity to the random and maximum overlap assumptions is also expressed in terms of a decorrelation length, a convenient scalar parameter for overlap parameters assumed to decay exponentially with separation distance. Both cloud fraction overlap and condensate overlap show significant seasonal variations with a clear tendency for more maximum overlap in the summer months. More maximum overlap is also generally observed when the domain size used to define cloud fractions increases. These tendencies also exist for rank correlations, but are significantly weaker. Hitherto unexplored overlap parameter dependencies are investigated by analyzing mean parameter differences at fixed separation distance within different layers of the atmospheric column, and by searching for possible systematic relationships between alpha and rank correlation. We find that for the same separation distance the overlap parameters are significantly distinct in different atmospheric layers, and that random cloud fraction overlap is usually associated with more randomly overlapped condensate ranks.

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