On the power of Chatterjee’s rank correlation

Biometrika ◽  
2021 ◽  
Author(s):  
H Shi ◽  
M Drton ◽  
F Han
Keyword(s):  
Correlation Coefficient ◽  
Computational Efficiency ◽  
Random Variables ◽  
Rank Correlation ◽  
Asymptotically Normal ◽  
Local Rotation ◽  
New Correlation ◽  
Testing Independence ◽  
Recent Attention ◽  
Tests Of Independence

Abstract Chatterjee (2021+) introduced a simple new rank correlation coefficient that has attracted much recent attention. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee’s new correlation coefficient to three established rank correlations that also facilitate consistent tests of independence, namely, Hoeffding’s D, Blum–Kiefer– Rosenblatt’s R, and Bergsma–Dassios–Yanagimoto’s τ *. We contrast their computational efficiency in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee’s coefficient is unfortunately rate sub-optimal compared to D, R, and τ *. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favor D, R, and τ * over Chatterjee’s new correlation coefficient for the purpose of testing independence.

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.

scholarly journals The relationship between the effectiveness of performing technical elements and indicators of static and dynamic balance in young acrobats 6-7 years old

2021 ◽  
Vol 7 (4) ◽  
pp. 58-68
Author(s):  
T. Chernykh ◽  
V. Mulyk ◽  
K. Mulyk ◽  
А. Skaliy ◽  
А. Ostrowski ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Dynamic Equilibrium ◽  
Dynamic Balance ◽  
Rank Correlation ◽  
Young Athletes ◽  
Spearman’S Rank Correlation ◽  
Spearman’S Rank Correlation Coefficient ◽  
Initial Stage ◽  
Equilibrium Test ◽  
The Relationship

Purpose: to determine the relationship between the performance of basic elements and indicators of static and dynamic balance in the training process of young acrobats 6-7 years. Material and methods. The study involved 16 young acrobats at the stage of initial training (age 6-7 years). All parents of the participants gave written consent for the participation of children in the study. The study involved testing the technique of performing basic elements of sports acrobatics and assessing the static and dynamic balance of young athletes. The relationship between (swallow, shoulder blade, forward squat, wheel (sideways overturning), bridges) and static and dynamic equilibrium tests was determined. Spearman's rank correlation coefficient method was used as a method of statistical analysis. Results. It is established that the largest relationship between the performance of basic elements and static balance in the basic exercises of young acrobats have: Romberg's test with the elements "Swallow", "Stand on the shoulders", "Bridge"; Biryuk test with elements "Swallow", "Wheel", "Bridge"; balance "Swallow" with elements "Swallow", "Wheel"; static equilibrium test with the elements "Swallow", "Rack on the shoulders", "Rolling forward with a squat", "Wheel". Reliable values ​​of the correlation coefficient were established between the tests of dynamic balance and the basic elements of sports acrobatics in young athletes 6-7 years, namely: "Swallow", "Flip forward with a squat", "Wheel" and "Bridge". The analysis of special tests of static and dynamic balance in mastering the basic elements of acrobatics at the first stage of long-term training makes it possible to use them to determine the level of coordination capabilities of young athletes and further improve the use of acrobatic exercises. Conclusions. A reliable relationship between the performance of basic exercises and indicators of static and dynamic balance in young acrobats at the initial stage of training. It is shown that the level of static and dynamic balance is of great importance for the assimilation and improvement of basic elements of technology by young acrobats 6-7 years. Static and dynamic balance tests can be used to individually build training programs and young acrobats. It is shown that sports acrobatics is a significant means of developing the balance of children 6-7 years.

scholarly journals The association between parameters of oral mucosal immunity and 25-hydroxyvitamin D in patients with rampant caries

2022 ◽  
Vol 20 (4) ◽  
pp. 32-38
Author(s):  
A. S. Putneva ◽  
T. M. Karavaeva ◽  
M. V. Maksimenya ◽  
P. P. Tereshkov ◽  
M. N. Mishchenko ◽  
...  
Keyword(s):  
Plasma Level ◽  
Correlation Coefficient ◽  
Rank Correlation ◽  
Control Group ◽  
Hydroxyvitamin D ◽  
Spearman’S Rank Correlation ◽  
Spearman’S Rank Correlation Coefficient ◽  
25 Hydroxyvitamin D ◽  
Tgf Β1 ◽  
Rampant Caries

Aim. To determine the saliva level of immunoregulatory proteins in patients with rampant caries and 25-hydroxyvitamin D (25(OH)D) deficiency and evaluate the association of their concentration with 25(OH)D plasma level.Materials and methods. The study was performed in two groups. The experimental group included 15 patients aged 20–22 years with rampant caries and the 25(OH)D plasma level of < 20 ng / ml. The control group encompassed 15 healthy age-matched volunteers with the 25(OH)D plasma level of 20–100 ng / ml. The concentrations of B7.2 (CD86), free active TGF-β1, CTLA-4, PD-1, Tim-3, LAG-3, IGFBP-4, and ICAM-1 were assessed using flow cytometry. The levels of LL-37 and secretory immunoglobulin A (sIgA) were measured using ELISA. The Spearman’s rank correlation coefficient was used to reveal a correlation between the indicated proteins and the 25(OH)D plasma level.Results. A decrease in B7.2 (CD86), PD-1, Tim-3, sIgA, and LL-37 and elevation of IGFBP-4 and ICAM-1 saliva levels were detected in patients with rampant caries and 25-hydroxyvitamin D deficiency. A positive Spearman’s rank correlation coefficient was revealed between plasma 25(OH)D and saliva levels of free active TGF-β1, CTLA4, B7.2 (CD86), LL-37, and sIgA. A negative correlation was revealed between 25(OH)Dand ICAM-1.Conclusion. 25(OH)D deficiency in patients with rampant caries is associated with decreased levels of B7.2 (CD86), PD-1, Tim-3, sIgA, and LL-37 and elevated levels of IGFBP-4 and ICAM-1 in the saliva. 

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