Improved likelihood ratio tests and pearson chi-square tests for independence in two dimensional contingency tables

1986 ◽  
Vol 15 (6) ◽  
pp. 1875-1888 ◽  
Author(s):  
B.S. Hosmane
2018 ◽  
Vol 62 (1) ◽  
pp. 111-121
Author(s):  
Raúl Hileno ◽  
Antonio García-de-Alcaraz ◽  
Bernat Buscà ◽  
Cristòfol Salas ◽  
Oleguer Camerino

Abstract In volleyball, attack coverage is one of the play actions most neglected in coaching and research. The purpose of this study was to find out which attack coverage systems are used by high-level men’s teams in different game situations and the characteristics of the most effective systems. We analysed 15 matches from the 2010 Men’s Pan-American Volleyball Cup, with a total of 1,415 coverage actions. Chi-square tests for independence, adjusted residuals analysis and calculations of standardised mean difference were performed. The results show that high-level men’s volleyball uses many coverage systems other than the traditional 3-2-0 and 2-3-0. At this level of play, the most frequent systems were 1-3-1 and 1-2-2, which occurred significantly often at the culmination of a third-tempo attack at the wing. The most effective systems consisted of three coverage lines, with fewer than five players covering the spiker and at least one player in the first coverage line, in both the attack and counterattack phases. Given the large number of coverage systems identified in different game situations, we recommend flexible, loosely structured training in these systems, based on a set of guiding principles that all players on a team must internalise for the specific position they are playing. Regarding the systems’ efficacy, the main watchword is that on each coverage line there should always be at least one player, but the first line should not be exposed.


1966 ◽  
Vol 61 (316) ◽  
pp. 965-975 ◽  
Author(s):  
Rosa C. Meng ◽  
Douglas G. Chapman

2006 ◽  
Vol 131 (1) ◽  
pp. 53-58 ◽  
Author(s):  
Zhanao Deng ◽  
Brent K. Harbaugh

The ornamental value of caladium (Caladium ×hortulanum Birdsey) depends primarily on leaf characteristics, including leaf shape and main vein color. Caladium leaf shapes are closely associated with plant growth habit, stress tolerance, and tuber yield; leaf main vein colors are often used for cultivar identification. Thirty-eight crosses were made among 10 cultivars and two breeding lines; their progeny were analyzed to understand the inheritance of leaf shape and main vein color and to determine if there is a genetic linkage between these two traits. Results showed that a single locus with three alleles determined the main vein color in caladium. The locus was designated as V, with alleles Vr, Vw, and Vg for red, white, and green main veins, respectively. The white vein allele was dominant over the green vein allele, but it was recessive to the red vein allele, which was dominant over both white and green vein alleles; thus the dominance order of the alleles is Vr > Vw > Vg. Segregation data indicated that four major red-veined cultivars were heterozygous with the genotype Vr Vg, and that one white-veined cultivar was homozygous and one other white-veined cultivar and one breeding line were heterozygous. The observed segregation data confirmed that the three leaf shapes in caladium were controlled by two co-dominant alleles at one locus, designated as F and f, for fancy and strap leaves, respectively. The skewedness of leaf shape segregation in some of the crosses implied the existence of other factors that might contribute to the formation of leaf shape. Contingency chi-square tests for independence revealed that caladium leaf shape and main vein color were inherited independently. The chi-square tests for goodness-of-fit indicated that the five observed segregation patterns for leaf shape and main vein color fit well to the expected ratio assuming that two co-dominant and three dominant/recessive alleles control leaf shape and main vein color and they are inherited independently.


2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.


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