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Dependence and Independence: Structures, Testing, and Measuring
Published in Albert Vexler, Alan D. Hutson, Xiwei Chen, Statistical Testing Strategies in the Health Sciences, 2017
Albert Vexler, Alan D. Hutson, Xiwei Chen
Without ties in the data set, Hoeffding’s D measure of dependence is on the interval [–0.5, 1], with 1 indicating perfect dependence. However, when ties occur, Hoeffding’s D measure may result in a smaller value (Hollander et al. 2013). These traditional dependence measures can be difficult (1) to decide when a particular value indicates association strong enough for a given purpose, and (2) in a given situation, for weighing the losses involved in obtaining more strongly associated variables against the gains (Elffers 1980). Therefore, it is suggested to use functions of these traditional dependence measures that can be interpreted as the probability of making a wrong decision in certain situations, for example, the cube of correlation coefficient, correlation ratio, maximal correlation (sup correlation), and monotone correlations, as well as concordance measures such as the Gini index and Blomqvist’s β; we refer the reader to see Balakrishnan and Lai (2009) for more details.
Descriptive statistics
Published in Louis Cohen, Lawrence Manion, Keith Morrison, Research Methods in Education, 2017
Louis Cohen, Lawrence Manion, Keith Morrison
To conclude our explanation of terminology, readers should note the use of the term ‘discrete variable’ in the description of the fourth correlation ratio (eta) in Table 40.13. We said earlier that a continuous variable can take on any value between two points on a scale. A discrete variable, however, can only take on numerals or values that are specific points on a scale. The number of players in a football team is a discrete variable. It is usually eleven; it could be fewer than eleven, but it could never be seven-and-a-quarter!
The gene profile of Enterobacteriaceae virulence factors in relation to bacteriuria levels between the acute episodes of recurrent uncomplicated lower urinary tract infection
Published in Expert Review of Anti-infective Therapy, 2021
Yulia L. Naboka, Ayrat R. Mavzyutov, Michel I. Kogan, Irina A. Gudima, Kseniya T. Dzhalagoniya, Sergey N. Ivanov, Kurt G. Naber
Statistical analysis included calculating the detection frequencies of microorganisms. The relationships between the detection frequencies of virulence genes were analyzed by the Pearson contingency coefficient (PCC). To analyze the relationship between the occurrence of VFG and leukocyturia, the Eta coefficient was used. This coefficient was calculated using the formula η = √ (δ2/σ2), where δ2 is the intergroup dispersion, and σ2 is the total dispersion of the quantitative trait. This indicator of the correlation ratio assesses the influence of a variable expressed in an ordinal or nominal scale (presence or absence of VFG) on the degree of dispersion of a quantitative variable (leukocyturia). Statistical data processing was implemented using a special software tool, the statistical package SPSS version 23.
Evaluation of relationship between HbA1c levels and ovarian reserve in patients with type 1 diabetes mellitus
Published in Gynecological Endocrinology, 2020
Pınar Kadiroğulları, Esra Demir, Pinar Yalcin Bahat, Huseyin Kıyak, Kerem Doga Seckin
The analysis of the data was performed on the IBM SPSS-Statistics V-20 (SPSS Inc., Chicago, IL, USA) for Macintosh software-package. The Kolmogorov − Smirnov test was used to analyze whether the distribution of continuous variables was close to normal. Continuous variables were shown as mean ± standard deviation and nominal variables as the number of cases and (%). The Student’s t-test with the grouping variable or the Mann–Whitney U-test was used to detect the presence of differences in quantitative traits between the two analyzed groups. Nominal variables were evaluated with the Chi-Square test. Pearson’s correlation ratio and Spearman’s rank correlation ratio for the nonparametric test were used to determine the correlation between the studied traits. The logistic regression model was used to identify statistically significant variables. A p value of <.05 was accepted as statistically significant.
Categorical multiblock linear discriminant analysis
Published in Journal of Applied Statistics, 2018
The correlation ratio n individuals and a categorical variable G which describes the partition of these n individuals into g groups.