scholarly journals Directional nature of Goodman–Kruskal gamma and some consequences: identity of Goodman–Kruskal gamma and Somers delta, and their connection to Jonckheere–Terpstra test statistic

2021 ◽  
Author(s):  
Jari Metsämuuronen
Keyword(s):  
Response Pattern ◽  
Algebraic Relation ◽  
Criterion Variable ◽  
Test Statistic ◽  
Symmetric Measure ◽  
The Cross

AbstractAlthough usually taken as a symmetric measure, G is shown to be a directional coefficient of association. The direction in G is not related to rows or columns of the cross-table nor the identity of the variables to be a predictor or a criterion variable but, instead, to the number of categories in the scales. Under the conditions where there are no tied pairs in the dataset, G equals Somers’ D so directed that the variable with a wider scale (X) explains the response pattern in the variable with a narrower scale (g), that is, D(g│X). Hence, G = G(g│X) = D(g│X) but G ≠ D(X│g) and G ≠ D(symmetric). If there are tied pairs, the estimates by G = G(g│X) are more liberal in comparison with those by D(g│X). Algebraic relation of G and D with Jonckheere–Terpstra test statistic (JT) is derived. Because of the connection to JT, G = G(g│X) and D = D(g│X) indicate the proportion of logically ordered test-takers in the item after they are ordered by the score. It is strongly recommendable that gamma should not be used as a symmetric measure, and it should be used directionally only when willing to explain the behaviour of a variable with a narrower scale by the variable with a wider scale. This fits well with the measurement modelling settings.

scholarly journals Field Significance of Regression Patterns

2011 ◽  
Vol 24 (19) ◽  
pp. 5094-5107 ◽  
Author(s):  
Timothy DelSole ◽  
Xiaosong Yang
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Significance Test ◽  
Spatial Filter ◽  
Climate Index ◽  
Boreal Winter ◽  
Ratio Test ◽  
Test Statistic ◽  
Canonical Correlations ◽  
The Cross

Regression patterns often are used to diagnose the relation between a field and a climate index, but a significance test for the pattern “as a whole” that accounts for the multiplicity and interdependence of the tests has not been widely available. This paper argues that field significance can be framed as a test of the hypothesis that all regression coefficients vanish in a suitable multivariate regression model. A test for this hypothesis can be derived from the generalized likelihood ratio test. The resulting statistic depends on relevant covariance matrices and accounts for the multiplicity and interdependence of the tests. It also depends only on the canonical correlations between the predictors and predictands, thereby revealing a fundamental connection to canonical correlation analysis. Remarkably, the test statistic is invariant to a reversal of the predictors and predictands, allowing the field significance test to be reduced to a standard univariate hypothesis test. In practice, the test cannot be applied when the number of coefficients exceeds the sample size, reflecting the fact that testing more hypotheses than data is ill conceived. To formulate a proper significance test, the data are represented by a small number of principal components, with the number chosen based on cross-validation experiments. However, instead of selecting the model that minimizes the cross-validated mean square error, a confidence interval for the cross-validated error is estimated and the most parsimonious model whose error is within the confidence interval of the minimum error is chosen. This procedure avoids selecting complex models whose error is close to much simpler models. The procedure is applied to diagnose long-term trends in annual average sea surface temperature and boreal winter 300-hPa zonal wind. In both cases a statistically significant 50-yr trend pattern is extracted. The resulting spatial filter can be used to monitor the evolution of the regression pattern without temporal filtering.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Structures Resembling Striated Rootlets in Oocytes

1972 ◽  
Vol 30 ◽  
pp. 124-125
Author(s):  
Valerie V. Ernst
Keyword(s):  
Golgi Complex ◽  
Fibrous Structure ◽  
Oocyte Development ◽  
The Cross

During the earliest stage of oocyte development in the limpet, Acmea scutum, Golgi complexes are small, few and randomly dispersed in the cytoplasm. As growth proceeds, the Golgi complexes increase in size and number and migrate to the periphery of the cell. At this time, fibrous structures resembling striated rootlets occur associated with the Golgi complexes. Only one fibrous structure appears to be associated with a Golgi complex.The fibers are periodically cross banded with an average of 4 dense fibrils and 6 lighter fibrils per period (Fig. 1). The cross fibrils have a center to center spacing of about 7 run which appears to be the same as that of the striated rootlets of the gill cilia in this animal.

Energy Distribution in Electron Beams

1972 ◽  
Vol 30 ◽  
pp. 568-569
Author(s):  
Tamotsu Ohno
Keyword(s):  
Electron Beam ◽  
Energy Distribution ◽  
Cross Section ◽  
Integral Curve ◽  
Electron Beams ◽  
Electron Gun ◽  
Angular Divergence ◽  
Apparent Increase ◽  
Integral Width ◽  
The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

On the cross-sectional shape of the cellulose crystallites in the tunicate Halocynthia papillosa

1990 ◽  
Vol 48 (3) ◽  
pp. 566-567
Author(s):  
J.-F. Revol ◽  
Y. Van Daele ◽  
F. Gaill
Keyword(s):  
Contrast Imaging ◽  
Animal Kingdom ◽  
Bright Field ◽  
Field Mode ◽  
Cross Sectional ◽  
Ultrathin Sections ◽  
The Cross ◽  
Sectional Shape ◽  
Valonia Ventricosa ◽  
C Nmr

The only form of cellulose which could unequivocally be ascribed to the animal kingdom is the tunicin that occurs in the tests of the tunicates. Recently, high-resolution solid-state l3C NMR revealed that tunicin belongs to the Iβ form of cellulose as opposed to the Iα form found in Valonia and bacterial celluloses. The high perfection of the tunicin crystallites led us to study its crosssectional shape and to compare it with the shape of those in Valonia ventricosa (V.v.), the goal being to relate the cross-section of cellulose crystallites with the two allomorphs Iα and Iβ.In the present work the source of tunicin was the test of the ascidian Halocvnthia papillosa (H.p.). Diffraction contrast imaging in the bright field mode was applied on ultrathin sections of the V.v. cell wall and H.p. test with cellulose crystallites perpendicular to the plane of the sections. The electron microscope, a Philips 400T, was operated at 120 kV in a low intensity beam condition.

Stimulus Ratio Effects on Speech Discrimination by Children and Adults

1991 ◽  
Vol 34 (3) ◽  
pp. 671-678 ◽  
Author(s):  
Joan E. Sussman
Keyword(s):  
Discrimination Task ◽  
Response Pattern ◽  
Response Patterns ◽  
Speech Discrimination ◽  
Adult Group ◽  
Discrimination Accuracy ◽  
Formant Frequency ◽  
Response Strategies ◽  
Place Of Articulation ◽  
Adults And Children

This investigation examined the response strategies and discrimination accuracy of adults and children aged 5–10 as the ratio of same to different trials was varied across three conditions of a “change/no-change” discrimination task. The conditions varied as follows: (a) a ratio of one-third same to two-thirds different trials (33% same), (b) an equal ratio of same to different trials (50% same), and (c) a ratio of two-thirds same to one-third different trials (67% same). Stimuli were synthetic consonant-vowel syllables that changed along a place of articulation dimension by formant frequency transition. Results showed that all subjects changed their response strategies depending on the ratio of same-to-different trials. The most lax response pattern was observed for the 50% same condition, and the most conservative pattern was observed for the 67% same condition. Adult response patterns were most conservative across condition. Differences in discrimination accuracy as measured by P(C) were found, with the largest difference in the 5- to 6-year-old group and the smallest change in the adult group. These findings suggest that children’s response strategies, like those of adults, can be manipulated by changing the ratio of same-to-different trials. Furthermore, interpretation of sensitivity measures must be referenced to task variables such as the ratio of same-to-different trials.

A Longitudinal Study of Mental Health in Emerging Adults

2014 ◽  
Vol 73 (3) ◽  
pp. 135-141 ◽  
Author(s):  
Monica S. Bachmann ◽  
Hansjörg Znoj ◽  
Katja Haemmerli
Keyword(s):  
Mental Health ◽  
Longitudinal Study ◽  
Emerging Adults ◽  
Poor Mental Health ◽  
Need Satisfaction ◽  
Computer Assisted ◽  
Consistency Model ◽  
Negative Effect ◽  
The Cross ◽  
Health Model

Emerging adulthood is a time of instability. This longitudinal study investigated the relationship between mental health and need satisfaction among emerging adults over a period of five years and focused on gender-specific differences. Two possible causal models were examined: (1) the mental health model, which predicts that incongruence is due to the presence of impaired mental health at an earlier point in time; (2) the consistency model, which predicts that impaired mental health is due to a higher level of incongruence reported at an earlier point in time. Emerging adults (N = 1,017) aged 18–24 completed computer-assisted telephone interviews in 2003 (T1), 2005 (T2), and 2008 (T3). The results indicate that better mental health at T1 predicts a lower level of incongruence two years later (T2), when prior level of incongruence is controlled for. The same cross-lagged effect is shown for T3. However, the cross-lagged paths from incongruence to mental health are marginally associated when prior mental health is controlled for. No gender differences were found in the cross-lagged model. The results support the mental health model and show that incongruence does not have a long-lasting negative effect on mental health. The results highlight the importance of identifying emerging adults with poor mental health early to provide support regarding need satisfaction.

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