Parallel Regression Lines Research Articles

Hydrogen Evolution Reaction: Log j0 Versus Work Function Φ As Viewed from Transition State Theory As an Eyring Plot

In 1972, Trasatti correlated the log of the exchange current density (j0) for the hydrogen evolution reaction (HER) with the work functions of 31 metal electrodes to yield two parallel regression lines. [1] The lines are separated by Δ log j0 = 3. Thermodynamically, work function 𝚽 is the energy to remove an electron from a metal to infinity. Perhaps counterintuitively, platinum group metals (PGMs) with the highest 𝚽 sustain the highest j0 values.The elementary, interfacial electron transfer occurs between the electrode and adsorbed hydrogen cation and adsorbed hydrogen atom.H+ ads + e ⇌ H● ads A materials dependent rate expression is developed as follows. [2]The properties of the metal are introduced explicitly into reaction mechanism, characterized by M(e) and M(0), the metal electrode with and without the electron.M(e) + H+ ads ⇄ M(0) + H● ads Classical transition state theory (TST) characterizes the free energy of activation ΔG‡ as the energy difference between the transition state (TS) and the minimum energy of the reactants. The TS forms at equilibrium, where adsorbed hydrogen and metal electrode share the electron.M(e) + H+ ads ⇌ [M ●●● e ●●● Hads]‡ ⇌ M(0) + H● ads Electrochemical potentials set the energy difference in the products and reactant, which sets ΔG‡. Chemical potential (𝞵) difference for the metal without and with the electron define 𝚽. F𝚽 = 𝞵M(0) - 𝞵M(e) F𝚽 is further defined as a chemical free energy that that lowers ΔG‡. F𝚽 is a material specific property that is atypically specified in the rate equation. Because log j0 ∝ - ΔG‡, and chemical free energy F𝚽 lowers ΔG‡, log j0 ∝ F𝚽. Thus, j0 increases exponentially with F𝚽, so PGMs with highest 𝚽 sustain highest j0. Further, the rate expression embeds material specific property 𝚽.The classical Eyring perspective for generic rate constant k’ is k’ = A’ exp[-ΔG‡/RT]. Rate constant is typically determined by varying temperature in a plot of ln k’ versus T-1, where ln k’ = ln A’ - ΔG‡/RT. For isothermal measurements, log j0 is linear with 𝚽 because F𝚽 is a term ΔG‡ chem that is a component in the total ΔG‡. For metals, where 𝚽 > 0, F𝚽 always lowers ΔG‡ for HER; the total activation energy is lowered in proportion to F𝚽. The slopes of log j0 versus 𝚽 is proportional to 𝝰𝚽F𝚽/2.303, where partition coefficient 𝝰𝚽 characterizes ∂ΔG‡/∂𝚽. For the parallel lines in Trasatti’s plot, 𝝰𝚽 = 0.38. The intercepts are independent of 𝚽.The material specific rate expressions derived from classical TST and electrochemical potentials may provide guidance on design of electrocatalysts and provide a path to integration of classical and contemporary modeling of important reaction processes such as HER.

Classifying chemicals into toxicity categories based on LC50 values- Pros and cons

Classifying chemicals into toxicity categories based on LC50 values- Pros and cons

Validity of Quantitative Measurements By the Joint Tissue Examination and Damage Exam (JADE) with Musculoskeletal Ultrasound for the Longitudinal Assessment of Hemophilic Arthropathy

Introduction: Clinical scoring systems, such as the Hemophilia Joint Health Score (HJHS), and imaging modalities (radiographs and magnetic resonance) are important instruments for the evaluation of hemophilic joint health. However, they are semi-quantitative scales, exhibit ceiling effects, and may not capture subtle dynamic changes of intra-articular structures. We developed the Joint tissue Activity and Damage Exam (JADE) protocol to quantitatively evaluate the extent of hemophilic arthropathy at the tissue level, individualize management, and objectively assess the efficacy of novel therapies. JADE is an economical, convenient, and radiation free point-of-care musculoskeletal ultrasound protocol. JADE uses quantitative numerical measurements (1/10th of millimeter) for osteochondral alterations, cartilage thickness and soft tissue expansion in hemophilic joints and is validated per international OMERACT guidelines for pathological tissue recognition with high intra/inter-rater and inter-operator reliability. Furthermore, we previously reported JADE association with clinical and functional joint assessments at baseline for patients with hemophilia. Herein, we examined JADE protocol ability to capture tissue changes over time and their associations with HJHS, a clinical joint assessment. We assumed the regression lines for joint HJHS on each JADE measurement at each time point would lie parallel to each other. Verifying this assumption would enhance JADE protocol validity and provide confidence that it could be used to monitor hemophilic arthropathy progression by quantifying specific tissue abnormalities. Methodology: We recruited adult patients (≥ 18 years) with congenital hemophilia and arthropathy in a prospective study performed at 3 sites in North America. We assessed joint HJHS and JADE parameters for each patient (n=44; 264 joints [bilateral elbows, ankles, and knees]) at study entry (baseline), at ~12-18 months (midpoint), and ~24-36 months (final). JADE measurements included osteochondral alterations, cartilage thickness, and soft tissue expansion at sentinel positions for each joint. The association between joint HJHS and each JADE variable was examined by fitting random intercept models with outcomes transformed to ensure normal residuals. We examined the assumption of parallel regression lines for the three time points by applying a test for homogeneity of slopes. If no difference between slopes was found, then we applied an analysis of covariance to test whether the lines for each joint were coincident. Results: Joint HJHSs deteriorated measurably during the study period, reflecting clinically worsening arthropathy over time. Importantly, clinical assessment of deterioration for the elbows, knees, and ankles was associated with JADE measurements that changed in the expected direction, namely increased length of osteochondral alterations, decreased cartilage thickness, and increased soft tissue expansion. As an example, figure 1 shows the association of deteriorating HJHS and osteochondral alterations for elbows, knees, and ankles at baseline, midpoint, and final visits. In each graph, the regression lines were similar in shape. Lines were parallel for the elbow (midpoint vs baseline: p = 0.185; final vs baseline: p = 0.398), and the ankle (midpoint vs baseline: p = 0.225; final vs baseline: p = 0.293). But, the assumption of parallel lines was rejected for the knee (midpoint vs baseline: p = 0.047; final vs baseline: p = 0.024). Conclusions: This study demonstrates a tight association between JADE direct ultrasonographic measurements and clinical deterioration (HJHSs) during several assessments over 3 years. Importantly, the associations are consistent across time, despite clinical joint health examinations and ultrasound measurements being performed at three different centers by multiple providers, with long intervals between assessments. Altogether, these findings constitute a major milestone for the clinical relevance validity of the JADE protocol as a precise instrument for tissue-specific alterations measurements over time. These findings support the use of the JADE protocol to monitor the progression of hemophilic arthropathy longitudinally, permit prompt identification of potentially reversible osteochondral and/or soft tissue changes, and study early interventions that could curb arthropathic progression. Disclosures Kruse-Jarres: F. Hoffmann-La Roche Ltd: Speakers Bureau; Biomarin, Chugai Pharmaceutical Co., CSL Behring, CRISPR Therapeutics, Genentech, Inc.: Honoraria; CSL Behring, Genentech, Inc., Spark: Research Funding; Biomarin, Chugai Pharmaceutical Co., CSL Behring, CRISPR Therapeutics, Genentech, Inc.: Consultancy. Steiner:Uniqure: Consultancy, Membership on an entity's Board of Directors or advisory committees; Sanofi/Genzyme: Consultancy, Membership on an entity's Board of Directors or advisory committees; Genentech: Consultancy, Membership on an entity's Board of Directors or advisory committees; Roche: Consultancy, Membership on an entity's Board of Directors or advisory committees. Quon:Bayer: Honoraria; Orthopaedic Institute for Children: Current Employment; Biomarin: Honoraria, Speakers Bureau; Novo Nordisk: Honoraria, Speakers Bureau; Bioverativ/Sanofi: Honoraria, Speakers Bureau; Genentech, Inc./F. Hoffmann-La Roche Ltd: Honoraria, Speakers Bureau; Octapharma: Honoraria; Shire/Takeda: Speakers Bureau. von Drygalski:Biomarin: Honoraria; Hematherix LLC: Membership on an entity's Board of Directors or advisory committees, Other: co-founder; Uniqure: Honoraria; Bioverativ/Sanofi: Honoraria, Research Funding; Pfizer: Research Funding; Novo-Nordisk: Honoraria; Takeda: Honoraria.

The correlation regression equations between metacognitive skills and concept gaining of science and biology of Indonesian students

In the field of education metacognitive skills can be used as predictors of students’ concept gaining. There have been many researches on the correlation between metacognitive skills and concept gaining both at the elementary school level and high school levels. Several further researches were also conducted to uncover the factors that influenced the regression lines of the correlation. However, to date the actual factors affecting the coefficient value of the slope and intercept of the regression equations on the correlation between metacognitive skills and concept gaining have not been revealed. This research aimed at investigating the factors affecting the slope coefficient and intercept of the regression equation of the correlation between metacognitive skills and concept gaining of students in different educational levels implementing of one learning model. The design of this research was a correlational research in order to investigate the correlation between metacognitive skills as the predictor and the concept gaining as the criterion. Among the 27 regression equations related to the correlation between metacognitive skills and concept gaining of the students undergoing various learning models, that have been analyzed, 77.50% of them are parallel, and only 22.50% of them are intersected. Although there were some intersecting lines, the percentage of parallel lines was bigger. Several factors (education level, class level, academic ability, and learning models) which had been predicted to affect the slope coefficient as well as the intercept were finally proved to be non-affecting factors, because both parallel regression lines and intersecting regression lines were still found in the various conditions compared. This research revealed two factors affecting the slope coefficient and the intercept. These factors are the presence of shared variables that affect the value of X and Y and the measurement error. Further researches related to these factors are necessary to be carried out to uncover more accurate results.

The Correlation between Metacognitive Skills and Critical Thinking Skills at the Implementation of Four Different Learning Strategies in Animal Physiology Lectures

<p style="text-align:justify">The empowerment of metacognitive skills has an important role in increasing the capacity of critical thinking and active control of students' cognitive processes in learning. Metacognitive skills can be enhanced through the implementation of learning strategies involving higher-order thinking. The RQA, ADI, RQA integrated with ADI are constructivistic learning strategies that can accommodate these skills. The researches specifically examining the correlation between metacognitive skills and critical thinking skills at the implementation of RQA, ADI, and RQA integrated with ADI learning strategies are still rarely found. This research is a correlational research, aiming at revealing the correlation between metacognitive skills and critical thinking skills. The data of metacognitive skills and critical thinking skills are collected by using a valid and reliable essay test. The samples of this research are the fourth semester (IV) biology education students programming Animal Physiology course in the 2016/2017 academic year consisting of 109 students. The results of this research show that (1) there was a significant correlation between metacognitive skills and critical thinking skills at the implementation of the four learning strategies, (2) the regression equations analyzed using Anova obtain regression lines (not coincide), and non parallel regression lines (intersected); meaning that there is a difference in the increase rate and magnitude of the critical thinking skills influenced by the four learning strategies. It is expected that the teachers and the lecturers always strive to improve the quality of the learning process through the implementation of active and constructive learning strategies.</p>

Loop energy: A useful indicator of the hardness of minerals from depth-sensing indentation tests

Depth-sensing indentation tests were performed to obtain the loop energy (equivalent to the energy consumed to produce the indentation) and the residual depth of the indentation using a triangular pyramidal diamond indenter for the minerals in Mohs hardness scale except for diamond, as well as other minerals (apophyllite, forsterite, and tourmaline), at a maximum load ranging from 30 to 100 mN. A new graphic presentation is proposed that shows the hardness of minerals in log(penetration depth)−log(loop energy) space. The data for each mineral under different loads give a straight regression line with a slope of 2.6–2.9 (except for talc, which yields a slope of 2.2), while the data for different minerals under a given load yield a straight regression line with a slope of 1.1–1.2. A theoretical analysis of ideal materials, in terms of log(penetration depth)−log(loop energy) space, shows the existence of two series of parallel regression lines with slopes of 3 (data for each mineral at different loads) and 1 (data for different minerals under a given load). The results show a slight deviation between the measured and theoretical slopes, probably reflecting a progressive change in the mechanical properties of the minerals during the indentation tests.

Isolation of Rhamnocitrin Insecticide from Retamaraetam via Shephadex LH-20

Retamaraetam is a medicinal herb growing wild in the mountain alkurvillage was collected in the flowering stage and after treatment in ways different methods of chromatography for isolated Rhamnocitrin has been purified bySephadex LH-20 and identified by spectroscopic methods (UV, NMR).showed that despite the differences in potency of Retamaraetamand Rhamnocitrinsubstances they were found to possess parallel regression lines. This may suggest that these extracts have the same mode of action against the tested insect larvae.

Estimating Energy Expenditure During Front Crawl Swimming Using Accelerometers

The determination of energy expenditure is of major interest in training load and performance assessment. Small, wireless accelerometer units have the potential to characterise energy expenditure during swimming. The correlation between absorbed oxygen versus flume swimming speed and absorbed oxygen versus the three axis acceleration recorded on the sacrum, wrist and ankle for swimmers of varying abilities was calculated using Bland-Altman analysis of variance through parallel regression lines fitted for 60 participants, who swam at three different speeds for 6min duration with 2min rest times. Swimmers showed a strong positive relationship between VO2 and RMS acceleration on the wrist (r = 0.77) and ankle (r = 0.73) sensors but not on the sacrum (r = 0.46). The sacrum data was split into elite and novice swimmers, resulting in a strong correlation for elite swimmers and a poor correlation for novice swimmers.A robust biomechanical technique for the determination of the energy expenditure of swimmers of different categories and genders from acceleration data has been developed.

Compatibility of the entomopathogenic fungus Beauveria bassiana with flufenoxuron and azadirachtin against Tetranychus urticae

Laboratory studies were developed to evaluate the compatibility of flufenoxuron and azadirachtin with Beauveria bassiana against Tetranychus urticae larvae along with the required Probit analysis of the involved chemicals on all of the life stages of this mite. Flufenoxuron displayed parallel regression lines for the mortality of eggs, deutonymphs and adults. Larvae and protonymphs were the most susceptible life stages. Protonymphs were 35 times more sensitive than eggs and adults. Azadirachtin gave equal mortality on proto- and deutonymphs. The response of eggs and adults was equivalent when treated with azadirachtin. The regression lines for proto- and deutonymphs were parallel to those of adults and eggs yet three times more sensitive. The effects of separate combinations of the entomopathogenic fungus Beauveria bassiana at its LC(20) with flufenoxuron and azadirachtin at their corresponding LC(40) were evaluated on mite larvae. The application of flufenoxuron with B. bassiana revealed a clear synergy. While the combination of azadirachtin and B. bassiana had an additive effect. These combinations with B. bassiana could improve mite control by contributing to a decline in the likelihood of resistance so often described in the literature.

A structure–activity analysis of the variation in oxime efficacy against nerve agents

A structure–activity analysis was used to evaluate the variation in oxime efficacy of 2-PAM, obidoxime, HI-6 and ICD585 against nerve agents. In vivo oxime protection and in vitro oxime reactivation were used as indicators of oxime efficacy against VX, sarin, VR and cyclosarin. Analysis of in vivo oxime protection was conducted with oxime protective ratios (PR) from guinea pigs receiving oxime and atropine therapy after sc administration of nerve agent. Analysis of in vitro reactivation was conducted with second-order rate contants ( k r2) for oxime reactivation of agent-inhibited acetylcholinesterase (AChE) from guinea pig erythrocytes. In vivo oxime PR and in vitro k r2 decreased as the volume of the alkylmethylphosphonate moiety of nerve agents increased from VX to cyclosarin. This effect was greater with 2-PAM and obidoxime (> 14-fold decrease in PR) than with HI-6 and ICD585 (< 3.7-fold decrease in PR). The decrease in oxime PR and k r2 as the volume of the agent moiety conjugated to AChE increased was consistent with a steric hindrance mechanism. Linear regression of log (PR-1) against log ( k r2 ∙ [oxime dose]) produced two offset parallel regression lines that delineated a significant difference between the coupling of oxime reactivation and oxime protection for HI-6 and ICD585 compared to 2-PAM and obidoxime. HI-6 and ICD585 appeared to be 6.8-fold more effective than 2-PAM and obidoxime at coupling oxime reactivation to oxime protection, which suggested that the isonicotinamide group that is common to both of these oximes, but absent from 2-PAM and obidoxime, is important for oxime efficacy.

Statistical Analysis of Data Fom Infertility Patients: How to Explicitly Consider the Decline in Fertility Associated With Age

The decline in fertility with age is well documented. The objective of this study was to evaluate multiple regression as a strategy to address changes in fertility associated with age. Retrospective chart review of 2573 patients down regulated with GnRH agonists. This group includes a broad spectrum of infertility patients with ages 22-44. The data set used for the preparation of 2004 ASRM Abstract P-293 (Beltsos et al., Fert Steril 2004; 82, Suppl 2: S239-240) was re-examined using multiple regression. Previously, two-way ANOVA and chi square tests were used to identify changes resulting from treatment with recombinant FSH (r-hFSH) alone versus a combination protocol consisting of hMG plus r-hFSH, in patients classified as younger (< 35 years) versus older (≥ 35 years). That is, the effect of age was noted by dividing patients into arbitrary age groups. Herein, the data were re-analyzed by multiple linear and logistic regression. A p < 0.05 was considered statistically significant. Two different types of responses were taken as prototypic. Oocytes Retrieved was taken as an example of continuous data while Clinical Pregnancy Rates were taken as an example of a categorical variable. Age was treated as an independent variable and was graphed on the abscissa. Patient responses were treated as dependent variables and were graphed on the ordinate. All responses examined were adequately described by equations that included an intercept and slope for AGE over the 20 to 44 age range. Multiple regression models included AGE and ADDITION OF hMG (hMG) as main effects plus an AGE * hMG interaction term. When the AGE * hMG interaction was not significant, the model was re-calculated without the interaction. For multiple linear regression, a non-significant interaction means that the data can be appropriately described as two parallel regression lines, one for r-hFSH+hMG and one for r-hFSH alone. The difference in position of the regression lines represents the effect of adding hMG. Figure 1 illustrates results obtained for the continuous variable Oocytes Retrieved. Treatment of patients with r-hFSH alone yielded an additional 1.4 oocytes retrieved over the entire 20 to 44 age range. Analogous results were obtained for the categorical variable Clinical Pregnancy Rate analyzed by multiple logistic regression. Irrespective of the patient’s age, r-hFSH protocols resulted in about 7.5% higher pregnancy rates compared to r-hFSH+hMG protocols. Multiple regression analysis appears to be superior to the two-way ANOVA and Chi square tests used previously, particularly if the data include a broad range of patient ages. Multiple linear and logistic regression for the analysis of continuous and categorical variables, respectively, can be used to examine the effects of factors that affect treatment outcome while explicitly addressing known changes in fertility associated with age. Dealing with age by multiple regression allows other factors affecting patient responses to be characterized and quantified in a statistically robust manner.

Ammonia, respiration, and longevity in nematodes: insights on metabolic regulation of life span from temporal rescaling.

To better understand metabolic correlates of longevity, we used a graphical technique to compare the adult temporal patterns of several markers of metabolic activity - ammonia elimination, oxygen consumption rate, ATP levels, and (in freeze-permeabilized worms) the rate of NADPH-activated, lucigenin-mediated superoxide formation - as observed by us and others in normal and long-lived mutant Caenorhabditis elegans strains. All of these traits declined with time, and when their logarithms were plotted against time, appeared reasonably linear for most of the duration of the experiments. The profiles for ammonia output conformed well to parallel regression lines; those for the other metabolic parameters varied widely in slope as originally plotted by the authors, but much less so when replotted as logarithms against adjusted time, scaled by the reciprocal of strain longevity. This is consistent with coregulation of life span, respiration rate, ATP levels, lucigenin reactivity, but not ammonia excretion, by a physiological clock distinguishable from chronologic time. Plots, scaled appropriately for equalized slopes, highlighted y-axis intercept differences among strains. On rescaled plots, these constitute deviations from the expectation based on 'strain-specific clock' differences alone. With one exception, y-intercept effects were observed only for mutants in an insulin-like signaling pathway.

Alluvial-fan slope as a function of sediment transport efficiency

ABSTRACT The nature of slope acquisition by alluvial fans was studied by comparing the slope evolution of 37 tributary fans to the San Juan river in an arid region of western Argentina. Each of these fans is characterized by truncation of the distal end as a result of incision by the San Juan river. The alluvial-fan slope prior to incision and the slope of the active channel for each fan was measured. River accumulation terraces indicate that fan incision was probably synchronous along the valley. Incised channels in each fan evolved over the same interval, but they show different degrees of advance of erosion. Values of old fan slope fit well with known power laws relating them to drainage area (r = 0.865). Slopes of incised channels also fit with power laws, but with a lower regression coefficient (r = 0.741). The regression lines in each case have almost the same slope (0.218, sd = 0.02, and 0.215, sd = 0.03, respectively), which suggests that, although the incised-channel slope is not an equilibrium feature, both the original and the secondary fans follow the same law of variation. An explanation for this phenomenon is that the transport efficiency of the fans may be related to the size of the basin. If mean runoff and peak floods are roughly regulated by drainage area, fan slopes of larger drainage basins will evolve faster than those of smaller basins. Apparently, as a group of fans approach an equilibrated state, their slopes become distributed along successive parallel regression lines, progressively displaced upward in the diagram, as long as climatic conditions remain constant. To see the effects of water availability on fan slope, we also compared slopes and drainage-basin areas of fans located in settings with different specific runoff, which is approximately a function of annual rainfall. The regression lines for each set of alluvial fans are roughly parallel. The smaller intercept value for humid fans indicates that for a given drainage area, fans in arid settings are steeper than those in more humid settings. Fans dominated by mud flows and dilute flash floods were plotted together, but no major differences were observed in this general behavior. This suggests that the steepness of a fan is not primarily related to compositional factors or to the sediment transport process, but to transport efficiency. Episodic-flood fans of Argentina show slopes comparable to the mudflow fans of Death Valley because water supply and therefore transport efficiency are similar. Drainage-basin area combined with mean annual rainfall may largely determine transport efficiency, by controlling mean runoff across the fan. As a result, transport efficiency may define not only alluvial-fan slope but also the rate at which the alluvial-fan slope reestablishes equilibrium after some external change.

Petrogenesis of ferromanganese nodules from east of the Chagos Archipelago, Central Indian Basin, Indian Ocean

Deep-sea ferromanganese nodules occur over a large area and on many different sediment types of the Central Indian Basin, Indian Ocean. Selected samples were studied to determine their chemical and mineralogical compositions and microstructural features. Repeated laminations of variable thickness, alternately dominated by todorokite and vernadite, are characteristic of these nodules. These laminae show, on electron microprobe line scans, corresponding interlaminar partitioning of Mn–Cu–Ni and Fe–Co. The bulk chemical compositions of these nodules plot in both the hydrogenetic and early diagenetic fields on the Fe–Mn–(Ni + Cu + Co) ×10 ternary diagram. The binary diagram depicting the covariation of Mn + Ni + Cu against Fe + Co shows two distinct parallel regression lines, one delineated by nodules from terrigenous, siliceous ooze and siliceous ooze–terrigenous sediments and the other by nodules from red clay, siliceous ooze–red clay and calcareous ooze–red clay. An increasing diagenetic influence in the nodules with the nature of the host sediment types was observed in the sequence: terrigenous → siliceous ooze and red clay → siliceous/calcareous ooze–red clay. A negative correlation between Mn/Fe ratio and Co and a positive correlation between Mn/Fe ratio and (Ni + Cu) was established. The nodules show dendritic, laminated, and globular microstructures formed by primary growth of Fe–Mn oxide laminae. Depositional hiatuses in the primary microstructures indicate that the growth of these nodules was episodic. The oxide laminations show extremely complex growth patterns. Scattered biogenic remains and mineral grains acted as accessory `seeds' for growth of oxide layers in addition to the main nuclei. None of the primary microstructures can be uniquely linked to a particular growth process or growth rate. Radial cracks, cutting across primary microstructures, are often filled by todorokite of a later generation. Post-depositional modifications of the nodules were largely controlled by accreted biogenic remains as indicated by their progressive dissolution with increasing depth from nodule surfaces, their pseudomorphic replacement by todorokite and the later growth of phillipsite and todorokite in the microfossil molds. The growth patterns of the in-filled oxides are often controlled entirely by the cavity-walls and are discordant with the primary growth fabric. Primary todorokite was recrystallized to coarser grains of different chemical composition. Later generation veins of todorokite cut across and chaotically disrupted primary laminae.

On restricted hypotheses in extreme value regression models

This paper discusses one-sided tests for extreme value regression models with non-constant scale parameter and uncensored data. It gives the asymptotic null distribution of three asymptotically equivalent statistics for two situations of general one-sided hypotheses. For some particular cases, such as those of testing the hypotheses of simple order or simple tree order for location parameters and scale parameters in g populations and for the intercepts in parallel regression lines, the asymptotic null distribution reduces to the chi-bar squared distribution, χ −2. Consequently, all the approximations developed for this distribution, especially for four or more constraints, may be applied in the above cases. Finally, one example concerning the comparison of five different preparations is given to illustrate the methodology.

ANCOVA based on comparing a robust measure of location at empirically determined design points

For two independent groups, let (Yij), Xij), i = 1, …, nj; J = 1, 2 be a random sample of nj observations from the jth group. Suppose that for the jth group, the population trimmed mean of Y, given that X = x, is given by some unknown function mj(x). The paper describes a method of comparing the two regression lines at q design points determined empirically. The proposed procedure is based in part on a simple application of the running interval smoother which allows mj(x) to be modelled non‐parametrically. In contrast to extant methods, it is not assumed that the error term associated with the jth group has constant variance, nor is it assumed that the variance of Y, given X, is the same for both groups. The power of the new method compares well to the conventional method when the standard assumptions of normality, parallel regression lines, and homogeneity of variance are true. The new method can have substantially higher power when standard assumptions are violated, it provides good control over the probability of a Type I error for a much wider range of situations, and it provides a more detailed indication of where regression lines differ and by how much.

The "size principle" and synaptic effectiveness of muscle afferent projections to human extensor carpi radialis motoneurones during wrist extension.

The question of whether muscle spindle afferents might control human motoneurone activity on the basis of the "size principle" during voluntary contraction was investigated by recording the discharge of single motor units (n = 196) in wrist extensor muscles while stimulating the homonymous muscle spindles by means of tendon taps. The mechanical stimuli were delivered with a constant post-spike delay of 80 ms so that the resulting afferent volleys could be expected to reach the motoneurones towards the end of the inter-spike interval (mean +/- SD duration: 124.7 +/- 11.9 ms). In the six subjects tested, the response probability was found to be significantly correlated with the motor units' functional parameters. Differences in twitch rise times, twitch amplitudes, recruitment thresholds and macro-potential areas were found to account for 18%, 9%, 6% and 2% of the differences in the response probability observed within the whole population of motor units tested. These differences could not be due to differences in firing rate for two reasons: first, the motor units were found to discharge with a similar range of inter-spike intervals whatever their functional characteristics; secondly, the weak positive correlation observed between the response probability and the motor unit firing rate showed parallel regression lines between the late-recruited fast-contracting motor units and the first-recruited slowly contracting motor units, but the y-intercept was significantly higher in the latter case. This confirmed that the responses of the first-recruited slowly contracting motor units tended to be larger whatever the firing rates. In most of the pairs tested in the same experiment, the motor units which had the lowest recruitment thresholds, longest contraction times, smallest contraction forces or smallest motor unit macro-potentials tended to produce the largest responses, which also had the longest latencies. Taking the response latency to be an index of a motoneurone's conduction velocity and therefore of its size, the data obtained with this index and with other functional indices such as the twitch rise times and amplitudes, the macro-potential areas and the recruitment thresholds-can be said to be fully consistent with the "size principle", as previously found in anaesthetized animals. It can be inferred that the presynaptic inhibition which is liable to take action during voluntary contraction does not seem to alter the graded distribution of the muscle afferent projections to human wrist extensor motoneurones.

On approximation of the level probabilities for testing ordered parallel regression lines

Approximations for the level probabilities in testing order-restricted hypotheses are examined in this paper for generalized linear models with common slope. It is showed, in particular, that the asymptotic null distribution of the likelihood ratio statistic is a mixture of chi-squared distributions for the cases of simple order and simple tree order. Under a balanced structure, the asymptotic null distribution reduces to the well-known chi-bar-squared distribution. The use of the equal-weights level probabilities is also investigated. This approximation seems to be satisfactory when the sample sizes and the levels of the covariate are not too different among the strata.

Corrections: One-Sided Tests in Generalized Linear Models with Parallel Regression Lines

Corrections: One-Sided Tests in Generalized Linear Models with Parallel Regression Lines

Cognitive slowing in patients with acquired brain damage: an experimental approach.

Nine brain-damaged patients (19-54 years old) with "cognitive slowing", and 10 healthy subjects (26-56 years old) were tested with a slightly modified version of a Sternberg memory task (varied-set procedure). Cognitive slowing in the sense of reduced information-processing speed is reflected by mean RTs and slopes and intercepts derived from the RTs as a function of memory set size. Patients showed a marked increase of these parameters. While the results obtained from the control subjects are in accordance with typical Sternberg findings, patients showed no parallel regression lines for positive and negative responses. As an alternative explanation for this result an extended "self-terminating" process is proposed that also appears to be helpful in explaining the overall cognitive slowing in the patients.