The Mean Difference and the Mean Deviation of Some Discontinuous Distributions

Biometrika ◽  
1958 ◽  
Vol 45 (3/4) ◽  
pp. 549
Author(s):  
T. A. Ramasubban
Keyword(s):  
Mean Difference ◽  
Mean Deviation ◽  
The Mean

scholarly journals The accuracy of the determination of terrestrial refraction from reciprocal zenith angles

1979 ◽  
Vol 89 ◽  
pp. 203-212 ◽  
Author(s):  
K. Ramsayer
Keyword(s):  
Mean Difference ◽  
Mean Deviation ◽  
Refraction Coefficient ◽  
Refraction Angle ◽  
Observation Station ◽  
The Mean ◽  
True Values ◽  
Better Than

To investigate the accuracy of the determination of terrestrial refraction from reciprocal zenith angles and astronomical latitudes and longitudes at both ends of a line a test net with lines from 4 km to 23 km was observed and three dimensionally adjusted. As the measurements of the zenith angles were repeated every hour 40 times in an average the adjusted values were taken as a substitute for the true values. It is shown, that the mean refraction coefficient k, which is changing from k = 0.10 at day up to k = 0.34 at night, and the corresponding refraction angle can be determined very accurately, if both angles are measured simultaneously. Observations with day light are better than observations in the night. For observations with day light the mean difference between the true refraction angle at the observation station and the mean refraction angle of the observed line was smaller than ± 1″ independent of the length of the line. That means that the mean deviation of the true effective refraction coefficient in the observation station and the mean refraction coefficient of the observed line was inverse proportional to the distance.

The relation between the mean difference and the mean deviation in 11 continuous distribution models

2016 ◽  
Vol 51 (2) ◽  
pp. 595-615
Author(s):  
Angela Maria D’Uggento ◽  
Giovanni Girone ◽  
Claudia Marin
Keyword(s):  
Continuous Distribution ◽  
Mean Difference ◽  
Mean Deviation ◽  
Distribution Models ◽  
The Mean

DFT Benchmark Study of the O--O Bond Dissociation Energy in Peroxides Validated with High-Level Ab-Initio Calculations

2019 ◽  
Author(s):  
Danilo Carmona ◽  
Pablo Jaque ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Reference Value ◽  
Basis Set ◽  
Basis Sets ◽  
Mean Deviation ◽  
Bond Dissociation ◽  
Dissociation Energies ◽  
The Mean ◽  
Experimental Values ◽  
High Level ◽  
Almost All

<div><div><div><p>Peroxides play a central role in many chemical and biological pro- cesses such as the Fenton reaction. The relevance of these compounds lies in the low stability of the O–O bond which upon dissociation results in radical species able to initiate various chemical or biological processes. In this work, a set of 64 DFT functional-basis set combinations has been validated in terms of their capability to describe bond dissociation energies (BDE) for the O–O bond in a database of 14 ROOH peroxides for which experimental values ofBDE are available. Moreover, the electronic contributions to the BDE were obtained for four of the peroxides and the anion H2O2− at the CBS limit at CCSD(T) level with Dunning’s basis sets up to triple–ζ quality provid- ing a reference value for the hydrogen peroxide anion as a model. Almost all the functionals considered here yielded mean absolute deviations around 5.0 kcal mol−1. The smallest values were observed for the ωB97 family and the Minnesota M11 functional with a marked basis set dependence. Despite the mean deviation, order relations among BDE experimental values of peroxides were also considered. The ωB97 family was able to reproduce the relations correctly whereas other functionals presented a marked dependence on the chemical nature of the R group. Interestingly, M11 functional did not show a very good agreement with the established order despite its good performance in the mean error. The obtained results support the use of similar validation strategies for proper prediction of BDE or other molecular properties by DF Tmethods in subsequent related studies.</p></div></div></div>

Der Sommer und Herbst 2003 aus phänologischer Sicht | Summer and autumn 2003 from a phenological point of view

2004 ◽  
Vol 155 (5) ◽  
pp. 142-145 ◽  
Author(s):  
Claudio Defila
Keyword(s):  
Time Series ◽  
New Record ◽  
Point Of View ◽  
Late Spring ◽  
Mean Deviation ◽  
Leaf Shedding ◽  
The Mean ◽  
Very High ◽  
Selection Of

The record-breaking heatwave of 2003 also had an impact on the vegetation in Switzerland. To examine its influences seven phenological late spring and summer phases were evaluated together with six phases in the autumn from a selection of stations. 30% of the 122 chosen phenological time series in late spring and summer phases set a new record (earliest arrival). The proportion of very early arrivals is very high and the mean deviation from the norm is between 10 and 20 days. The situation was less extreme in autumn, where 20% of the 103 time series chosen set a new record. The majority of the phenological arrivals were found in the class «normal» but the class«very early» is still well represented. The mean precocity lies between five and twenty days. As far as the leaf shedding of the beech is concerned, there was even a slight delay of around six days. The evaluation serves to show that the heatwave of 2003 strongly influenced the phenological events of summer and spring.

scholarly journals Correlation between fundus autofluorescence and visual function in patients with cone-rod dystrophy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Satoru Kanda ◽  
Takumi Hara ◽  
Ryosuke Fujino ◽  
Keiko Azuma ◽  
Hirotsugu Soga ◽  
...  
Keyword(s):  
Visual Field ◽  
Significant Relationship ◽  
Fundus Autofluorescence ◽  
Univariate Analysis ◽  
Retrospective Chart Review ◽  
Mean Deviation ◽  
Wide Field ◽  
The Mean ◽  
The Relationship ◽  
Field Imaging

AbstractThis study aimed to investigate the relationship between autofluorescence (AF) signal measured with ultra-wide field imaging and visual functions in patients with cone-rod dystrophy (CORD). A retrospective chart review was performed for CORD patients. We performed the visual field test and fundus autofluorescence (FAF) measurement and visualized retinal structures with optical coherence tomography (OCT) on the same day. Using binarised FAF images, we identified a low FAF area ratio (LFAR: low FAF/30°). Relationships between age and logMAR visual acuity (VA), central retinal thickness (CRT), central choroidal thickness (CCT), mean deviation (MD) value, and LFAR were investigated. Thirty-seven eyes of 21 CORD patients (8 men and 13 women) were enrolled. The mean patient age was 49.8 years. LogMAR VA and MD were 0.52 ± 0.47 and − 17.91 ± 10.59 dB, respectively. There was a significant relationship between logMAR VA and MD (p = 0.001). LogMAR VA significantly correlated with CRT (p = 0.006) but not with other parameters. Conversely, univariate analysis suggested a significant relationship between MD and LFAR (p = 0.001). In the multivariate analysis, LFAR was significantly associated with MD (p = 0.002). In conclusion, it is useful to measure the low FAF area in patients with CORD. The AF measurement reflects the visual field deterioration but not VA in CORD.

scholarly journals Do we need to improve the reporting of evidence in tendinopathy management? A critical appraisal of systematic reviews with recommendations on strength of evidence assessment

2021 ◽  
Vol 7 (1) ◽  
pp. e000920
Author(s):  
Dimitris Challoumas ◽  
Neal L Millar
Keyword(s):  
Systematic Reviews ◽  
Assessment Tool ◽  
Data Extraction ◽  
Cochrane Collaboration ◽  
Mean Difference ◽  
Strength Of Evidence ◽  
The Mean ◽  
Randomised Controlled ◽  
Meta Analyses ◽  
The Cochrane Collaboration

ObjectiveTo critically appraise the quality of published systematic reviews (SRs) of randomised controlled trials (RCTs) in tendinopathy with regard to handling and reporting of results with special emphasis on strength of evidence assessment.Data sourcesMedline from inception to June 2020.Study eligibilityAll SRs of RCTs assessing the effectiveness of any intervention(s) on any location of tendinopathy.Data extraction and synthesisIncluded SRs were appraised with the use of a 12-item tool devised by the authors arising from the Preferred Reporting Items in Systematic Reviews and Meta-Analyses statement and other relevant guidance. Subgroup analyses were performed based on impact factor (IF) of publishing journals and date of publication.ResultsA total of 57 SRs were included published in 38 journals between 2006 and 2020. The most commonly used risk-of-bias (RoB) assessment tool and strength of evidence assessment tool were the Cochrane Collaboration RoB tool and the Cochrane Collaboration Back Review Group tool, respectively. The mean score on the appraisal tool was 46.5% (range 0%–100%). SRs published in higher IF journals (>4.7) were associated with a higher mean score than those in lower IF journals (mean difference 26.4%±8.8%, p=0.004). The mean score of the 10 most recently published SRs was similar to that of the first 10 published SRs (mean difference 8.3%±13.7%, p=0.54). Only 23 SRs (40%) used the results of their RoB assessment in data synthesis and more than half (n=30; 50%) did not assess the strength of evidence of their results. Only 12 SRs (21%) assessed their strength of evidence appropriately.ConclusionsIn light of the poor presentation of evidence identified by our review, we provide recommendations to increase transparency and reproducibility in future SRs.

scholarly journals The Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) Study—Defining a Threshold for Non-Cycloplegic Myopia Prevalence in Children

2021 ◽  
Vol 10 (6) ◽  
pp. 1215
Author(s):  
Aparna Gopalakrishnan ◽  
Jameel Rizwana Hussaindeen ◽  
Viswanathan Sivaraman ◽  
Meenakshi Swaminathan ◽  
Yee Ling Wong ◽  
...  
Keyword(s):  
Open Field ◽  
Tamil Nadu ◽  
Mean Difference ◽  
School Vision ◽  
Elite School ◽  
Prevalence Estimates ◽  
The Mean ◽  
Clinically Significant ◽  
Set Up ◽  
Definition Of

The aim of this study was to investigate the agreement between cycloplegic and non-cycloplegic autorefraction with an open-field auto refractor in a school vision screening set up, and to define a threshold for myopia that agrees with the standard cycloplegic refraction threshold. The study was conducted as part of the Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) study, which investigated the prevalence, incidence, and risk factors for myopia among children in South India. Children from two schools aged 5 to 15 years, with no ocular abnormalities and whose parents gave informed consent for cycloplegic refraction were included in the study. All the children underwent visual acuity assessment (Pocket Vision Screener, Elite school of Optometry, India), followed by non-cycloplegic and cycloplegic (1% tropicamide) open-field autorefraction (Grand Seiko, WAM-5500). A total of 387 children were included in the study, of whom 201 were boys. The mean (SD) age of the children was 12.2 (±2.1) years. Overall, the mean difference between cycloplegic and non-cycloplegic spherical equivalent (SE) open-field autorefraction measures was 0.34 D (limits of agreement (LOA), 1.06 D to −0.38 D). For myopes, the mean difference between cycloplegic and non-cycloplegic SE was 0.13 D (LOA, 0.63D to −0.36D). The prevalence of myopia was 12% (95% CI, 8% to 15%) using the threshold of cycloplegic SE ≤ −0.50 D, and was 14% (95% CI, 11% to 17%) with SE ≤ −0.50 D using non-cycloplegic refraction. When myopia was defined as SE of ≤−0.75 D under non-cycloplegic conditions, there was no difference between cycloplegic and non-cycloplegic open-field autorefraction prevalence estimates (12%; 95% CI, 8% to 15%; p = 1.00). Overall, non-cycloplegic refraction underestimates hyperopia and overestimates myopia; but for subjects with myopia, this difference is minimal and not clinically significant. A threshold of SE ≤ −0.75 D agrees well for the estimation of myopia prevalence among children when using non-cycloplegic refraction and is comparable with the standard definition of cycloplegic myopic refraction of SE ≤ −0.50 D.

scholarly journals Estimates of the mean difference in orthopaedic randomized trials: obligatory yet obscure

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Lauri Raittio ◽  
Antti Launonen ◽  
Ville M. Mattila ◽  
Aleksi Reito
Keyword(s):  
Primary Outcome ◽  
Outcome Measure ◽  
Patient Reported Outcome ◽  
Ceiling Effect ◽  
Mean Difference ◽  
Discussion Section ◽  
Power Calculations ◽  
Randomized Controlled ◽  
Patient Reported ◽  
The Mean

Abstract Background Randomized controlled trials in orthopaedics are powered to mainly find large effect sizes. A possible discrepancy between the estimated and the real mean difference is a challenge for statistical inference based on p-values. We explored the justifications of the mean difference estimates used in power calculations. The assessment of distribution of observations in the primary outcome and the possibility of ceiling effects were also assessed. Methods Systematic review of the randomized controlled trials with power calculations in eight clinical orthopaedic journals published between 2016 and 2019. Trials with one continuous primary outcome and 1:1 allocation were eligible. Rationales and references for the mean difference estimate were recorded from the Methods sections. The possibility of ceiling effect was addressed by the assessment of the weighted mean and standard deviation of the primary outcome and its elaboration in the Discussion section of each RCT where available. Results 264 trials were included in this study. Of these, 108 (41 %) trials provided some rationale or reference for the mean difference estimate. The most common rationales or references for the estimate of mean difference were minimal clinical important difference (16 %), observational studies on the same subject (8 %) and the ‘clinical relevance’ of the authors (6 %). In a third of the trials, the weighted mean plus 1 standard deviation of the primary outcome reached over the best value in the patient-reported outcome measure scale, indicating the possibility of ceiling effect in the outcome. Conclusions The chosen mean difference estimates in power calculations are rarely properly justified in orthopaedic trials. In general, trials with a patient-reported outcome measure as the primary outcome do not assess or report the possibility of the ceiling effect in the primary outcome or elaborate further in the Discussion section.

scholarly journals Corneal Biomechanical Parameters and Central Corneal Thickness in Glaucoma Patients, Glaucoma Suspects, and a Healthy Population

2021 ◽  
Vol 10 (12) ◽  
pp. 2637
Author(s):  
Mª. Ángeles del Buey-Sayas ◽  
Elena Lanchares-Sancho ◽  
Pilar Campins-Falcó ◽  
María Dolores Pinazo-Durán ◽  
Cristina Peris-Martínez
Keyword(s):  
Central Corneal Thickness ◽  
Corneal Thickness ◽  
Mean Difference ◽  
The Other ◽  
Control Group ◽  
Healthy Population ◽  
Diagnostic Categories ◽  
Significant Difference ◽  
Biomechanical Parameters ◽  
The Mean

Purpose: To evaluate and compare corneal hysteresis (CH), corneal resistance factor (CRF), and central corneal thickness (CCT), measurements were taken between a healthy population (controls), patients diagnosed with glaucoma (DG), and glaucoma suspect patients due to ocular hypertension (OHT), family history of glaucoma (FHG), or glaucoma-like optic discs (GLD). Additionally, Goldmann-correlated intraocular pressure (IOPg) and corneal-compensated IOP (IOPcc) were compared between the different groups of patients. Methods: In this prospective analytical-observational study, a total of 1065 patients (one eye of each) were recruited to undergo Ocular Response Analyzer (ORA) testing, ultrasound pachymetry, and clinical examination. Corneal biomechanical parameters (CH, CRF), CCT, IOPg, and IOPcc were measured in the control group (n = 574) and the other groups: DG (n = 147), FHG (n = 78), GLD (n = 90), and OHT (n = 176). We performed a variance analysis (ANOVA) for all the dependent variables according to the different diagnostic categories with multiple comparisons to identify the differences between the diagnostic categories, deeming p < 0.05 as statistically significant. Results: The mean CH in the DG group (9.69 mmHg) was significantly lower compared to controls (10.75 mmHg; mean difference 1.05, p < 0.001), FHG (10.70 mmHg; mean difference 1.00, p < 0.05), GLD (10.63 mmHg; mean difference 0.93, p < 0.05) and OHT (10.54 mmHg; mean difference 0.84, p < 0.05). No glaucoma suspects (FHG, GLD, OHT groups) presented significant differences between themselves and the control group (p = 1.00). No statistically significant differences were found in the mean CRF between DG (11.18 mmHg) and the control group (10.75 mmHg; mean difference 0.42, p = 0.40). The FHG and OHT groups showed significantly higher mean CRF values (12.32 and 12.41 mmHg, respectively) than the DG group (11.18 mmHg), with mean differences of 1.13 (p < 0.05) and 1.22 (p < 0.001), respectively. No statistically significant differences were found in CCT in the analysis between DG (562 μ) and the other groups (control = 556 μ, FHG = 576 μ, GLD = 569 μ, OHT = 570 μ). The means of IOPg and IOPcc values were higher in the DG patient and suspect groups than in the control group, with statistically significant differences in all groups (p < 0.001). Conclusion: This study presents corneal biomechanical values (CH, CRF), CCT, IOPg, and IOPcc for diagnosed glaucoma patients, three suspected glaucoma groups, and a healthy population, using the ORA. Mean CH values were markedly lower in the DG group (diagnosed with glaucoma damage) compared to the other groups. No significant difference was found in CCT between the DG and control groups. Unexpectedly, CRF showed higher values in all groups than in the control group, but the difference was only statistically significant in the suspect groups (FHG, GLD, and OHT), not in the DG group.

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