Correction for Rhiel's Theory for the Range Estimator of the Coefficient of Variation for Skewed Distributions

2010 ◽  
Vol 106 (1) ◽  
pp. 93-94
Author(s):  
G. Steven Rhiel
Keyword(s):  
Standard Deviation ◽  
Correction Factor ◽  
Coefficient Of Variation ◽  
Unbiased Estimate ◽  
Correction Factors ◽  
Skewed Distributions ◽  
The Mean

In 2007, Rhiel presented a technique to estimate the coefficient of variation from the range when sampling from skewed distributions. To provide an unbiased estimate, a correction factor ( an) for the mean was included. Numerical correction factors for a number of skewed distributions were provided. In a follow-up paper, he provided a proof he claimed showed the correction factor was independent of the mean and standard deviation, making the factors useful as these parameters vary; however, that proof did not establish independence. Herein is a proof which establishes the independence.

A Proof for Rhiel's Range Estimator of the Coefficient of Variation for Skewed Distributions

2007 ◽  
Vol 100 (1) ◽  
pp. 208-210 ◽  
Author(s):  
G. Steven Rhiel
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Research Study ◽  
Skewed Distributions ◽  
The Mean ◽  
Standard Deviations

In this research study is proof that the coefficient of variation ( CVhigh-low) calculated from the highest and lowest values in a set of data is applicable to specific skewed distributions with varying means and standard deviations. Earlier Rhiel provided values for dn, the standardized mean range, and an, an adjustment for bias in the range estimator of μ. These values are used in estimating the coefficient of variation from the range for skewed distributions. The dn and an values were specified for specific skewed distributions with a fixed mean and standard deviation. In this proof it is shown that the dn and an values are applicable for the specific skewed distributions when the mean and standard deviation can take on differing values. This will give the researcher confidence in using this statistic for skewed distributions regardless of the mean and standard deviation.

scholarly journals Classification and Statistical Trend Analysis in Detecting Glaucomatous Visual Field Progression

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Cristiana Valente ◽  
Elisa D’Alessandro ◽  
Michele Iester
Keyword(s):  
Statistical Analysis ◽  
Standard Deviation ◽  
Visual Field ◽  
Trend Analysis ◽  
Open Angle Glaucoma ◽  
Mean Deviation ◽  
Threshold Strategy ◽  
Visual Field Progression ◽  
The Mean

Aim. To evaluate the agreement between different methods in detection of glaucomatous visual field progression using two classification-based methods and four statistical approaches based on trend analysis. Methods. This is a retrospective and longitudinal study. Twenty Caucasian patients (mean age 73.8 ± 13.43 years) with open-angle glaucoma were recruited in the study. Each visual field was assessed by Humphrey Field Analyzer, program SITA standard 30-2 or 24-2 (Carl Zeiss Meditec, Inc., Dublin, CA). Full threshold strategy was also accepted for baseline tests. Progression was analyzed by using Hodapp–Parrish–Anderson classification and the Advanced Glaucoma Intervention Study visual field defect score. For the statistical analysis, linear regression (r2) was calculated for mean deviation (MD), pattern standard deviation (PSD), and visual field index (VFI), and when it was significant, each series of visual field was considered progressive. We also used Progressor to look for a significant progression of each visual field series. The agreement between methods, based on statistical analysis and classification, was evaluated using a weighted kappa statistic. Results. Thirty-eight visual field series were analyzed. The mean follow-up time was 6.2 ± 1.53 years (mean ± standard deviation). At baseline, the mean MD was −7.34 ± 7.18 dB; at the end of the follow-up, the mean MD was −9.25 ± 8.65 dB; this difference was statistically significant (p<0.001). The agreement to detect progression was fair between all methods based on statistical analysis and classification except for PSD r2. A substantial agreement (κ = 0.698 ± 0.126) was found between MD r2 and VFI r2. With the use of all the statistical analysis, there was a better time-saving. Conclusions. The best agreement to detect progression was found between MD r2 and VFI r2. VFI r2 showed the best agreement with all the other methods. GPA2 can help ophthalmologists to detect glaucoma progression and to help in treatment decisions. PSD r2 was the worse method to detect progression.

Outcome of facial physiotherapy in patients with prolonged idiopathic facial palsy

2015 ◽  
Vol 129 (4) ◽  
pp. 348-352 ◽  
Author(s):  
G J Watson ◽  
S Glover ◽  
S Allen ◽  
R M Irving
Keyword(s):  
Standard Deviation ◽  
Facial Paralysis ◽  
Grading System ◽  
Duration Of Treatment ◽  
Duration Of Symptoms ◽  
Average Improvement ◽  
The Mean ◽  
Pre Treatment ◽  
Idiopathic Facial Palsy

AbstractObjective:This study investigated whether patients who remain symptomatic more than a year following idiopathic facial paralysis gain benefit from tailored facial physiotherapy.Methods:A two-year retrospective review was conducted of all symptomatic patients. Data collected included: age, gender, duration of symptoms, Sunnybrook facial grading system scores pre-treatment and at last visit, and duration of treatment.Results:The study comprised 22 patients (with a mean age of 50.5 years (range, 22–75 years)) who had been symptomatic for more than a year following idiopathic facial paralysis. The mean duration of symptoms was 45 months (range, 12–240 months). The mean duration of follow up was 10.4 months (range, 2–36 months). Prior to treatment, the mean Sunnybrook facial grading system score was 59 (standard deviation = 3.5); this had increased to 83 (standard deviation = 2.7) at the last visit, with an average improvement in score of 23 (standard deviation = 2.9). This increase was significant (p < 0.001).Conclusion:Tailored facial therapy can improve facial grading scores in patients who remain symptomatic for prolonged periods.

scholarly journals P577 Withdrawal of thiopurines in patients with Ulcerative Colitis in remission

2021 ◽  
Vol 15 (Supplement_1) ◽  
pp. S534-S534
Author(s):  
C Amor Costa ◽  
C Suárez Ferrer ◽  
J Poza Cordón ◽  
J L Rueda García ◽  
M Sánchez Azofra ◽  
...  
Keyword(s):  
Risk Factors ◽  
Ulcerative Colitis ◽  
Standard Deviation ◽  
Adverse Effects ◽  
Medical Decision ◽  
Concomitant Treatment ◽  
Duration Of Treatment ◽  
The Mean ◽  
Time To Relapse

Abstract Background Thiopurines (TP) are widely used in monotherapy in patients with ulcerative colitis (UC), mainly for the maintenance of remission in case of corticodependence or corticoresistance after cyclosporine use. However, these are drugs with significant side effects, especially in the long term. The optimal duration of treatment with TP remains unknown, so it is important to determine the risk factors for relapse in order to identify the group of patients in which treatment can be withdrawn. Methods A retrospective study was performed. Patients with UC in remission, in maintenance treatment with TP, who had discontinued the drug due to either maintained remission or the onset of adverse effects were included. Results 26 patients were included, 1 with proctitis, 9 with left colitis and 16 with pancolitis. 24 (92.31%) were treated with azathioprine and 2 (7.69%) with mercaptopurine. The mean treatment time with TP was 68.09 months (standard deviation 56.65). 11 patients (42.31%) discontinued TP due to adverse effects and the remaining patients (57.69%) discontinued it by medical decision because they were in prolonged remission. After withdrawal of TP, 92.34% of patients continued treatment with mesalazine and the remaining 7.69% without concomitant treatment. During follow-up, 10 patients (38.4%) relapsed and 16 patients (61.53%) had no relapse until the end of follow-up. The mean time from TP withdrawal to the onset of relapse was 69.15 months (standard deviation 52.53). Of the 10 patients who presented a flare, 5 (50%) were controlled by optimizing the dose of mesalazine, 4 (40%) required the addition of oral corticosteroids and 1 (10%) required biologics. No significant differences were found when comparing the time to relapse if the reason for discontinuation of TP was having had an adverse effect (65.05 months) or maintained remission (79.79 months) (p=0.42). No statistically significant differences were found in time to relapse when comparing time on TP treatment, presence of concomitant treatment with mesalazine or active smoking. Conclusion One third of patients relapsed after TP withdrawal. Discontinuation of TP in patients with UC in remission should be individualized according to the patient’s risk factors, the indication and the duration of treatment.

scholarly journals Properties of the Standard Deviation that are Rarely Mentioned in Classrooms

2016 ◽  
Vol 38 (3) ◽  
Author(s):  
Mohammad Fraiwan Al-Saleh ◽  
Adil Eltayeb Yousif
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Sample Variance ◽  
Mean Absolute Deviation ◽  
Hidden Information ◽  
Absolute Deviation ◽  
Sample Mean ◽  
The Mean ◽  
Vague Concept ◽  
Chebyshev's Inequality

Unlike the mean, the standard deviation ¾ is a vague concept. In this paper, several properties of ¾ are highlighted. These properties include the minimum and the maximum of ¾, its relationship to the mean absolute deviation and the range of the data, its role in Chebyshev’s inequality and the coefficient of variation. The hidden information in the formula itself is extracted. The confusion about the denominator of the sample variance being n ¡ 1 is also addressed. Some properties of the sample mean and varianceof normal data are carefully explained. Pointing out these and other properties in classrooms may have significant effects on the understanding and the retention of the concept.

scholarly journals Long-term glycemic variability and risk of stroke in patients with diabetes: a meta-analysis

2022 ◽  
Vol 14 (1) ◽  
Author(s):  
Xiaoli Ren ◽  
Zhiyun Wang ◽  
Congfang Guo
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Meta Analysis ◽  
Glycemic Variability ◽  
Diabetic Patients ◽  
Increased Risk ◽  
Follow Up Studies ◽  
Patients With Diabetes

Abstract Objectives Long-term glycemic variability has been related to increased risk of vascular complication in patients with diabetes. However, the association between parameters of long-term glycemic variability and risk of stroke remains not fully determined. We performed a meta-analysis to systematically evaluate the above association. Methods Medline, Embase, and Web of Science databases were searched for longitudinal follow-up studies comparing the incidence of stroke in diabetic patients with higher or lower long-term glycemic variability. A random-effect model incorporating the potential heterogeneity among the included studies were used to pool the results. Results Seven follow-up studies with 725,784 diabetic patients were included, and 98% of them were with type 2 diabetes mellitus (T2DM). The mean follow-up duration was 7.7 years. Pooled results showed that compared to those with lowest category of glycemic variability, diabetic patients with the highest patients had significantly increased risk of stroke, as evidenced by glycemic variability analyzed by fasting plasma glucose coefficient of variation (FPG-CV: risk ratio [RR] = 1.24, 95% confidence interval [CI] 1.11 to 1.39, P < 0.001; I2 = 53%), standard deviation of FPG (FPG-SD: RR = 1.16, 95% CI 1.02 to 1.31, P = 0.02; I2 = 74%), HbA1c coefficient of variation (HbA1c-CV: RR = 1.88, 95% CI 1.61 to 2.19 P < 0.001; I2 = 0%), and standard deviation of HbA1c (HbA1c-SD: RR = 1.73, 95% CI 1.49 to 2.00, P < 0.001; I2 = 0%). Conclusions Long-term glycemic variability is associated with higher risk of stroke in T2DM patients.

scholarly journals Correction of a lunar irradiance model for aerosol optical depth retrieval and comparison with star photometer

2020 ◽  
Author(s):  
Roberto Román ◽  
Ramiro González ◽  
Carlos Toledano ◽  
África Barreto ◽  
Daniel Pérez-Ramírez ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Correction Factor ◽  
The Moon ◽  
Night Time ◽  
Technological Advances ◽  
Fast Change ◽  
The Mean ◽  
Cycle Dependent

Abstract. The emergence of Moon photometers is allowing measurements of lunar irradiance over the world and increasing the potential to derive aerosol optical depth (AOD) at night-time, that is very relevant in polar areas. Actually, new photometers implement the latest technological advances that permit lunar irradiance measurements together with classical Sun photometry measurements. However, a proper use of these instruments for AOD retrieval requires accurate time-dependent knowledge of the extraterrestrial lunar irradiance over time, due to its fast change throughout the Moon's cycle. This paper uses the RIMO model (an implementation of the ROLO model) to estimate the AOD at night-time assuming that the calibration of the solar channels can be transferred to the Moon by a vicarious method. However, the obtained AOD values using a Cimel CE318-T Sun/sky/Moon photometer for 98 pristine nights with low and stable AOD at the Izaña Observatory (Tenerife, Spain) are not in agreement with the expected (low and stable) AOD values, estimated by linear interpolations from daytime values obtained during the previous evening and the following morning. Actually, AOD calculated using RIMO shows negative values and with a marked cycle dependent on the optical airmass. The differences between the AOD obtained using RIMO and the expected values are assumed to be associated with inaccuracies in the RIMO model, and these differences are used to calculate the RIMO correction factor (RCF). The RCF is a proposed correction factor that, multiplied by RIMO value, gives an effective extraterrestrial lunar irradiance that provides the expected AOD values. The RCF varies with the Moon phase angle (MPA) and with wavelength, ranging from 1.01 to 1.14, which reveals an overall underestimation of RIMO to the lunar irradiance. These obtained RCF values are modeled for each photometer wavelength to a second order polynomial as function of MPA. The AOD derived by this proposed method is compared with the independent AOD measurements obtained by a star photometer at Granada (Spain) for two years. The mean of the Moon-star AOD differences are between −0.015 and −0.005 and the standard deviation between 0.03 and 0.04 (which is reduced to about 0.01 if one month of data affected by instrumental issues is not included in the analysis), for 440, 500, 675 ad 870 nm; however, for 380 nm, the mean and standard deviation of these differences are higher. The Moon-star AOD differences are also analyzed as a function of MPA, showing no significant dependence.

scholarly journals Factors associated with institutionalization among home-dwelling patients of Urgent Geriatric Outpatient Clinic: a 3-year follow-up study

2020 ◽  
Vol 11 (5) ◽  
pp. 745-751
Author(s):  
Marika Salminen ◽  
Jonna Laine ◽  
Tero Vahlberg ◽  
Paula Viikari ◽  
Maarit Wuorela ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Outpatient Clinic ◽  
Older Patients ◽  
Cox Regression ◽  
Regression Analyses ◽  
Factors Associated ◽  
Follow Up Study ◽  
The Mean ◽  
First Time

Abstract Purpose To examine the effect of predictive factors on institutionalization among older patients. Methods The participants were older (aged 75 years or older) home-dwelling citizens evaluated at Urgent Geriatric Outpatient Clinic (UrGeriC) for the first time between the 1st of September 2013 and the 1st of September 2014 (n = 1300). They were followed up for institutionalization for 3 years. Death was used as a competing risk in Cox regression analyses. Results The mean age of the participants was 85.1 years (standard deviation [SD] 5.5, range 75–103 years), and 74% were female. The rates of institutionalization and mortality were 29.9% and 46.1%, respectively. The mean age for institutionalization was 86.1 (SD 5.6) years. According to multivariate Cox regression analyses, the use of home care (hazard ratio 2.43, 95% confidence interval 1.80–3.27, p < 0.001), dementia (2.38, 1.90–2.99, p < 0.001), higher age (≥ 95 vs. 75–84; 1.65, 1.03–2.62, p = 0.036), and falls during the previous 12 months (≥ 2 vs. no falls; 1.54, 1.10–2.16, p = 0.012) significantly predicted institutionalization during the 3-year follow-up. Conclusion Cognitive and/or functional impairment mainly predicted institutionalization among older patients of UrGeriC having health problems and acute difficulties in managing at home.

scholarly journals Fourth ventricle computed tomography indexes: standardisation and characteristics in neurocysticercosis

2002 ◽  
Vol 60 (2A) ◽  
pp. 211-218 ◽  
Author(s):  
Svetlana Agapejev
Keyword(s):  
Computed Tomography ◽  
Standard Deviation ◽  
Fourth Ventricle ◽  
Control Group ◽  
Mean Values ◽  
Lateral Ventricles ◽  
The Mean ◽  
Ventricular Shunting

OBJECTIVES: to propose standardisation of fourth ventricle dimensions and to study its characteristics in neurocysticercosis. METHOD: a control group (CG) constituted by 114 individuals with normal CT, and 80 patients with neurocysticercosis composed the group with neurocysticercosis (GN). Measures of the inner cranial diameter (Cr), fronto-polar distance between both lateral ventricles (FP), antero-posterior (AP) and latero-lateral (LL) fourth ventricle width based the standardisation of six indexes. RESULTS: AP/Cr, AP/LL and AP/FP were the more discriminative indexes, presenting in CG the mean values of 0.063, 0.267 and 0.582, respectively. The indexes in GN had values statistically higher than in CG. From GN, 51patients had increased indexes values above 2 standard deviation of the CG mean. AP/Ll was > or = 1 in 95% of patients with ventricular shunting and in 88% with depression. It also occurred in 73% patients with satisfactory follow-up and in everybody who died. CONCLUSION: AP/Cr, AP/LL and AP/FP may represent fourth ventricle dimensions.

scholarly journals Comparison of Four Radiographic Angular Measures of Lumbar Lordosis

2018 ◽  
Vol 09 (03) ◽  
pp. 298-304 ◽  
Author(s):  
Francis Osita Okpala
Keyword(s):  
Standard Deviation ◽  
Lumbar Lordosis ◽  
Joint Angle ◽  
Mean Values ◽  
Normal Individuals ◽  
Wide Range ◽  
Normal Mean ◽  
The Mean ◽  
Range Of Values

ABSTRACT Background: Several attempts (radiographic and nonradiographic) have been made to measure the lumbar lordosis (LL), but the results differ substantially as investigators have used different parameters. Radiography is the gold standard, and the methods include lumbosacral angle (LSA), lumbosacral joint angle (LSJA), Cobb angle, and tangential radiologic assessment of LL (TRALL) angle. The traditional method, the Cobb technique, has a wide range of normal mean values, with a large standard deviation. Using a more reliable radiographic angle will hopefully simply and standardize LL measurement in the diagnosis, treatment, and follow-up of patients. Aim: To compare in normal individuals with fully developed LL the LSA, LSJA, TRALL, and Cobb angles, by determining (a) if any correlation exists between them and (b) the most reliable measures of LL, based on, least (i) number of measurement lines, (ii) range of values, (iii) mean, (iv) standard deviation, and (v) variance. Materials and Methods: The four angles were retrospectively measured in each supine lateral lumbosacral radiograph of 100 males and 100 females, aged 15 years and above. Data were analyzed with IBM SPSS Statistics 23.0 (NY, USA); P < 0.05 was considered statistically significant. Results: No correlation existed between the mean values of the four angles, and in each angle, there was no male-versus-female correlation. LSJA had the best reliability criteria for LL measurement. Conclusion: The mean LSA, LSJA, TRALL, and Cobb angles have no significant Pearson's correlation, and of the four angular measures of LL, LSJA was the most reliable.

Sign in / Sign up

Export Citation Format

Share Document