scholarly journals Meta-analysis of the variance ratio

2017 ◽  
Author(s):  
Nicolas Traut
Keyword(s):  
Standard Deviation ◽  
Meta Analysis ◽  
Mean Difference ◽  
Variance Ratio ◽  
Mean Values ◽  
Variance Ratios ◽  
The Mean ◽  
Standard Deviations ◽  
The Difference ◽  
Fisher’S Ratio

IntroductionThe most commonly used effect size when using meta-analysis to compare a measurement of interest in two different populations is the standardised mean difference. This is the mean difference of the measurement divided by the pooled standard deviation in the two groups. The standard deviation is usually supposed to be the same for both groups, although this assumption is often made without any particular evidence. It is possible, however, that the difference of the measurement in the two populations resides precisely in their standard deviations. This could be the case, for example, if a population of patients exhibited more “abnormal” values than a control population – both large and small – even if the mean values were the same. Fisher’s test of equality of variance is designed to compare standard deviations. A variance ratio is a Fisher’s ratio and Fisher distribution can be used to give confidence intervals to the estimate for one study. However, confidence interval for one study can be very wide if the study does not contain enough subjects. Here we present an approach to combine variance ratios of different studies in a meta-analytic way which produces more robust estimates under these circumstances.

scholarly journals The Effectiveness of Mix Impact Aerobic Gymnastics Exercises With SKJ 2000 On Improvement of Physical Freshness

2021 ◽  
Vol 12 (03) ◽  
pp. 39-44
Author(s):  
Anik Maryani ◽  
Fahmy Fachrezzy ◽  
Ramdan Pelana
Keyword(s):  
Standard Deviation ◽  
Physical Fitness ◽  
Aerobic Exercise ◽  
Standard Error ◽  
Exercise Group ◽  
Mean Value ◽  
Mean Difference ◽  
Final Test ◽  
The Mean ◽  
The Difference

This study aims to determine the effectiveness of the effect of aerobic mix impact and SKJ 2000 version (core exercise) to improve physical fitness in female students. The research was conducted at SMEA YASMA Sudirman Cijantung for 8 weeks with 24 meetings. The method used is an experimental method with a pre and post-test design. The sampling technique was random sampling from a total of 40 grade 1 students and 30 samples were taken. The data collection technique used was a physical fitness test using the Indonesian Physical Fitness Test (TKJI). Hypothesis testing uses the t-test at the significant level (α) 0.05. The results showed that the difference between the mean value of the initial test (x) and the final test (y) in the mixed impact aerobic exercise group was obtained = -6.47; the value of the standard deviation of the difference = 1,2; the standard error value of the mean difference = 0.32; and the value becomes = -20,2. The initial test (x) and the final test (y) in the 2000 version of the Physical Fitness exercise obtained the difference in the mean value is = -5; the value of the standard deviation of the difference = 1.1; the standard error value of the mean difference = 0.29; and the value becomes = -17.24. The final test of the mixed impact aerobic exercise group (x) and the final test of the aerobic exercise group (y) version 2000, obtained the mean value of the variable x = 19.33; variable value y = 17; the standard deviation value x = 1.48; standard deviation of the variable y = 2.31; standard error variable x = 0.4; standard error for the variable y = 0.62; standard error for the mean difference between x and variable = 0.74; Hypothesis test results obtained t observation = 3.15, at 28 degrees of freedom and a significant level (α) 0.05, the value of t table = 2.048 is obtained. The conclusion of the study is that the effect of mix impact aerobic exercise is more effective in improving physical fitness compared to those using the 2000 version of the fitness gymnastics version of aerobic exercise.

scholarly journals Improved information about the vertical location and extent of cloud layers from POLDER3 measurements in the oxygen A band

2013 ◽  
Vol 6 (2) ◽  
pp. 2533-2581 ◽  
Author(s):  
M. Desmons ◽  
N. Ferlay ◽  
F. Parol ◽  
L. Mcharek ◽  
C. Vanbauce
Keyword(s):  
Standard Deviation ◽  
Oxygen Pressure ◽  
Optical Thickness ◽  
Mean Difference ◽  
Vertical Extent ◽  
Satellite Platform ◽  
Cloud Optical Thickness ◽  
The Mean ◽  
The Difference ◽  
The One

Abstract. This paper describes new advances in the exploitation of oxygen A band measurements from POLDER3 sensor aboard PARASOL, satellite platform within the A-Train. These developments result from a better account of the dependence of POLDER oxygen parameters to cloud optical thickness τ and to the scene's geometrical conditions, but also and more importantly from the finer understanding of the sensitivity of these parameters to cloud vertical extent. This sensitivity is made possible thanks to the multidirectional character of POLDER measurements. In the case of monolayer clouds that represent most of cloudy conditions, new oxygen parameters are obtained and calibrated from POLDER3 data colocalized with the measurements of the two active sensors of the A-Train, CALIOP/CALIPSO and CPR/CloudSat. From a parameterization that is (μs, τ) dependent, with μs the cosine of the solar zenith angle, a cloud top oxygen pressure (CTOP) and a cloud middle oxygen pressure (CMOP) are obtained which are estimates of actual cloud top and middle pressures. The performance of CTOP and CMOP are presented for the most numerous ISCCP cases in 2008. The coefficient of the correlation between CMOP and the actual cloud middle pressure is 0.81 for cirrostratus, 0.79 for stratocumulus, 0.75 for deep convective clouds. The coefficient of the correlation between CTOP and the actual cloud top pressure is 0.75, 0.73, and 0.79 for the same cloud types respectively. The score obtained by CTOP, defined as the confidence in the retrieval for a particular range of infered value and for a given error, is higher than the one of MODIS CTP. For liquid and ice clouds, the score reaches 50 and 70% respectively for bin value of CTP superior in numbers and accepted errors of 30 and 50 hPa. From the difference between CTOP and CMOP, a first estimate of the cloud vertical extent H is possible. Then, the correlation between the angular standard deviation of POLDER oxygen pressure σPO2 and the cloud vertical extent is described in detail in the case of liquid clouds. The correlation is shown to be spatially and temporally robust, excepted for clouds above land during winter months. The study of the correlation's dependence to cloud optical thickness and to the scene's geometrical conditions leads to parameterizations which provide a second way for retrieving H for this type of clouds. For liquid water clouds above ocean in 2008, the mean difference between the actual cloud vertical extent and the one retrieved from σPO2 (from the pressure difference) is 5 m (−12 m). The standard deviation of the mean difference is close to 1000 m for the two methods. The score of 50% confidence for the retrieval of H corresponds to an error of 20 and 40% for ice and liquid clouds respectively over ocean. These promising results need to be validated outside of the CALIPSO/CloudSat track.

scholarly journals Choice of positive distribution law for nuclear data

2018 ◽  
Vol 4 ◽  
pp. 38
Author(s):  
Sébastien Lahaye
Keyword(s):  
Standard Deviation ◽  
Nuclear Data ◽  
Mean Value ◽  
Distribution Law ◽  
Mean Values ◽  
Relative Standard ◽  
Distribution Laws ◽  
The Mean ◽  
Standard Deviations ◽  
Truncated Gaussian

Nuclear data evaluation files in the ENDF6 format provide mean values and associated uncertainties for physical quantities relevant in nuclear physics. Uncertainties are denoted as Δ in the format description, and are commonly understood as standard deviations. Uncertainties can be completed by covariance matrices. The evaluations do not provide any indication on the probability density function to be used when sampling. Three constraints must be observed: the mean value, the standard deviation and the positivity of the physical quantity. MENDEL code generally uses positively truncated Gaussian distribution laws for small relative standard deviations and a lognormal law for larger uncertainty levels (>50%). Indeed, the use of truncated Gaussian laws can modify the mean and standard deviation value. In this paper, we will make explicit the error in the mean value and the standard deviation when using different types of distribution laws. We also employ the principle of maximum entropy as a criterion to choose among the truncated Gaussian, the fitted Gaussian and the lognormal distribution. Remarkably, the difference in terms of entropy between the candidate distribution laws is a function of the relative standard deviation only. The obtained results provide therefore general guidance for the choice among these distributions.

scholarly journals Technical note: analytical estimation of the optimal parameters for the EOF retrievals of the IASI Level 2 Product Processing Facility and its application using AIRS and ECMWF data

2006 ◽  
Vol 6 (3) ◽  
pp. 831-846 ◽  
Author(s):  
X. Calbet ◽  
P. Schlüssel
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Mean Difference ◽  
Training Data ◽  
Data Set ◽  
The Real ◽  
Atmospheric Profiles ◽  
The Mean ◽  
Atmospheric State ◽  
The Difference

Abstract. The Empirical Orthogonal Function (EOF) retrieval technique consists of calculating the eigenvectors of the spectra to later perform a linear regression between these and the atmospheric states, this first step is known as training. At a later stage, known as performing the retrievals, atmospheric profiles are derived from measured atmospheric radiances. When EOF retrievals are trained with a statistically different data set than the one used for retrievals two basic problems arise: significant biases appear in the retrievals and differences between the covariances of the training data set and the measured data set degrade them. The retrieved profiles will show a bias with respect to the real profiles which comes from the combined effect of the mean difference between the training and the real spectra projected into the atmospheric state space and the mean difference between the training and the atmospheric profiles. The standard deviations of the difference between the retrieved profiles and the real ones show different behavior depending on whether the covariance of the training spectra is bigger, equal or smaller than the covariance of the measured spectra with which the retrievals are performed. The procedure to correct for these effects is shown both analytically and with a measured example. It consists of first calculating the average and standard deviation of the difference between real observed spectra and the calculated spectra obtained from the real atmospheric state and the radiative transfer model used to create the training spectra. In a later step, measured spectra must be bias corrected with this average before performing the retrievals and the linear regression of the training must be performed adding noise to the spectra corresponding to the aforementioned calculated standard deviation. This procedure is optimal in the sense that to improve the retrievals one must resort to using a different training data set or a different algorithm.

scholarly journals Improved information about the vertical location and extent of monolayer clouds from POLDER3 measurements in the oxygen A-band

2013 ◽  
Vol 6 (8) ◽  
pp. 2221-2238 ◽  
Author(s):  
M. Desmons ◽  
N. Ferlay ◽  
F. Parol ◽  
L. Mcharek ◽  
C. Vanbauce
Keyword(s):  
Standard Deviation ◽  
Oxygen Pressure ◽  
Mean Difference ◽  
Active Sensors ◽  
Convective Clouds ◽  
Vertical Extent ◽  
Satellite Platform ◽  
The Mean ◽  
The Difference ◽  
The One

Abstract. This paper describes new advances in the exploitation of oxygen A-band measurements from POLDER3 sensor onboard PARASOL, satellite platform within the A-Train. These developments result from not only an account of the dependence of POLDER oxygen parameters to cloud optical thickness τ and to the scene's geometrical conditions but also, and more importantly, from the finer understanding of the sensitivity of these parameters to cloud vertical extent. This sensitivity is made possible thanks to the multidirectional character of POLDER measurements. In the case of monolayer clouds that represent most of cloudy conditions, new oxygen parameters are obtained and calibrated from POLDER3 data colocalized with the measurements of the two active sensors of the A-Train: CALIOP/CALIPSO and CPR/CloudSat. From a parameterization that is (μs, τ) dependent, with μs the cosine of the solar zenith angle, a cloud top oxygen pressure (CTOP) and a cloud middle oxygen pressure (CMOP) are obtained, which are estimates of actual cloud top and middle pressures (CTP and CMP). Performances of CTOP and CMOP are presented by class of clouds following the ISCCP classification. In 2008, the coefficient of the correlation between CMOP and CMP is 0.81 for cirrostratus, 0.79 for stratocumulus, 0.75 for deep convective clouds. The coefficient of the correlation between CTOP and CTP is 0.75, 0.73, and 0.79 for the same cloud types. The score obtained by CTOP, defined as the confidence in the retrieval for a particular range of inferred value and for a given error, is higher than the one of MODIS CTP estimate. Scores of CTOP are the highest for bin value of CTP superior in numbers. For liquid (ice) clouds and an error of 30 hPa (50 hPa), the score of CTOP reaches 50% (70%). From the difference between CTOP and CMOP, a first estimate of the cloud vertical extent h is possible. A second estimate of h comes from the correlation between the angular standard deviation of POLDER oxygen pressure σPO2 and the cloud vertical extent. This correlation is studied in detail in the case of liquid clouds. It is shown to be spatially and temporally robust, except for clouds above land during winter months. The analysis of the correlation's dependence on the scene's characteristics leads to a parameterization providing h from σPO2. For liquid water clouds above ocean in 2008, the mean difference between the actual cloud vertical extent and the one retrieved from σPO2 (from the pressure difference) is 5 m (−12 m). The standard deviation of the mean difference is close to 1000 m for the two methods. POLDER estimates of the cloud geometrical thickness obtain a global score of 50% confidence for a relative error of 20% (40%) of the estimate for ice (liquid) clouds over ocean. These results need to be validated outside of the CALIPSO/CloudSat track.

scholarly journals Sirius Scheimpflug–Placido versus ultrasound pachymetry for central corneal thickness: meta-analysis

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yili Jin ◽  
Colm McAlinden ◽  
Yong Sun ◽  
Daizong Wen ◽  
Yiran Wang ◽  
...  
Keyword(s):  
Central Corneal Thickness ◽  
Meta Analysis ◽  
Corneal Thickness ◽  
Mean Difference ◽  
Cochrane Library ◽  
Ultrasound Pachymetry ◽  
Significant Difference ◽  
The Mean ◽  
The Difference ◽  
Clinically Significant

Abstract Background To compare the difference in central corneal thickness (CCT) measurements in normal eyes between a rotating Scheimpflug camera combined with a Placido-disk corneal topographer (Sirius, CSO, Italy) and ultrasound pachymetry (USP). Methods A systematic literature search was conducted for relevant studies published on PubMed, Medline, EMBASE, and the Cochrane Library and ClinicalTrials.gov from inception to August 1st, 2019. Primary outcome measures were CCT measurements between Sirius and USP. A random effects model was used to pool CCT measurements. Results A total of twelve studies involving 862 eyes were included in this meta-analysis. The meta-analysis found CCT measurements between Sirius and USP to be statistically significantly different (P < 0.0001). The mean difference between Sirius and USP was −11.26 μm with a 95% confidence interval (CI) (−16.92 μm, −5.60 μm). The heterogeneity was I2 = 60% (P = 0.004). Conclusion CCT measurements with the Sirius Scheimpflug-Placido topographer were statistically significantly lower than USP. However, it may be argued that the mean difference of 11.26 μm is not a clinically significant difference.

scholarly journals Technical note: analytical estimation of the optimal parameters for the EOF retrievals of the IASI Level 2 Product Processing Facility and its application using AIRS and ECMWF data

2005 ◽  
Vol 5 (5) ◽  
pp. 9691-9730
Author(s):  
X. Calbet ◽  
P. Schlüssel
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Mean Difference ◽  
Training Data ◽  
Data Set ◽  
The Real ◽  
Atmospheric Profiles ◽  
The Mean ◽  
Atmospheric State ◽  
The Difference

Abstract. The Empirical Orthogonal Function (EOF) retrieval technique consists of calculating the eigenvectors of the spectra to later perform a linear regression between these and the atmospheric states, this first step is known as training. At a later stage, known as performing the retrievals, atmospheric profiles are derived from measured atmospheric radiances. When EOF retrievals are trained with a statistically different data set than the one used for retrievals two basic problems arise: significant biases appear in the retrievals and differences between the covariances of the training data set and the measured data set degrade them. The retrieved profiles will show a bias with respect to the real profiles which comes from the combined effect of the mean difference between the training and the real spectra projected into the atmospheric state space and the mean difference between the training and the atmospheric profiles. The standard deviations of the difference between the retrieved profiles and the real ones show different behavior depending on whether the covariance of the training spectra is bigger, equal or smaller than the covariance of the measured spectra with which the retrievals are performed. The procedure to correct for these effects is shown both analytically and with a measured example. It consists of first calculating the average and standard deviation of the difference between real observed spectra and the calculated spectra obtained from the real atmospheric state and the radiative transfer model used to create the training spectra. In a later step, measured spectra must be bias corrected with this average before performing the retrievals and the linear regression of the training must be performed adding noise to the spectra corresponding to the aforementioned calculated standard deviation. This procedure is optimal in the sense that to improve the retrievals one must resort to using a different training data set or a different algorithm.

Seasonal trends in the stable isotopic composition of snow and meltwater runoff in a subarctic catchment at Okstindan, Norway

2004 ◽  
Vol 35 (2) ◽  
pp. 119-137 ◽  
Author(s):  
S.D. Gurney ◽  
D.S.L. Lawrence
Keyword(s):  
Isotopic Composition ◽  
Mean Value ◽  
Mean Values ◽  
Stable Isotopic Composition ◽  
Meltwater Runoff ◽  
Stable Isotopic ◽  
The Mean ◽  
The Difference ◽  
Δ18o And Δd

Seasonal variations in the stable isotopic composition of snow and meltwater were investigated in a sub-arctic, mountainous, but non-glacial, catchment at Okstindan in northern Norway based on analyses of δ18O and δD. Samples were collected during four field periods (August 1998; April 1999; June 1999 and August 1999) at three sites lying on an altitudinal transect (740–970 m a.s.l.). Snowpack data display an increase in the mean values of δ18O (increasing from a mean value of −13.51 to −11.49‰ between April and August), as well as a decrease in variability through the melt period. Comparison with a regional meteoric water line indicates that the slope of the δ18O–δD line for the snowpacks decreases over the same period, dropping from 7.49 to approximately 6.2.This change points to the role of evaporation in snowpack ablation and is confirmed by the vertical profile of deuterium excess. Snowpack seepage data, although limited, also suggest reduced values of δD, as might be associated with local evaporation during meltwater generation. In general, meltwaters were depleted in δ18O relative to the source snowpack at the peak of the melt (June), but later in the year (August) the difference between the two was not statistically significant. The diurnal pattern of isotopic composition indicates that the most depleted meltwaters coincide with the peak in temperature and, hence, meltwater production.

DIE AUSSCHEIDUNG VON TESTOSTERON UND EPITESTOSTERON BEI FRAUEN AM ENDE DER SCHWANGERSCHAFT

1969 ◽  
Vol 60 (4) ◽  
pp. 579-585
Author(s):  
K. Schollberg ◽  
E. Seiler ◽  
J. Holtorff
Keyword(s):  
Urinary Excretion ◽  
Late Pregnancy ◽  
Mean Values ◽  
Pregnant Females ◽  
Female Foetus ◽  
The Mean ◽  
The Difference ◽  
Normal Women ◽  
In Pregnancy

ABSTRACT The urinary excretion of testosterone and epitestosterone by women in late pregnancy has been studied. The mean values of 22 normal women in pregnancy mens X are 12.9 ± 9.2 μg/24 h in the case of testosterone and 16.1 ± 16.2 μg/24 h in the case of epitestosterone. Both values do not differ significantly from those of non-pregnant females. The excretion values of mothers bearing a male foetus (17.3 ± 8.9 μg/24 h) are higher than those of mothers with a female foetus (6.4 ± 4.8 μg/24 h). The difference is statistically significant with P = 0.01.

A New Equal Area Method to Calculate and Represent Physiologic, Anatomical, and Alveolar Dead Spaces

2006 ◽  
Vol 104 (4) ◽  
pp. 696-700 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
A Barry Baker
Keyword(s):  
Carbon Dioxide ◽  
Dead Space ◽  
Graphical Method ◽  
Mean Difference ◽  
Equal Area ◽  
Area Method ◽  
Physiologic Dead Space ◽  
Anatomical Dead Space ◽  
The Mean ◽  
The Difference

Background Physiologic dead space is usually estimated by the Bohr-Enghoff equation or the Fletcher method. Alveolar dead space is calculated as the difference between anatomical dead space estimated by the Fowler equal area method and physiologic dead space. This study introduces a graphical method that uses similar principles for measuring and displaying anatomical, physiologic, and alveolar dead spaces. Methods A new graphical equal area method for estimating physiologic dead space is derived. Physiologic dead spaces of 1,200 carbon dioxide expirograms obtained from 10 ventilated patients were calculated by the Bohr-Enghoff equation, the Fletcher area method, and the new graphical equal area method and were compared by Bland-Altman analysis. Dead space was varied by varying tidal volume, end-expiratory pressure, inspiratory-to-expiratory ratio, and inspiratory hold in each patient. Results The new graphical equal area method for calculating physiologic dead space is shown analytically to be identical to the Bohr-Enghoff calculation. The mean difference (limits of agreement) between the physiologic dead spaces calculated by the new equal area method and Bohr-Enghoff equation was -0.07 ml (-1.27 to 1.13 ml). The mean difference between new equal area method and the Fletcher area method was -0.09 ml (-1.52 to 1.34 ml). Conclusions The authors' equal area method for calculating, displaying, and visualizing physiologic dead space is easy to understand and yields the same results as the classic Bohr-Enghoff equation and Fletcher area method. All three dead spaces--physiologic, anatomical, and alveolar--together with their relations to expired volume, can be displayed conveniently on the x-axis of a carbon dioxide expirogram.

Sign in / Sign up

Export Citation Format

Share Document