Myth 3: Is the Correct Formula for Sample Standard Deviation

2015 ◽  
pp. 25-34
Keyword(s):  
Standard Deviation ◽  
Sample Standard Deviation ◽  
Correct Formula

Nucleic Acid Molecules Prepared by Monolayer Techniques

1972 ◽  
Vol 30 ◽  
pp. 178-179
Author(s):  
Dimitrij Lang
Keyword(s):  
Electron Microscopy ◽  
Standard Deviation ◽  
Nucleic Acid ◽  
Cytochrome C ◽  
Nucleic Acids ◽  
Contour Length ◽  
Sample Standard Deviation ◽  
Molecular Weights ◽  
Length Measurements ◽  
Protein Monolayer

The success of the protein monolayer technique for electron microscopy of individual DNA molecules is based on the prevention of aggregation and orientation of the molecules during drying on specimen grids. DNA adsorbs first to a surface-denatured, insoluble cytochrome c monolayer which is then transferred to grids, without major distortion, by touching. Fig. 1 shows three basic procedures which, modified or not, permit the study of various important properties of nucleic acids, either in concert with other methods or exclusively:1) Molecular weights relative to DNA standards as well as number distributions of molecular weights can be obtained from contour length measurements with a sample standard deviation between 1 and 4%.

Alveolar pressure inhomogeneity during low-frequency oscillation of excised canine lobes

1990 ◽  
Vol 69 (1) ◽  
pp. 155-161 ◽  
Author(s):  
D. O. Warner
Keyword(s):  
Standard Deviation ◽  
Lung Volume ◽  
Vital Capacity ◽  
Low Frequency ◽  
Absolute Amount ◽  
Frequency Oscillation ◽  
Low Frequency Oscillation ◽  
Sample Standard Deviation ◽  
Time Constants ◽  
Cyclic Changes

To quantify the inhomogeneity of alveolar pressures (PA) during cyclic changes in lung volume similar to those present during spontaneous breathing, inhomogeneity of PA was measured with an alveolar capsule technique in six excised canine lungs. The lungs were ventilated by a quasi-sinusoidal pump with a constant end-expiratory lung volume and tidal volumes of 10, 20, and 40% of vital capacity at breathing frequencies ranging from 5 to 45 breaths/min. Inhomogeneity of PA was quantified as the sample standard deviation of pressures measured in three capsules. A component of inhomogeneity in phase with flow and a smaller component out of phase with flow were present. The in-phase component increased approximately linearly with flow. The ratio of inhomogeneity to flow was smaller at large tidal volumes and, at the two higher tidal volumes studied, the ratio was greater during inspiration than during expiration. If these data are interpreted in terms of a simple circuit model, this degree of inhomogeneity implies an approximately twofold variation in regional time constants. Despite these considerable differences in time constants, the absolute amount of inhomogeneity as defined by the sample standard deviation of the three PA's was small (maximum 0.57 +/- 0.32 cmH2O at the highest breathing frequency and tidal volume) because airway resistance in the canine lung was small.

The Use of Downton’s Estimator in Dual Response Surface Optimization

2012 ◽  
Author(s):  
Chuan Kim Ch’ng ◽  
Boon Chong Michael Khoo
Keyword(s):  
Standard Deviation ◽  
Response Surface ◽  
Mean Squared Error ◽  
Extreme Points ◽  
Robust Estimator ◽  
Sample Standard Deviation ◽  
Response Surface Optimization ◽  
Squared Error ◽  
Dual Response ◽  
Surface Optimization

Kaedah sambutan dual terdiri daripada dua sambutan bagi suatu cirian kualiti. Dua sambutan tersebut ialah sambutan min dan sambutan sisihan piawai (varians) yang dianggarkan daripada reka bentuk eksperimen selepas penyuaian model dijalankan. Sambutan sisihan piawai biasanya dianggar daripada sisihan piawai sampel. Kelemahan utama penganggar yang berdasarkan sisihan piawai sampel adalah ia mudah dipengaruhi oleh titik ekstrim. Bagi kes sedemikian, model yang tersuai berdasarkan sisihan piawai sampel adalah mungkin tidak jitu. Oleh itu, penggunaan pendekatan ini mungkin tidak dapat memberi titik kompromi yang betul. Dalam kertas kerja ini, suatu anggaran sisihan piawai berdasarkan penganggar Downton dicadangkan dalam pengoptimuman kaedah sambutan dual. Penganggar teguh kurang dipengaruhi oleh titik ekstrim berbanding dengan sisihan piawai sampel. Dalam hal ini, suatu model tersuai yang berdasarkan penganggar teguh akan memberikan keputusan yang lebih baik. Suatu contoh digunakan untuk mengilustrasikan kecekapan cadangan kami dalam pengoptimuman. Dalam contoh ini ralat kuasadua min (MSE) akan digunakan sebagai ciri pengoptimuman. Kata kunci: Penganggar Downton, pengoptimuman sambutan dual, ralat min kuasa dua, pengoptimuman, titik kompromi A dual response surface approach consists of two responses of a quality characteristic. These two responses are the mean response and the standard deviation (variance) response, which are estimated from an experimental design after performing a model fitting. The standard deviation response is usually estimated using the sample standard deviation. The main drawback of this estimator by means of sample standard deviation is that it is easily influenced by extreme points. For this case, the fitted model based on the sample standard deviation may not be accurate. Thus, the use of this approach may not produce the correct compromised setting. In this paper, an estimation of the standard deviation based on Downton’s estimator in a dual response surface optimization is proposed. A Downton estimator is a robust estimator of standard deviation. A robust estimator is less affected by extreme points compared to the sample standard deviation. Here, a model based on a robust estimator will give better results. An example is used to illustrate the effectiveness of our proposal in optimization. In this example, mean squared error (MSE) will be used as the optimization criterion. Key words: Downton’s estimator, dual response surface optimization, mean squared error, optimization, compromise setting

Bounds for the Sample Standard Deviation

1984 ◽  
Vol 6 (3) ◽  
pp. 72-76 ◽  
Author(s):  
ALLAN J. MACLEOD ◽  
G. ROBIN HENDERSON
Keyword(s):  
Standard Deviation ◽  
Sample Standard Deviation

scholarly journals Analysis of measurements of defects in multiaxial warp knitted fabrics for CFRP composites

2021 ◽  
Author(s):  
Diane Suk-Ching Liu
Keyword(s):  
Image Analysis ◽  
Standard Deviation ◽  
Carbon Fibre ◽  
Compression Strength ◽  
Cell Model ◽  
Unit Cell ◽  
Sample Standard Deviation ◽  
Cfrp Laminates ◽  
Laboratory Results ◽  
Out Of Plane

Multiaxial Warp Knitted (MWK) Fabrics are used to create Carbon Fibre Reinforced Plastic (CFRP) laminates. In contrast to Prepregs, CFRP laminates made with MWK fabrics are of interest because they could lower costs and processing time by being already constructed with multiple layers and through the use of a hot air oven instead of an autoclave. Defect in the form of fibre angle orientation plays an important role in the compression strength for laminates made with MWK fabrics. The in-plane and out-of-plane waviness of the fibres were characterised by the standard deviation of the angular waviness: sample Standard deviation of Fibre In-plane (SFI) and the sample Standard deviation of Fibre Out-of-plane (SFO). The SFI value was found in two ways: analysis (Multiple Field Image Analysis (MFIA) technique) software and Fibre Image Analysis software. Measurements of the holes in the carbon fibre textile, colloquially known as “fisheyes,” caused by sewing the textile together were also gathered. The SFI, SFO, and “fisheye” dimensions were together used in the FMB-PMB model and the Unit Cell Model to calculate the compression strength. These predicted compression strengths were compared to the laboratory results. Also, a reliability model was developed to find R, the reliability of each textile, to be used as a textile classification tool. It has been found that the compression strength predictions found using analysis and Fibre Image Analysis yielded similar results, with predictions from analysis closer to the laboratory results. The R value yielded a positive correlation with the results from analysis. A large percentage of difference between the predicted and the actual compression strength was observed for some textiles. This could be attributed to the inherent lack of regularity for some of the examined textiles and variability in determining the SFI and “fisheye” parameters. Improvements would involve devising rules and methods to determine the SFI and “fisheye” parameters, modifying the FMB-PMB and Unit Cell Models, and making the analysis process faster and more applicable for on-line quality process control.

scholarly journals SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS

2017 ◽  
Vol 5 (6) ◽  
pp. 368-377
Author(s):  
Kalpesh S. Tailor
Keyword(s):  
Standard Deviation ◽  
Performance Analysis ◽  
Normal Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Curve Analysis ◽  
Mean Deviation ◽  
Sample Standard Deviation ◽  
Underlying Distribution ◽  
Control Limits

Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the control charts. On the basis of this fact Naik V.D. and Tailor K.S. have proposed 3δ control limits. In 3δ control limits, the upper and lower control limits are set at 3δ distance from the central line where δ is the mean deviation of sampling distribution of the statistic being used for constructing the control chart. In this paper assuming that the underlying distribution of the variable of interest follows moderate distribution proposed by Naik V.D and Desai J.M, 3δ control limits of sample standard deviation(s) chart are derived. Also the performance analysis of the control chart is carried out with the help of OC curve analysis and ARL curve analysis.

scholarly journals Improving the methodology for calculation of energy losses in axial turbine cascades

2021 ◽  
pp. 104-109
Author(s):  
М.Ю. Левенталь ◽  
Ю.М. Погодин ◽  
Ю.Р. Миронов
Keyword(s):  
Standard Deviation ◽  
Turbulence Model ◽  
Empirical Model ◽  
Turbulence Models ◽  
Operating Parameters ◽  
Cfd Analysis ◽  
Sample Standard Deviation ◽  
Rans Model ◽  
Wide Range ◽  
Turbine Cascades

Представлена оценка неопределенности прогнозирования потерь энергии в решетках профилей осевых турбин. В сравнении с экспериментальными данными рассмотрены эмпирическая модель ЦИАМ и метод CFD анализа в рамках RANS модели. Геометрические и режимные параметры решеток профилей варьируются в широком диапазоне. Результаты CFD расчета отличаются существенно в зависимости от модели турбулентности. Наименьшая неопределенность получена для модели рейнольдсовых напряжений RSM. Определено выборочное стандартное относительное отклонение для анализируемой базы данных. Применительно к CFD расчету данное отклонение составило 18,6%, применительно к эмпирической модели ЦИАМ 46,4%. Разработана эмпирическая модель коррекции потерь полученных по результатам CFD анализа с моделью турбулентности RSM. Корректирующая функция включает в себя геометрические и режимные параметры решеток и особенности течения в межлопаточном канале (всего 14 параметров). Использование разработанного подхода позволило снизить неопределённость прогнозирования потерь в 2 раза. В результате работы выборочное стандартное относительное отклонение предсказания потерь для рассматриваемой базы решеток профилей составило 9,3%. Estimation of the uncertainty in predicting profile losses using various models was performed. In comparison with the experimental data, empirical model of CIAM and method of CFD analysis are considered. RANS models are used. The geometric and operating parameters of the analyzed turbine cascades vary over a wide range. Turbulence models strongly influence loss prediction uncertainty. The smallest uncertainty was obtained using the RSM turbulence model. The sample standard deviation for the considered turbine cascades base was determined. The deviation for CFD analysis is 18.6%. For the empirical model of CIAM the deviation is 46.4%. The new empirical model has been created to correct the results of calculating losses according to the RANS model using the RSM turbulence model. The corrective function takes into account the influence of the geometric and operating parameters of the turbine cascades and the features of the airfoil flow (14 parameters in total). The developed approach allows reducing the uncertainty in the estimation of losses according to the RANS model by 2 times. As a result, the sample standard deviation in the prediction of losses is 9.3% for the considered turbine cascades base.

Effect of Infrared Analyzer Homogenization Efficiency on Repeatability of Uncorrected Fat A and Fat B Signals

1994 ◽  
Vol 77 (5) ◽  
pp. 1217-1223 ◽  
Author(s):  
Erika B Smith ◽  
David M Barbano ◽  
Joanna M Lynch ◽  
J Richard Fleming
Keyword(s):  
Standard Deviation ◽  
Light Scattering ◽  
Raw Milk ◽  
Mean Difference ◽  
Sample Standard Deviation ◽  
The Mean ◽  
Infrared Analyzer

Abstract Poor repeatability by infrared milk analyzers may be caused by inefficient homogenization as a result of light scattering and the Christiansen effect. The objectives of this study were to identify instruments with good and poor homogenization efficiency and to determine if a difference exists in repeatability performance between instruments with good vs poor homogenization efficiency. Unhomo-genized and homogenized portions of the same milk were tested 20 times consecutively on 22 instruments. An instrument was considered to have poor homogenization efficiency if the mean difference in the uncorrected signal between unhomo-genized and homogenized portions of the same milk was ≥1.43% of the fat test (i.e., ≥0.05% at 3.5% fat). Instruments were evaluated for repeatability by calculating the sample standard deviation and the range of the latter 19 uncorrected readings for un-homogenized and homogenized milks. When repeatability was evaluated as a function of homogenization efficiency, there was a significant (p = 0.001) correlation between poor homogenization efficiency and poor repeatability when testing unho-mogenized milk but not when testing homogenized milk. Improved homogenizer performance within infrared milk analyzers is needed to improve the repeatability of raw milk testing.

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