scholarly journals Determining a One-Tailed Upper Limit for Future Sample Relative Reproducibility Standard Deviations

2006 ◽  
Vol 89 (3) ◽  
pp. 797-803
Author(s):  
Foster D McClure ◽  
Jung K Lee
Keyword(s):  
Standard Deviation ◽  
Linear Combination ◽  
Square Root ◽  
Sample Mean ◽  
Upper Limit ◽  
Reproducibility Standard Deviation ◽  
The Future ◽  
Standard Deviations ◽  
Future Sample

Abstract A formula was developed to determine a one-tailed 100p% upper limit for future sample percent relative reproducibility standard deviations <inline-formula> <inline-graphic href="inline_eq1.gif"/> </inline-formula> , where sR is the sample reproducibility standard deviation, which is the square root of a linear combination of the sample repeatability variance ( <inline-formula> <inline-graphic href="inline_eq2.gif"/> </inline-formula> ) plus the sample laboratory-to-laboratory variance ( <inline-formula> <inline-graphic href="inline_eq3.gif"/> </inline-formula> ), i.e., <inline-formula> <inline-graphic href="inline_eq4.gif"/> </inline-formula> , and y is the sample mean. The future RSDR, % is expected to arise from a population of potential RSDR, % values whose true mean is <inline-formula> <inline-graphic href="inline_eq5.gif"/> </inline-formula> , where R and are the population reproducibility standard deviation and mean, respectively.

scholarly journals On Using an Approximate Noncentral t-Distribution in Determining a One-Side Upper Limit for Future Sample Relative Reproducibility Standard Deviations

2007 ◽  
Vol 90 (2) ◽  
pp. 575-581 ◽  
Author(s):  
Foster D McClure ◽  
Jung K Lee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Normal Approximation ◽  
Upper Limit ◽  
Standard Deviations ◽  
New Formula ◽  
T Distribution ◽  
Future Sample

Abstract For future sample relative reproducibility standard deviations (RSDR), collaboratively obtained under a completely randomized model (CRM), a new formula for determining a one-tailed 100p% upper limit (p) for such RSDR values was developed based on an approximate noncentral t-distribution with degrees of freedom obtained using Satterthwaite's adjustment. The accuracy of p was assessed by comparing p and its probability levels with similar values associated with a Monte Carlo simulation and with those obtained using another formula (p) that was developed for the same purpose but based on a normal approximation.

Properties of random variables

2019 ◽  
pp. 60-87
Author(s):  
M. D. Edge
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Linear Relationship ◽  
Random Variables ◽  
Square Root ◽  
Sample Mean ◽  
The Central Limit Theorem ◽  
Large Numbers

In this chapter, the behavior of random variables is summarized using the concepts of expectation, variance, and covariance. The expectation is a measurement of the location of a random variable’s distribution. The variance and its square root, the standard deviation, are measurements of the spread of a random variable’s distribution. Covariance and correlation are measurements of the extent of linear relationship between two random variables. The chapter also describe two important theorems that describe the distribution of means of samples from a distribution. As the sample size becomes larger, the distribution of the sample mean becomes bunched more tightly around the expectation—this is the law of large numbers—and the distribution of the sample mean approaches the shape of a normal distribution—this is the central limit theorem. Finally, a model describing a linear relationship between two random variables is considered, and the properties of those two random variables are analyzed.

scholarly journals On Using a Normal Approximation for the Noncentral t-Distribution in Determining Upper Limits for Future Sample Relative Repeatability and Reproducibility Standard Deviations

2009 ◽  
Vol 92 (1) ◽  
pp. 320-328
Author(s):  
Foster D McClure ◽  
Jung K Lee
Keyword(s):  
Normal Approximation ◽  
Approximation Formula ◽  
Monte Carlo Simulation Study ◽  
Upper Limit ◽  
Upper Limits ◽  
Repeatability And Reproducibility ◽  
Standard Deviations ◽  
The One ◽  
T Distribution ◽  
Future Sample

Abstract Formulas, based on a normal approximation for the noncentral t-distribution, were developed to compute 100p one-tailed upper limits for future sample relative repeatability and relative reproducibility standard deviations (RSDr, and RSDR,) collaboratively obtained under a completely randomized model. The accuracy of the formulas for obtaining a one-tailed upper limit for the future sample RSDr, was assessed by comparing the computed noncentral t-distribution-based upper limits with the one-tailed upper limits based on a normal approximation for the noncentral t-distribution. The accuracy of the normal approximation formula for obtaining a one-tailed upper limit for a future sample RSDR, was assessed by comparing the formula-based one-tailed upper limits with those obtained in a Monte Carlo simulation study.

Extractable Color of Capsicums and Oleoresin Paprika

1977 ◽  
Vol 60 (1) ◽  
pp. 1-4 ◽  
Author(s):  
James E Woodbury
Keyword(s):  
Standard Deviation ◽  
Collaborative Study ◽  
Trade Association ◽  
Reproducibility Standard Deviation ◽  
Glass Filter ◽  
Aoac Method ◽  
Standard Deviations ◽  
Color Value ◽  
Spice Trade

Abstract A collaborative study of the method for extractable color in capsicums and oleoresin paprika was conducted to determine if the NBS neutral glass filter standard is superior to the chemical standard now used as a spectrophotometer check. For a 1000 ASTA (American Spice Trade Association) color value sample, the reproducibility standard deviation was 49 with the chemical standard compared with 14 with the NBS filter. The repeatability standard deviations were 9.0 and 8.9, respectively. For a 2000 ASTA color value sample, the reproducibility standard deviation was 162 with the chemical standard compared with 44 with the NBS filter. The repeatability standard deviations were 12.9 and 10.1, respectively. The study also indicated that 16 hr in acetone extracted 8.0% more of a capsicum than the 4 hr in the present AOAC method. The repeatability standard deviations for 4 hr vs. 16 hr were 2.1 and 1.6. The method has been adopted as official first action.

scholarly journals On Determining a 1-Tailed Upper Limit for Future Sample HorRat Values

2006 ◽  
Vol 89 (6) ◽  
pp. 1650-1663 ◽  
Author(s):  
Foster D McClure ◽  
Jung K Lee
Keyword(s):  
Screening Tool ◽  
Collaborative Study ◽  
Worst Case ◽  
Sample Mean ◽  
Simulation Procedure ◽  
Upper Limit ◽  
Statistical Analysis System ◽  
Upper Limits ◽  
Analysis System ◽  
Future Sample

Abstract Two formulas were developed for use in computing 1-tailed upper limits for future HorRat values obtained from the collaborative study of materials. One formula is applicable when a future sample HorRat value <inline-formula> <inline-graphic href="inline_eq1.gif"/> </inline-formula> is computed based on a known concentration (e.g., C spike level and RSDR is the sample relative reproducibility standard deviation) and the other formula is applicable when the true concentration (C) is unknown and a future sample HorRat value <inline-formula> <inline-graphic href="inline_eq2.gif"/> </inline-formula> is computed using the sample mean (e.g., <inline-formula> <inline-graphic href="inline_eq3.gif"/> </inline-formula>, the collaborative study overall mean for an analyte). A Monte Carlo simulation procedure was developed using the Statistical Analysis System (SAS) software to assess the accuracy of the 2 developed formulas. Based on the degree of closeness between the simulated and calculated limits, the formulas for computing upper limits for future sample HorRat values will prove to be useful to Study Directors in determining worst case scenarios concerning a method's reproducibility precision relative to that predicted using the Horwitz equation. We also define the current empirical HorRat limits as 1-tailed 100p% upper limits to assess the statistical consequence, in a probability sense, of their application as an analytical methods screening tool.

On the sensibility of the Pairs Trading strategy: the case of the FTS stock market index

2020 ◽  
Vol 38 (3) ◽  
Author(s):  
Ainhoa Fernández-Pérez ◽  
María de las Nieves López-García ◽  
José Pedro Ramos Requena
Keyword(s):  
Standard Deviation ◽  
Stock Market ◽  
Trading Strategy ◽  
Stock Market Index ◽  
Pairs Trading ◽  
Empirical Application ◽  
Statistical Arbitrage ◽  
Market Index ◽  
Standard Deviations ◽  
Using Data

In this paper we present a non-conventional statistical arbitrage technique based in varying the number of standard deviations used to carry the trading strategy. We will show how values of 1 and 1,2 in the standard deviation provide better results that the classic strategy of Gatev et al (2006). An empirical application is performance using data of the FST100 index during the period 2010 to June 2019.

scholarly journals Phonological Awareness and Print Knowledge of Preschool Children With Cochlear Implants

2012 ◽  
Vol 55 (3) ◽  
pp. 811-823 ◽  
Author(s):  
Sophie E. Ambrose ◽  
Marc E. Fey ◽  
Laurie S. Eisenberg
Keyword(s):  
Standard Deviation ◽  
Speech Perception ◽  
Phonological Awareness ◽  
Speech Production ◽  
Cochlear Implants ◽  
Preschool Age ◽  
Speech And Language ◽  
Sample Mean ◽  
Print Knowledge ◽  
Age Appropriate

PurposeTo determine whether preschool-age children with cochlear implants have age-appropriate phonological awareness and print knowledge and to examine the relationships of these skills with related speech and language abilities.MethodThe sample comprised 24 children with cochlear implants (CIs) and 23 peers with normal hearing (NH), ages 36 to 60 months. Children's print knowledge, phonological awareness, language, speech production, and speech perception abilities were assessed.ResultsFor phonological awareness, the CI group's mean score fell within one standard deviation of the Test of Preschool Early Literacy's (Lonigan, Wagner, Torgesen, & Rashotte, 2007) normative sample mean but was more than one standard deviation below the NH group mean. The CI group's performance did not differ significantly from that of the NH group for print knowledge. For the CI group, phonological awareness and print knowledge were significantly correlated with language, speech production, and speech perception. Together these predictor variables accounted for 34% of variance in the CI group's phonological awareness but no significant variance in their print knowledge.ConclusionsChildren with CIs have the potential to develop age-appropriate early literacy skills by preschool age but are likely to lag behind their NH peers in phonological awareness. Intervention programs serving these children should target these skills with instruction and by facilitating speech and language development.

The Effects of Ethyl Alcohol on a Driver's Driving Skill, Visual Perception, Risk Acceptance, Choice Reaction Times and Information Processing Rates

1974 ◽  
Vol 18 (2) ◽  
pp. 116-116
Author(s):  
Helmut T. Zwahlen
Keyword(s):  
Information Processing ◽  
Standard Deviation ◽  
Visual Perception ◽  
Reaction Times ◽  
Driving Skill ◽  
Alcohol Condition ◽  
The Mean ◽  
Risk Acceptance ◽  
Standard Deviations ◽  
Choice Reaction Times

Twelve subjects (20–37 years old) were tested in the laboratory and eleven out of these were also tested in a car in the field, first under a no alcohol condition and then under an alcohol condition (approximately 0.10% BAC). In the laboratory the subjects simple and choice reaction times for two uncertainty modes were measured and their information processing rates (3 bits unsertainty) were determined. In the field the subjects driving skill for driving through a gap with 20 inches total clearance at 20 MPH was measured, as well as their static visual perceptual capabilities and risk acceptance decisions for a 46 feet viewing distance using psychophysical experimental methods. Based upon the driving skill measure (standard deviation of centerline deviations in the gap), the mean of the psychometric visual gap perception function and the mean of the psychometric gap risk acceptance function, the “Safety Distance” and the “Driver Safety Index” (DSI) were obtained. Based upon a statistical analysis of the data we may conclude first that the effects of alcohol (approximately 0.10% BAC) vary widely from one subject to another (slighthly improved performance to highly impaired performance) and that the changes in the group averages of the means and standard deviations of the psychometric visual perception and risk acceptance functions, the driving skill distributions, the “Safety Distances” and the DSI's for the subjects (although all changes in the group averages are in the expected direction) are statistically not significant (α = .05). Second, the group average of the means of the choice reaction times for the subjects increased by 5% under the alcohol condition (statistically significant, α = .05), but more important the group average of the standard deviations of the choice reaction times for the subjects increased by 23% (statistically significant, α = .05). The group average of the information processing rates for the subjects decreased by 3% (statistically not significant, α = .05) under the alcohol condition. A system model in which the system demands on the driver are represented in terms of choice reaction times is used to demonstrate that the increase in performance variability (expressed by the standard deviation of choice reaction times) under the influence of alcohol provides a much better explanation for the higher accident involvement than the historically most frequently used rather small increase in average performance (expressed by the mean of choice reaction times).

scholarly journals Synthesis of Plans to Increase the Results of Ordinary National Education Test by All-Round Tutoring Process for Primary School Grade 6

2021 ◽  
Vol 14 (2) ◽  
pp. 63
Author(s):  
Nuttakan Pakprod ◽  
Kanokrat Jirasatjanukul ◽  
Damrong Tumthong ◽  
Prapa Amklad ◽  
Wipa Lekchom
Keyword(s):  
Standard Deviation ◽  
Primary School ◽  
Target Group ◽  
Educational Testing ◽  
School Grade ◽  
National Education ◽  
Standard Deviations ◽  
The Difference ◽  
High Level ◽  
Basic Level

The objective of this research is to study the results of activities to increase the scores of Ordinary National Education Test. Cluster; teachers of Phetchaburi Rajabhat University comparing the results of Ordinary National Education Test in 2017-2018 and studying the satisfaction of the activities. The target group is 49 schools in Phetchaburi and Prachuap Khiri Khan Provinces, data were analyzed using mean and standard deviation. The study found that the difference of the scores of the Ordinary National Education Test was higher in 32 schools and there is a difference in scores of Ordinary National Education Test tests lower by 2 schools, representing 94.12, with the satisfaction of the participation in the activity of increasing the basic educational testing at the basic level is at a high level with an average of 4.22, standard deviations 0.73, which the participants are satisfied with the process. The process of organizing activities was at the highest with an average of 4.28, standard deviations 0.76 and continues organizing activities to increase the scores of Ordinary National Education Test.

The Content of IMF Staff Reports for Euro Area Countries

2014 ◽  
pp. 272-292
Author(s):  
Lena Golubovskaja
Keyword(s):  
Standard Deviation ◽  
Euro Area ◽  
Mean Value ◽  
Systematic Bias ◽  
Executive Board ◽  
Sample Mean ◽  
Warning Tone ◽  
The Mean ◽  
Run Up ◽  
The Imf

This chapter analyzes the tone and information content of the two external policy reports of the Internal Monetary Fund (IMF), the IMF Article IV Staff Reports, and Executive Board Assessments for Euro area countries. In particular, the researchers create a tone measure denoted WARNING based on the existing DICTION 5.0 Hardship dictionary. This study finds that in the run-up to the current credit crises, average WARNING tone levels of Staff Reports for Slovenia, Luxembourg, Greece, and Malta are one standard deviation above the EMU sample mean; and for Spain and Belgium, they are one standard deviation below the mean value. Furthermore, on average for Staff Reports over the period 2005-2007, there are insignificant differences between the EMU sample mean and Staff Reports’ yearly averages. Researchers find the presence of a significantly increased level of WARNING tone in 2006 (compared to the previous year) for the IMF Article IV Staff Reports. There is also a systematic bias of WARNING scores for Executive Board Assessments versus WARNING scores for the Staff Reports.

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