scholarly journals The precision of temporal judgement: milliseconds, many minutes, and beyond

2009 ◽  
Vol 364 (1525) ◽  
pp. 1897-1905 ◽  
Author(s):  
P.A. Lewis ◽  
R.C. Miall
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Human Subjects ◽  
Short Interval ◽  
Time Measurement ◽  
Scalar Property ◽  
Timing Mechanisms ◽  
Timing Data ◽  
The Mean ◽  
Different Levels

The principle that the standard deviation of estimates scales with the mean estimate, commonly known as the scalar property, is one of the most broadly accepted fundamentals of interval timing. This property is measured using the coefficient of variation (CV) calculated as the ratio between the standard deviation and the mean. In 1997, John Gibbon suggested that different time measurement mechanisms may have different levels of absolute precision, and would therefore be associated with different CVs. Here, we test this proposal by examining the CVs produced by human subjects timing a broad range of intervals (68 ms to 16.7 min). Our data reveal no evidence for multiple mechanisms, but instead show a continuous logarithmic decrease in CV as timed intervals increase. This finding joins other recent reports in demonstrating a systematic violation of the scalar property in timing data. Interestingly, the estimated CV of circadian judgements fits onto the regression of decreasing CV, suggesting a link between short interval and circadian timing mechanisms.

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 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.

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.

Progeny testing dairy bulls at different management levels

1960 ◽  
Vol 2 (2) ◽  
pp. 141-152 ◽  
Author(s):  
Alan Robertson ◽  
L. K. O'Connor ◽  
J. Edwards
Keyword(s):  
Milk Yield ◽  
Coefficient Of Variation ◽  
Progeny Testing ◽  
Gradual Change ◽  
Breeding Values ◽  
England And Wales ◽  
True Breeding ◽  
The Mean ◽  
Dairy Bulls ◽  
Different Levels

1. Records used to compile the Contemporary Comparisons of 57 Friesian, 8 English Ayrshire and 11 Scottish Ayrshire A.I. bulls, each with at least 100 ‘effective daughters’ were analysed.2. For each bull, the herd-years were divided into three equal groups on the basis of the average heifer yield of both daughters and contemporaries (high-, medium-, and low-producing herd-years) and three independent Contemporary Comparisons were calculated for each bull, one at each of the three yield levels.3. In the data from England and Wales, the mean Contemporary Comparison declined with increasing mean level of production. This decline was such as to imply that some 20% of the differences in production between herds were genetic in origin. A possible explanation lies in the gradual change from Dairy Shorthorn to Friesian and Ayrshire which has taken place in England and Wales, but not in Scotland, during the last 15 years.4. The variance within progeny groups within herd-years increased from the low level to the high but the coefficient of variation decreased slightly. The variance between sires also increased with the mean level of production but almost exactly in parallel with that within sires so that the heritability and consequently the accuracy of the progeny test for milk yield was effectively the same at all production levels.5. The correlation between the true breeding values of the bulls at the different levels was very close to one.6. From these results it is concluded that there is no need to provide special strains within breeds to suit particular management levels or to concentrate progeny testing in the higher-producing herds and that daughter records from all herds, irrespective of level of production, can be used with equal confidence.

Firing Variability Is Higher than Deduced from the Empirical Coefficient of Variation

2011 ◽  
Vol 23 (8) ◽  
pp. 1944-1966 ◽  
Author(s):  
Susanne Ditlevsen ◽  
Petr Lansky
Keyword(s):  
Experimental Data ◽  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Estimation Methods ◽  
Interspike Intervals ◽  
Estimation Errors ◽  
Empirical Standard Deviation ◽  
Receptor Neurons ◽  
The Mean ◽  
Empirical Standard

A convenient and often used summary measure to quantify the firing variability in neurons is the coefficient of variation (CV), defined as the standard deviation divided by the mean. It is therefore important to find an estimator that gives reliable results from experimental data, that is, the estimator should be unbiased and have low estimation variance. When the CV is evaluated in the standard way (empirical standard deviation of interspike intervals divided by their average), then the estimator is biased, underestimating the true CV, especially if the distribution of the interspike intervals is positively skewed. Moreover, the estimator has a large variance for commonly used distributions. The aim of this letter is to quantify the bias and propose alternative estimation methods. If the distribution is assumed known or can be determined from data, parametric estimators are proposed, which not only remove the bias but also decrease the estimation errors. If no distribution is assumed and the data are very positively skewed, we propose to correct the standard estimator. When defining the corrected estimator, we simply use that it is more stable to work on the log scale for positively skewed distributions. The estimators are evaluated through simulations and applied to experimental data from olfactory receptor neurons in rats.

scholarly journals Climate resources analysis for use of planning in crop production and rainfall water management in the central highlands of Ethiopia, the case of Bishoftu district, Oromia region

2010 ◽  
Vol 7 (3) ◽  
pp. 3733-3763 ◽  
Author(s):  
F. Yemenu ◽  
D. Chemeda
Keyword(s):  
Markov Chain ◽  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Rainy Season ◽  
Growing Season ◽  
Entire Study ◽  
Dry Spell ◽  
The Mean ◽  
Central Highlands ◽  
Main Rainy Season

Abstract. Agricultural practices and water resources management in the central highlands of Ethiopia is highly dependant and associated with climatic resources and their pattern and hence wise use of those resources is a priority for the region. Accordingly, a study was conducted to asses and critically quantity the climate resources of the central high lands of Ethiop, Bishoftu district. Thirty three years of weather record data has been used for the work. The onset, duration and end of the growing seasons were defined and quantified based on FAO and Reddy models while the dry and wet spell distributions and the drought events were calculated using the Markov chain models and the standardized precipitation index (SPI) respectively. The results revealed that the mean onset of the main (Kiremt) growing season was found to occur during the second meteorological decade and ended during the end of September. Similarly, though unreliable and only few occurred during the entire study period, the mean onset of the shorter (Belg) season was found to occur during the beginning of the first decade of April. The length of the growing season during the main rainy season, (Kiremt,) ranged from 112 to 144 days with a standard deviation of 9.6 days and coefficient of variation of 7.5%. However, the mean growing length during the Belg season was found to be 22.4 days with a standard deviation of 27 days and coefficient of variation of 122%. The results of analysis obtained both from the Markov Chain and Reddy models indicated higher probabilities of dry spell occurrences during the shorter season (Belg) but the occurrences of the same in the main rainy season (Kiremt) was very minimal. Like wise, the SPI model detected some drought events ranging from mild to severe classes in both seasons based on one a month time scale analysis. A considerable attention of maximizing crop harvest during the main rainy season is practically important.

scholarly journals Modelling Feedback Effects on the Production of Short Time Intervals

2021 ◽  
Vol 10 (1) ◽  
pp. 56-74
Author(s):  
John H. Wearden ◽  
Jordan Wehrman
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Time Intervals ◽  
Average Deviation ◽  
Feedback Effects ◽  
Absolute Change ◽  
Target Time ◽  
The Mean ◽  
Short Time ◽  
Relative Variability

Abstract People produced time intervals of 500 to 1250 ms, with accurate feedback in ms provided after each production. The mean times produced tracked the target times closely, and the coefficient of variation (standard deviation/mean) declined with increasing target time. The mean absolute change from one trial to another, and its standard deviation, measures of trial-by-trial change, also increased with target time. A model of feedback was fitted to all four measures. It assumed that the time produced resulted from a combination of a scalar timing process and a non-timing process. Although the non-timing process was on average invariant with target time, the timing process was assumed to be sensitive to feedback, in two different ways. If the previous production was close to the target the model repeated it (a repeat process), but if it was further away the next production was adjusted by an amount related to the discrepancy between the previous production and the target (an adjust process). The balance between the two was governed by a threshold, which was on average constant, and it was further assumed that the relative variability of the repeat process was lower than that of the adjust process. The model produced output which fitted three of the four measures well (average deviation of 3 or 4%) but fitted the standard deviation of change less well. Reducing the magnitude of the non-timing process produced output which conformed approximately to scalar timing, and the model could also mimic data resulting from the provision of inaccurate feedback.

Improved Fluorometric Method for Determining Selenium

1978 ◽  
Vol 61 (4) ◽  
pp. 927-930 ◽  
Author(s):  
Phyllis A Whetter ◽  
Duane E Ullrey
Keyword(s):  
Skeletal Muscle ◽  
Standard Deviation ◽  
Standard Error ◽  
Coefficient Of Variation ◽  
Biological Materials ◽  
Mean Difference ◽  
Fluorometric Method ◽  
Aoac Method ◽  
The Mean ◽  
Selenium Analysis

Abstract A previously reported method for selenium analysis of biological materials has been modified to reduce equipment requirements and labor, resulting in 40—80 determinations in an 8-hr period. Digestions are performed on hot plates in Erlenmeyer flasks, and neutralization, chelation with EDTA, complexing with 2,3- diaminonaphthalene, and extraction of the piazoselenol into cyclohexane are completed in the same vessel. Flotation of the cyclohexane layer into the neck of the flask with water allows convenient transfer to fluorometer tubes. Representative analytical values for serum, skeletal muscle, liver, kidney, corn, and alfalfa hay are presented. The mean recovery (± standard deviation) of added selenite selenium in 84 determinations was 98.1±7.1%. The mean coefficient of variation (± standard error) of repeated analyses of the same samples was 6.98±0.78%. The mean difference (± standard error) between values determined by the proposed method and the AOAC method was -0.03±0.60%.

An Approximate Method via Coefficient of Variation for Strength Prediction of Self-Piercing Riveted Joints

2010 ◽  
Vol 26-28 ◽  
pp. 334-339 ◽  
Author(s):  
Xiao Cong He
Keyword(s):  
Standard Deviation ◽  
Coefficient Of Variation ◽  
Taylor Expansion ◽  
Expansion Method ◽  
The Self ◽  
Strength Prediction ◽  
Reliability Based Design ◽  
Riveted Joints ◽  
The Mean ◽  
Definition Of

This study deals with an application of the method of the coefficient of variation in strength prediction of the self-piercing riveted joints. Defined as the ratio of the standard deviation to the mean, the coefficient of variation may be used in both the reliability-based design of self-piercing riveted joints and in the evaluation of existing products. In this study, the concept and definition of the coefficient of variation are stated. The procedure of the use of coefficient of variation for approximate calculations of strength of the self-piercing riveted joints is presented and compared with the classical Taylor expansion method. This is illustrated with a numerical example.

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