scholarly journals Some Implications of Distinguishing Between Unexplained Variance That Is Systematic or Random

2017 ◽  
Vol 78 (3) ◽  
pp. 482-503 ◽  
Author(s):  
David Trafimow
Keyword(s):  
Computer Simulations ◽  
Variance Components ◽  
Measurement Theory ◽  
Error Variance ◽  
Total Variance ◽  
Classical Measurement ◽  
Observable Data ◽  
Independent Variable ◽  
Unexplained Variance ◽  
Random Variance

Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the independent variable, variance in the dependent variable that is unexplained but systematic (associated with variance in unknown variables), and random variance. Based on the tripartite assumption, classical measurement theory, and simple mathematics, it is shown that these components can be estimated using observable data. Mathematical and computer simulations illustrate some of the important issues and implications.

scholarly journals A novel metric of reliability in pressure pain threshold measurement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bernard Liew ◽  
Ho Yin Lee ◽  
David Rügamer ◽  
Alessandro Marco De Nunzio ◽  
Nicola R. Heneghan ◽  
...  
Keyword(s):  
Mixed Models ◽  
Variance Components ◽  
Pain Threshold ◽  
Intraclass Correlation ◽  
Pressure Pain Threshold ◽  
Total Variance ◽  
Lumbar Region ◽  
Pressure Pain ◽  
Pressure Algometer ◽  
Testing Protocols

AbstractThe inter-session Intraclass Correlation Coefficient (ICC) is a commonly investigated and clinically important metric of reliability for pressure pain threshold (PPT) measurement. However, current investigations do not account for inter-repetition variability when calculating inter-session ICC, even though a PPT measurement taken at different sessions must also imply different repetitions. The primary aim was to evaluate and report a novel metric of reliability in PPT measurement: the inter-session-repetition ICC. One rater recorded ten repetitions of PPT measurement over the lumbar region bilaterally at two sessions in twenty healthy adults using a pressure algometer. Variance components were computed using linear mixed-models and used to construct ICCs; most notably inter-session ICC and inter-session-repetition ICC. At 70.1% of the total variance, the source of greatest variability was between subjects ($${\sigma }_{subj}^{2}$$ σ subj 2 = 222.28 N2), whereas the source of least variability (1.5% total variance) was between sessions ($${\sigma }_{sess}^{2}$$ σ sess 2 = 4.83 N2). Derived inter-session and inter-session-repetition ICCs were 0.88 (95%CI: 0.77 to 0.94) and 0.73 (95%CI: 0.53 to 0.84) respectively. Inter-session-repetition ICC provides a more conservative estimate of reliability than inter-session ICC, with the magnitude of difference being clinically meaningful. Quantifying individual sources of variability enables ICC construction to be reflective of individual testing protocols.

Computer simulations of the effects of different synaptic input systems on motor unit recruitment

1993 ◽  
Vol 70 (5) ◽  
pp. 1827-1840 ◽  
Author(s):  
C. J. Heckman ◽  
M. D. Binder
Keyword(s):  
Motor Unit ◽  
Computer Simulations ◽  
Synaptic Input ◽  
Reciprocal Inhibition ◽  
Excitatory Input ◽  
Medial Gastrocnemius ◽  
Synaptic Inputs ◽  
Monte Carlo Techniques ◽  
Recruitment Order ◽  
Random Variance

1. The effects of four different synaptic input systems on the recruitment order within a mammalian motoneuron pool were investigated using computer simulations. The synaptic inputs and motor unit properties in the model were based as closely as possible on the available experimental data for the cat medial gastrocnemius pool and muscle. Monte Carlo techniques were employed to add random variance to the motor unit thresholds and forces and to sample the resulting recruitment orders. 2. The effects of the synaptic inputs on recruitment order depended on how they modified the range of recruitment thresholds established by differences in the intrinsic current thresholds of the motoneurons. Application of a uniform synaptic input to the pool (i.e., distributed equally to all motoneurons) resulted in a recruitment sequence that was quite stable even with the addition of large amounts of random variance. With 50% added random variance, the recruitment reversals did not exceed 8%. 3. The simulated monosynaptic input from homonymous Ia afferent fibers generated a twofold expansion of the range of recruitment thresholds beyond that attributed to the differences in the intrinsic current thresholds. The Ia input generated a small reduction in the number of recruitment reversals due to random variance (6% reversals at 50% random variance). The simulated monosynaptic vestibulospinal input generated a twofold compression of the range of recruitment thresholds that exerted a modest increase in the number of recruitment reversals (12% reversals at 50% random variance). 4. In comparison with the modest effects of the two monosynaptic inputs, the simulated oligosynpatic rubrospinal excitatory input exerted a nine-fold compression in the recruitment threshold range that resulted in a recruitment sequence that was highly sensitive to random variance. With 50% added random variance, the sequence became nearly random (40% reversals). 5. Reciprocal Ia inhibition was simulated by a uniform distribution within the pool, but its effects on recruitment order were highly dependent on the distribution of the excitatory input. Reciprocal inhibition exerted only minor effects on recruitment order when combined with the Ia or vestibulospinal inputs. However, when the excitatory drive was supplied by the rubrospinal input, even small amounts of reciprocal inhibition were sufficient to completely reverse the normal recruitment sequence. 6. The simulated monosynaptic Ia input was highly effective in compensating for the disruptive effects of rubrospinal excitation on recruitment order. Even a small Ia bias combined with the rubrospinal excitation was sufficient to halve the effects of random variance and to restore the normal recruitment sequence in the presence of rather large amounts of reciprocal inhibition.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals The affectability of writing assessment scores: a G-theory analysis of rater, task, and scoring method contribution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Khodi
Keyword(s):  
Writing Assessment ◽  
Generalizability Theory ◽  
Error Variance ◽  
Total Variance ◽  
Scoring Method ◽  
Writing Assessments ◽  
Assessment Scores ◽  
Peer Rating ◽  
Reliable Assessment ◽  
Writing Scores

AbstractThe present study attempted to to investigate  factors  which affect EFL writing scores through using generalizability theory (G-theory). To this purpose, one hundred and twenty students participated in one independent and one integrated writing tasks. Proceeding, their performances were scored by six raters: one self-rating,  three peers,-rating and two instructors-rating. The main purpose of the sudy was to determine the relative and absolute contributions of different facets such as student, rater, task, method of scoring, and background of education  to the validity of writing assessment scores. The results indicated three major sources of variance: (a) the student by task by method of scoring (nested in background of education) interaction (STM:B) with 31.8% contribution to the total variance, (b) the student by rater by task by method of scoring (nested in background of education) interaction (SRTM:B) with 26.5% of contribution to the total variance, and (c) the student by rater by method of scoring (nested in background of education) interaction (SRM:B) with 17.6% of the contribution. With regard to the G-coefficients in G-study (relative G-coefficient ≥ 0.86), it was also found that the result of the assessment was highly valid and reliable. The sources of error variance were detected as the student by rater (nested in background of education) (SR:B) and rater by background of education with 99.2% and 0.8% contribution to the error variance, respectively. Additionally, ten separate G-studies were conducted to investigate the contribution of different facets across rater, task, and methods of scoring as differentiation facet. These studies suggested that peer rating, analytical scoring method, and integrated writing tasks were the most reliable and generalizable designs of the writing assessments. Finally, five decision-making studies (D-studies) in optimization level were conducted and it was indicated that at least four raters (with G-coefficient = 0.80) are necessary for a valid and reliable assessment. Based on these results, to achieve the greatest gain in generalizability, teachers should have their students take two writing assessments and their performance should be rated on at least two scoring methods by at least four raters.

EVALUATION OF BEEF SIRES ACROSS BREEDS FOR CALVING EASE

1977 ◽  
Vol 57 (4) ◽  
pp. 635-645 ◽  
Author(s):  
L. R. SCHAEFFER ◽  
J. W. WILTON
Keyword(s):  
Maximum Likelihood ◽  
Scoring System ◽  
Variance Components ◽  
Error Variance ◽  
Best Linear Unbiased Prediction ◽  
Linear Unbiased Prediction ◽  
Calving Ease ◽  
Best Linear Unbiased ◽  
Maximum Likelihood Prediction ◽  
Unbiased Prediction

Agriculture Canada and Alberta Record of Performance calving ease records on 54,139 calves from 3,338 sires of 18 breeds were used to evaluate sires by comparisons across breeds of sire. An objective scoring system was applied to the calving ease codes to derive appropriate weights for each category rather than using percentage of unassisted births or assuming equal intervals between categories. Common sire and error variance components were assumed for all breeds of sire. Heritability of calving ease under the model used was estimated to be.10 by maximum likelihood. Prediction of sire values for calving ease scores of future calves were calculated by best linear unbiased prediction procedures. Shorthorn, Hereford, and Angus sires caused relatively few calving difficulties, while Maine-Anjou sires caused more difficulties. Age of dam and sex of calf differences were also important. The range of sire evaluations for calving ease was narrow, but the bulls in either extreme could be identified.

The Epworth Sleepiness Scale in Portuguese adults: from classical measurement theory to Rasch model analysis

2014 ◽  
Vol 19 (2) ◽  
pp. 693-701 ◽  
Author(s):  
Paulo Sargento ◽  
Victoria Perea ◽  
Valentina Ladera ◽  
Paulo Lopes ◽  
Jorge Oliveira
Keyword(s):  
Rasch Model ◽  
Epworth Sleepiness Scale ◽  
Measurement Theory ◽  
Model Analysis ◽  
Classical Measurement

scholarly journals Conjoint measurement undone

2018 ◽  
Vol 29 (1) ◽  
pp. 100-128 ◽  
Author(s):  
Günter Trendler
Keyword(s):  
Measurement Theory ◽  
Conjoint Measurement ◽  
Classical Measurement ◽  
Quantitative Indicators

According to classical measurement theory, fundamental measurement necessarily requires the operation of concatenation qua physical addition. Quantities which do not allow this operation are measurable only indirectly by means of derived measurement. Since only extensive quantities sustain the operation of physical addition, measurement in psychology has been considered problematic. In contrast, the theory of conjoint measurement, as developed in representational measurement theory, proposes that the operation of ordering is sufficient for establishing fundamental measurement. The validity of this view is questioned. The misconception about the advantages of conjoint measurement, it is argued, results from the failure to notice that magnitudes of derived quantities cannot be determined directly, i.e., without the help of associated quantitative indicators. This takes away the advantages conjoint measurement has over derived measurement, making it practically useless.

scholarly journals Variability of pollen viability in the flowers and inflorescences of the China aster (Callistephus chinensis Nees) caused by gamma rays in the M1 and M2 generations

2013 ◽  
Vol 37 (2) ◽  
pp. 133-139
Author(s):  
Wiesław Mądry ◽  
Alicja Wosińska ◽  
Leokadia Ubysz-Borucka
Keyword(s):  
Radiation Dose ◽  
Gamma Rays ◽  
Variance Components ◽  
Pollen Viability ◽  
Total Variance ◽  
Extremal Dependence ◽  
China Aster ◽  
Generation M

The influence of gamma rays (within range 3-12 kR) on the variations of pollen viability was investigated in four varieties of <i>Callistephus chinensis</i> Nees in the M<sub>1</sub> and M<sub>2</sub> generations. The variability, both in generation M<sub>1</sub>and M<sub>2</sub> of the studied character between the plants and flowers within the inflorescence proved to be dependent on the radiation dose and was as a rule higher in populations exposed to radiation than in the control ones. These regularities, however were not equal in the tested varieties. The total variance of pollen viability in the M<sub>2</sub> generation was in general lower as compared with that of the M<sub>1</sub> generation, whereas the particular variance components showed an extremal dependence (minimum after a 3 kR dose) on the radiation dose.

scholarly journals Variation and Heritability Estimates for Antioxidant Activity, Total Phenolic Content, and Anthocyanin Content in Blueberry Progenies

2002 ◽  
Vol 127 (1) ◽  
pp. 82-88 ◽  
Author(s):  
Ann Marie Connor ◽  
James J. Luby ◽  
Cindy B.S. Tong
Keyword(s):  
Antioxidant Activity ◽  
Total Phenolic Content ◽  
Variance Components ◽  
Phenolic Content ◽  
Total Variance ◽  
Total Phenolic ◽  
Anthocyanin Content ◽  
Narrow Sense Heritability ◽  
Transgressive Segregants ◽  
Heritability Estimates

Narrow-sense heritability and among-family and within-family variance components were estimated for antioxidant activity (AA), total phenolic content (TPH), and anthocyanin content (ACY) in blueberry (Vaccinium L. sp.) fruit. AA, TPH, and ACY were determined in the parents and in 10 offspring from each of 20 random crosses for each of 2 years at Becker, Minn. Offspring-midparent regression analysis provided combined-year heritability estimates of 0.43 ± 0.09 (P ≤ 0.0001) for AA, 0.46 ± 0.11 (P ≤ 0.0001) for TPH, and 0.56 ± 0.10 (P ≤ 0.0001) for ACY. Analyses of variance delineated variation among and within families for AA, TPH, and ACY (P ≤ 0.001). Year-to-year variation in the means for all offspring genotypes was not significant for AA or TPH, but there were changes in rank between years for families and for offspring within families for these traits. Year-to-year variation in the mean for all offspring genotypes was significant for ACY, but rank changes were observed only among offspring within families, not among families. In total, 18 of 200 offspring from 7 of the 20 crosses were transgressive segregants for AA, exceeding the higher parent of the cross by at least two sds. Estimates of variance components showed that variation among families accounted for 24% to 27% of total variance for the three traits. However, variation within families was greater than that among families, accounting for 38% to 56% of total variance for the three traits. These results suggest that increasing antioxidant activity in blueberry through breeding is feasible, and that the breeding strategies utilized should exploit the large within-family variation that exists.

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