To measure pulmonary function changes over time the mass flow sensor and the pneumotachograph are widely used instruments. Due to international equipment requirements, calibration, validation and measurement procedures both measurement devices are assumed to have identical reliability [1,2]. However the smallest detectable change, which is the smallest significant change that can be detected between individual mea- surements, has in neither device, been determined. The smallest detectable change is a very useful parameter for clinical practice because it shows which changes in a single patient can be considered a ‘ real ’ change. Hence, pulmonary function instruments with the smallest detectable change are best suited for evaluating changes as a result of disease progress or applied therapy.
Measurement error can be expressed as the standard deviation of repeated measurements in a single patient, referred to as the standard error of measurement (SEM). The SEM was calculated from the square root of the vari- ance between the measurements and the error variance of the ICC. Subsequently, the SEM can be transformed into the smallest detectable change (SDC = 1.96*√2*SEM). The SDC represents the minimal change that a patient must show to ensure that the observed change is real, and not a measurement error . The SDC is thus calcu- lated; it is not derived from clinical observations follow- ing treatment.
Interpretability is also important in regard to change scores; it is important to know when it can be said that a patient has improved. With many PROMs, change scores are often difficult or impossible to interpret, sim- ply because we do not know exactly what a given differ- ence in score means. Interpreting change in PROM scores requires two benchmarks: the measurement error, expressed as the smallest detectable change (SDC), and the minimal important change (MIC). The SDC is a measure of the variation in a scale due to measurement error. Thus, a change score can only be considered to represent a real change if it is larger than the SDC. The SDC is also known as the minimal detectable change; when using its 95% confidence interval, it can be abbre- viated as MDC95%.
Many studies have addressed measurement properties of the NDI, and two systematic reviews of these studies were recently published. In a review by MacDermid et al. three comprehensive review articles and 41 stud- ies that addressed at least one psychometric property were identified . The authors concluded that the NDI is reliable, valid and responsive in various patient populations, including patients with acute and chronic conditions, as well as those suffering from neck pain associated from musculoskeletal dysfunction, whiplash- associated disorders, and cervical radiculopathy. The authors stated that the work on smallest detectable change (SDC) and minimal important change (MIC) is sparse and inconsistent but followed Vernon in
Background: Many tinnitus scales are available, but all of them have certain limitations. The aim of the current study was to present a psychometric data of a new brief and reliable questionnaire that could be conveniently used for evaluating tinnitus complaint in adults (either with normal or impaired hearing)—Skarzynski Tinnitus Scale (STS). Methods: The study included 125 participants with at least 1 month of tinnitus duration. All participants were asked to complete the STS, Tinnitus and Hearing Survey (THS), Tinnitus Functional Index (TFI), Tinnitus Handicap Inventory (THI), and Beck Depression Inventory. Psychometric properties of the new tool were tested using exploratory factor analysis (EFA), Pearson bivariate correlation with other tinnitus questionnaires, Pearson bivariate correlation with pure‑ tone audiometry, Cronbach’s alpha coefficient, limits of agreement, smallest detectable change, and floor and ceiling effects. Norms for tinnitus severity as measured by the STS are proposed.
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of the minimum change measured by a given tool that is considered to be more than simple measurement error . This minimum change is referred to as the minimal detectable change (MDC) [5-7] or smallest detectable change (SDC) [4,8,9] and is mathematically (linearly) related to the error of the measurement. Put simply, the MDC or the SDC reflects the smallest within-person change in score that can be interpreted as real and statisti- cally significant . In terms of clinimetrics, the MDC is a metric for reproducibility (specifically, a measure of agree- ment), and is determined by performing repeat measure- ments on patients over a short period of time . The short time interval renders significant clinical change between assessments unlikely , and it also avoids the problem of response shift - a change in the meaning or a recalibration of an outcome - if the tool captures a patient-reported outcome .
The distribution-based and the anchor-based approaches were both used to determine the CIDs of the subscales of the SS-QOL. The distribution-based CID estimate was determined using the between-participant baseline SD and the SEM within-participant methods to estimate the CID scores . An effect size is a standardized measure of change over time and represents individual change in terms of the number of pretest SDs. For example, an effect size of 0.5 indicates an increase of 0.5 SD. Cohen  has provided benchmarks that serve to guide the interpretations of effects size. According to Ringash et al , CIDs are generally close to an effect size of 0.2, and an effect size of 0.5 represents humans’ limitation in discrimination . We chose 0.5 SD units to estimate the minimal threshold of CIDs. The SD var- ies with the heterogeneity of the sample and does not take patient variability of change into consideration. The SEM, which simultaneously incorporates both the sam- ple ’ s reliability and variability into the formula and is relatively sample-independent, is used as another indica- tor of minimal CID .
Very few studies have been conducted to evaluate the reliability of QUS measurements of the AT. This is worrisome considering that the reliability of the QUS measurement of AT thickness, a key diagnostic criterion for Achilles tendinopathy, is rarely reported. To our knowledge, studies that have investigated test-retest reli- ability of QUS measurements of the AT have shown a moderate to good level of reliability [29–33]. In addition, it was shown that ultrasound image recording is greatly influenced by the evaluator, even among highly experi- enced ultrasonographers (weak inter-evaluator reliability ). Various factors such as the pressure applied on the probe and its alignment can influence recorded image properties and thus alter the quantitative values extracted [35, 36]. Information about the reliability and minimal de- tectable change is essential in order to develop evidence- based measurement taking protocols, empowering clini- cians and researchers to quantify the tendinous changes observed in Achilles tendinopathy and incorporate these findings into clinical practice.
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cation: ICC “ 0.75 which indicate as "excel- lent" reliability; ICC value contained between 0.41 and 0.74 "fair to good" reliability; and ICC value < 0.40 "poor" reliability . For each ICC, 95% confidence interval (CI) was calcu- lated to take the sampling distribution into ac- count. To assess absolute reliability, the stan- dard error of measurement (SEM) was calculat- ed as the square root of the mean square error term derived from the analysis of variance table . In addition, the coefficient of variation (CV) was determined for comparison of ab- solute reliability between the COP measure of test and retest sessions (S.D./mean 100). This was achieved by calculating mean of CV from individual CVs . The SEM is useful for com- puting the minimal detectable change (MDC) or change that could be considered clinical dif- ference between two measurements. The MDC was defined as 95% CI of SEM of the COP measure ( 1.96 2 SEM). The multiplier of 2 was used to account for the additional uncer- tainty introduced by using difference scores from measurements at 2 points in time .
Another way to quantify the ES is to compare it with the minimal important difference (MID) [9-12]. The MID can be defined as the smallest change in health status that causes a significant change in the patient’s symptoms, jus- tifying the performance or modification of a treatment if there are no significant side effects or excessive costs. It is estimated based on a determination of the standard error of measurement (SEM) and is estimated as 1 x SEM. The SEM is a statistical technique that estimates the possible magnitude of error in a measurement and is defined as be- ing the standard error in an observed result that masks the true result. An important property of the SEM is that its value is independent of the sample. This property means it yields a good estimate of individual changes in a health-related QoL indicator.
Sylvie Corteel and Jeremy Lovejoy  defined overpartitions and George E Andrews derived formula for the number of smallest parts of partitions of a positive integer n. In this paper we derived the formula for the number of smallest parts of overpartitions of a positive integer n by using the concepts of r overpartitions .
In order to overcome these limitations, it has been developed the Simplified Erosion and Narrowing Score (called “SENS”), that is entire- ly based on the van der Heijde modification of the Sharp score  and the Short Erosion Scale (SES), a change of the Larsen method . The SENS was developed by van der Heijde and is a simplified method by summing the number of eroded and narrowed joints on selected joints on hand and foot radiographs . It exploits the same joints of hands and feet, but as opposed to applying a semiquanti- tative scale of 0-4 for joint space narrowing and 0-5 for erosions, the SENS simply dichotomizes (bimodal answer modality) whether an erosion is absent (score of 0) or present (score of 1), and whether joint space narrowing is absent (score of 0) or present (score of 1) . The hand score per joint can, therefore, range from 0 to 2. Joint erosions are scored in 32 joints in the hands and wrists and 12 joints in the feet. JSN is scored in 30 joints in the hands and wrists and in 12 joints in the feet. Consequently, the maximum total erosion score is 44, the maximum total JSN score is 42 and the maxi- mum total score is 86 (Figure 8) . The SENS showed a good intra- and inter-reader reliability, and is sensitive to change . The SES considers 12 joints: three of four regions of the wrist as defined by Larsen (medi- al-proximal, medial-distal, and lateral-proximal) and MCP 2, 3, and 5 . Each joint is graded as in the 1995 Larsen system .
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Recently, the Osteoarthritis Research Society Inter- national (OARSI) recommended a set of five performance- based tests of physical function, including the TUG test in individuals diagnosed with hip or knee OA . The au- thors recommended TUG test because it demonstrated good measurement properties in people with OA and other populations [16–20]. In addition, Dobson et al.  conducted a systematic review on the measurement prop- erties of performance-based measures to assess physical function in hip and knee OA. They reported that sit to stand tests with the best measurement evidence included the TUG test and the 30-second chair stand test for hip/ knee OA. In a previous study, Norén et al.  investigated the applicability and reliability of some balance assessment methods, including the TUG test, in individuals with per- ipheral arthritis. They reported that the individuals with se- vere disability were generally able to perform the TUG test. Although Kennedy et al.  investigated measure- ment properties of four performance measures including TUG test in patients with advanced OA undergoing total hip or knee arthroplasty, no study to date has esti- mated the reliability and minimal detectable change of TUG test in a population with doubtful to moderate (Grade 1–3) knee OA. Hence, the purpose of this study was to estimate the reliability and MDC of TUG test in individuals with doubtful to moderate knee OA.
Although the chemical shift changes are small, and no change in the secondary structure content of aSyn is detectable within the cell, some differences are nevertheless apparent in the spectra, notably marked intensity changes in the HNCO spectrum of intracellular aSyn relative to the bulk solution state (Figure 2G). Decreased intensities are observed over much of the sequence, particularly in the region of the N and C-termini, and indeed as a result of this broadening no Ca and Cb resonances could be detected between residues 1 and 26. Such peak broadening could arise from intermediate chemical exchange, indicating conforma- tional fluctuations on a millisecond timescale, which has been observed previously in NMR studies of binding interactions involving aSyn [49,50]. In particular, decreased intensities within Figure 1. Multidimensional deconvolution of in-cell NMR
The forgotten topological index of a molecular graph is defined as F(G) = ∑ ∈ ( ) ( ) , where ( ) denotes the degree of vertex in . The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number = 1, 2, the first through the fourth for = 3, and the first and the second for = 4, 5 are determined. These results are compared with those obtained for the first Zagreb index.
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The operational costs of large-scale computing environ- ments are continuing to increase. In order to address this problem, self-managing systems are being developed that reduce the supervisory needs of computing environments. Self-healing systems are one such example, and operate by autonomously detecting then recovering from faults. Although there have been numerous advances in both of these aspects, most self-healing systems continue to require periodic human oversight , , , . This constraint poses challenges for the continued reduction of costs, and re- stricts self-healing recovery strategies to reactive approaches . The importance of reducing human oversight in man- aging computing environments is multi-faceted. Although numerous direct benefits exist–such as the reduction staff involvement and their associated operating costs–further achievements can also be realised. Notably, self-healing systems have properties that are showing inherent benefits to change control schemas, and preserving baseline config- urations .
Abstract—We consider an application of the least squares piecewise monotonic data approximation method to the problem of locating significant extrema in univariate observations that are contaminated by random errors. The piecewise monotonic approximation method makes the smallest change to the data such that the first differences of the smoothed values change sign a prescribed number of times, but the positions of the sign changes are unknowns of the optimization process. We present a numerical example in order to show the efficiency of the method for peak finding. The example is an application to 31959 noisy observations of daily sunspots. Our results suggest some subjects for future research in automatic peak finding.
change separately for each dimension of their measure- ment instrument [10,19]. For example, in a study deter- mining the MIC of the Chronic Respiratory Disease Scale the patients' global rating has been asked separately for the subscales dyspnoea, fatigue and emotional function . In the rating of change in overall health status patients have to weigh the relative contribution of the dif- ferent dimensions on their health status. For example, if patients with asthma judge dyspnoea to be much more important for their quality of life than emotional func- tioning, a small change in dyspnoea will affect the global rating of overall health, while for emotional functioning the change must be larger to be influential. The observed MIC value will be smallest for the anchor that shows the highest correlation with the health status scale under study.
Absolute reliability reflects the magnitude of the differ- ences between two measures . Examples of these sta- tistics are the standard error of measurement (SEM), the corresponding 95% confidence interval, the smallest detectable difference (SDD), and the limits of agreement (LA). To be clinically useful, an assessment with an HHD must have only a small amount of measurement error in detecting real change over time. A retest difference in a patient with a value smaller than the SEM is likely to be the result of 'measurement noise' and is unlikely to be detected reliably in practice; a difference greater than the SDD is likely to be a real difference with 95% certainty . The absolute reliability of HHD has been reported by several authors [16,26,27,31,33,34]. However, meas- ures of reliability are specific to the populations and test- ing procedures used. This implies that the findings of previous studies may not be applicable to patients with haematological malignancies. Disease- and treatment- related symptoms, including de-conditioning, muscle weakness, and fatigue may affect not only the reliability, but also the safety of performing HHD [16,22]. Therefore, the investigation of the measurement error of an HHD in patients with haematological malignancies is warranted. In daily physiotherapy or rehabilitation practice, strength measurements for the same patient are often performed by several examiners. However, the measurement error associated with the assessment of strength by one observer (intra-observer reliability) may be different than that asso- ciated with the assessment of strength by several observers (inter-observer reliability). For this reason, it is important to determine both the intra- and inter-observer reliability of the measurements obtained with a HHD. This study aimed to determine the relative and absolute reliability (measurement error) of intra and inter-observer strength measurements with a HHD in a sample of patients with haematological malignancies.
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However, arbitrary designations cannot be considered 'significant' in the traditional, statistical sense unless ex- perimental variance is taken into consideration. An evolv- ing method of analysis is to define significant changes in gene expression in terms of a particular P-value after per- forming appropriate statistical tests that take into account the variability of gene expression data and sample size [6– 10]. However, care must be taken to use appropriate sta- tistical tests, P-value thresholds for significance, and suffi- cient n, otherwise, variance-based methods, as with less rigorous fold-change approaches, will generate high error rates. Recent studies have discussed the utility of the 'Z score', the parametric t-test, and the nonparametric Wil- coxon rank sum test for expression profiling [9,10]. How- ever, the effects of inadequate sample size and P-value correction methods are only beginning to be addressed .
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