Statnote 34 : the Kolmogorov-Smirnov (KS) test

The Kolmogorov-Smirnov (KS) test is a non-parametric test which can be used in two different circumstances. First, it can be used as an alternative to chi-square (?2) as a ‘goodness-of-fit’ test to compare whether a given ‘observed’ sample of observations conforms to an ‘expected’ distribution of results (KS, one-sample test). An example of the use of the one-sample test to determine whether a sample of observations was normally distributed was described previously. Second, it can be used as an alternative to the Mann-Whitney test to compare two independent samples of observations (KS, two-sample test). Hence, this statnote describes the use of the KS test with reference to two scenarios: (1) to compare the observed frequency (Fo) of soil samples containing cysts of the protozoan Naegleria collected each month for a year with an expected equal frequency (Fe) across months (one-sample test), and (2) to compare the abundance of bacteria on cloths and sponges sampled in a domestic kitchen environment (two-sample test).

Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.

Sobre a natureza dos processos físicos de aquecimento da atmosfera de estrelas do tipo solar

In the present work, we have studied the nature of the physical processes of the coronal heating, considering as basis significant samples of single and binary evolved stars, that have been achieved with the ROSAT satellite. In a total of 191 simple stars were studied, classified in the literature as giants with spectral type F, G and K. The results were compared with those obtained from 106 evolved stars of spectral type F, G and K, which belong to the spectroscopic binary systems. Accurate measurements on rotation and information about binarity were obtained from De Medeiros s catalog. We have analysed the behavior of the coronal activity in function of diverse stellar parameters. With the purpose to better clarify the profile of the stars evolution, the HR diagram was built for the two samples of stars, the single and the binary ones. The evolved traces added in the diagram were obtained from the Toulouse-Geneve code, Nascimento et al. (2000). The stars were segregated in this diagram not only in range of rotational speed but also in range of X-ray flux. Our analysis shows clearly that the single stars and the binary ones have coronal activity controlled by physical process independent on the rotation. Non magnetic processes seem to be strongly influencing the coronal heating. For the binary stars, we have also studied the behavior of the coronal emission as a function of orbital parameters, such as period and eccentricity, in which it was revealed the existence of a discontinuity in the emission of X-rays around an orbital period of 100 days. The study helped to conclude that circular orbits of the binary stars are presented as a necessary property for the existence of a higher level ofX-rays emission, suggesting that the effect of the gravitational tide has an important role in the coronal activity level. When applied the Kolmogorov-Smirnov test (KS test ) for the Vsini and FX parameters to the samples of single and binary stars, we could evidence very relevant aspects for the understanding of the mechanisms inherent to the coronal activity. For the Vsini parameter, the differences between the single stars and the binary ones for rotation over 6.3 km/s were really remarkable. We believe, therefore, that the existence of gravitational tide is, at least, one of the factors that most contribute for this behavior. About the X-rays flux, the KS test showed that the behavior of the single and the binary stars, regarding the coronal activity, comes from the same origin

Estágio menopausal e níveis hormonais no desenvolvimento muscular e funcional em mulheres de meia idade: um estudo transversal

Introduction: Hypoestrogenism is the main characteristic of female aging. It promotes significant changes in body composition, both in fat mass as in lean body mass, leading to a decrease in muscle strength and physical performance. Objective: The aim of this study was to test whether menopausal status and hormone levels are associated with muscular strength and physical performance in middle-aged women. Methods: In a cross-sectional study it was collected sociodemographic data, gynecological history, anthropometric and biochemical measures in women aged 40 to 65 years in Parnamirim-RN. The menopause status (pre, peri and post menopause) was determined by menstrual history. All women underwent three dimensions of physical performance assessment: handgrip dynamometry, gait speed and chair stands test - Short Physical Performance Battery (SPPB). Categorical data were presented as absolute and relative frequencies. Quantitative data were showed as mean and standard deviation and the normality of distribution was verified with Kolmogorov-Smirnov (KS) test. Biochemical measures of estradiol and follicle-stimulating hormone (FSH) were transformed to log10. ANOVA with Tukey post-test for comparison of variables between the groups pre, peri and post-menopausal was performed and then multiple linear regression analyzes. Results: Two hundred and seventy eight women aged 50.2 (±5.58) years composed this study, being 50 women in premenopausal status (18%), 122 in perimenopausal (43.9%), and 106 postmenopausal stage (38.1%). The groups were different in age (p=0.001), marital relationship duration (p <0.001), number of pregnancies (p=0.001) and parity (p=0.001). Differences in biochemical measures were observed among the groups: estradiol (p<0.001), FSH (p<0.001), total cholesterol (p=0.001). There were no differences in gait velocity between menopausal status. Values in mean of grip strength decreased by postmenopausal women to perimenopausal and premenopausal ones (24.5 ± 5.1, 25.6 ± 5.4, 26.9 ± 4.9 for post-stage, pre and peri menopausas, respectively, p = 0.02) and the performance of chair stands test was better in premenopausal women compared with that in peri and postmenopausal status (p = 0.02). In multiple linear regression for muscle strength, the variables that remained were: age, estradiol and somatic symptoms measured by Menopause Rating Scale-MRS (R2=0.15). While for the xiv chair-stands test the predictors were number of births and FSH values (R2=0.04). Conclusion: There is a relationship between the stages of menopause and muscle performance in measures of grip strength and sit-up test and these are influenced by the fall of estrogens levels. Data suggest that the decrease in muscle strength and physical performance already appear in the transition to menopause stage, pointing to the need for more research in this area and appropriate preventive interventions

Statistical detection of spurious variations in daily raingauge data caused by changes in observation practices, as applied to records from various parts of the world

In the instrumental records of daily precipitation, we often encounter one or more periods in which values below some threshold were not registered. Such periods, besides lacking small values, also have a large number of dry days. Their cumulative distribution function is shifted to the right in relation to that for other portions of the record having more reliable observations. Such problems are examined in this work, based mostly on the two-sample Kolmogorov–Smirnov (KS) test, where the portion of the series with more number of dry days is compared with the portion with less number of dry days. Another relatively common problem in daily rainfall data is the prevalence of integers either throughout the period of record or in some part of it, likely resulting from truncation during data compilation prior to archiving or by coarse rounding of daily readings by observers. This problem is identified by simple calculation of the proportion of integers in the series, taking the expected proportion as 10%. The above two procedures were applied to the daily rainfall data sets from the European Climate Assessment (ECA), Southeast Asian Climate Assessment (SACA), and Brazilian Water Resources Agency (BRA). Taking the statistic D of the KS test >0.15 and the corresponding p-value <0.001 as the condition to classify a given series as suspicious, the proportions of the ECA, SACA, and BRA series falling into this category are, respectively, 34.5%, 54.3%, and 62.5%. With relation to coarse rounding problem, the proportions of series exceeding twice the 10% reference level are 3%, 60%, and 43% for the ECA, SACA, and BRA data sets, respectively. A simple way to visualize the two problems addressed here is by plotting the time series of daily rainfall for a limited range, for instance, 0–10 mm day−1.

Statnote 1: is the data normal?

Testing whether an observed distribution of observations deviates from normality is a common type of statistical test available in statistics software. Most software offer two ways of judging whether there are significant deviations of the observed from the expected distributions, viz., chi-square and the KS test. These tests have different sensitivities and problems and often give conflicting results. The results of these tests together with observations of the shape of the observed distribution should be used to judge normality.

Efeito tardio do kinesio taping na função do membro inferior e no desempenho neuromuscular do quadríceps femoral de mulheres saudáveis: ensaio clínico e randomizado

Introduction: Kinesio Taping (KT) has been used in healthy people to improve neuromuscular performance, however, few studies have evaluated its chronic effects, despite being suggested. Objective: To analyze the chronic effects of KT on neuromuscular performance of the quadriceps, the oscillation of the center of pressure and lower limb function in healthy women. Methods: blinded, randomized, controlled trial, composed of 60 women (mean age 21.9 ± 3.3 years and BMI 22.3 ± 2.2 kg / m2) submitted to the evaluation of oscillation of the center of pressure through the baropodometry, the lower limb function by the hop test, isokinetic knee performance, the electromyographic activity of the vastus lateralis (VL) and joint position sense of the knee (JPS). Then, participants were randomly divided into three groups of twenty: control - did not apply the KT; placebo - application of KT without tension on the quadriceps; Kinesio Taping - application of KT with tension in the same muscle group. The evaluations were conducted in five moments: prior to application of KT, immediately after the application, 24h, 48h after application and 24 hours after its removal (72h). SPSS 20.0 was used for statistical analysis. The KS test was used to verify the data normality, the Levene test for homogeneity of variances and a mixed-model ANOVA 3x5 to check intra and inter-group differences. Results: there was no difference in peak torque, the power, nor the electromyographic activity or SPA (p> 0.05) between groups. The displacement speed of center of pressure reduced immediately after the application on kinesio taping group (p <0.001), but with no differences between the groups (p = 0.28). There was a reduction in the time of peak torque among the three groups in the evaluations after KT application (p <0.001) and an increase in single hop in all groups (p <0.001), but with no differences between them. Conclusion: KT can not change, in a chronic way, the lower limb function, the oscillation of the center of pressure, the isokinetic performance, the JPS of the knee and the electromyographic activity of VL muscle in healthy women.

SAMPLING BIAS IN EVALUATING THE PROBABILITY OF SEISMICALLY INDUCED SOIL LIQUEFACTION WITH SPT & CPT CASE HISTORIES

Several deterministic and probabilistic methods are used to evaluate the probability of seismically induced liquefaction of a soil. The probabilistic models usually possess some uncertainty in that model and uncertainties in the parameters used to develop that model. These model uncertainties vary from one statistical model to another. Most of the model uncertainties are epistemic, and can be addressed through appropriate knowledge of the statistical model. One such epistemic model uncertainty in evaluating liquefaction potential using a probabilistic model such as logistic regression is sampling bias. Sampling bias is the difference between the class distribution in the sample used for developing the statistical model and the true population distribution of liquefaction and non-liquefaction instances. Recent studies have shown that sampling bias can significantly affect the predicted probability using a statistical model. To address this epistemic uncertainty, a new approach was developed for evaluating the probability of seismically-induced soil liquefaction, in which a logistic regression model in combination with Hosmer-Lemeshow statistic was used. This approach was used to estimate the population (true) distribution of liquefaction to non-liquefaction instances of standard penetration test (SPT) and cone penetration test (CPT) based most updated case histories. Apart from this, other model uncertainties such as distribution of explanatory variables and significance of explanatory variables were also addressed using KS test and Wald statistic respectively. Moreover, based on estimated population distribution, logistic regression equations were proposed to calculate the probability of liquefaction for both SPT and CPT based case history. Additionally, the proposed probability curves were compared with existing probability curves based on SPT and CPT case histories.

AIPE-active green phosphorescent iridium(III) complex impregnated test strips for the vapor-phase detection of 2,4,6-trinitrotoluene (TNT)

Detection of explosives, especially trinitrotoluene (TNT), is of utmost importance due to its highly explosive nature and environmental hazard. Therefore, detection of TNT has been a matter of great concern to the scientific community worldwide. Herein, a new aggregation-induced phosphorescent emission (AIPE)-active iridium(III) bis(2-(2,4-difluorophenyl)pyridinato-NC2') (2-(2-pyridyl)benzimidazolato-N,N') complex FIrPyBiz] has been developed and serves as a molecular probe for the detection of TNT in the vapor phase, solid phase, and aqueous media. In addition, phosphorescent test strips have been constructed by impregnating Whatman filter paper with aggregates of FIrPyBiz for trace detection of TNT in contact mode, with detection limits in nanograms, by taking advantage of the excited state interaction of AIPE-active phosphorescent iridium(III) complex with that of TNT and the associated photophysical properties.

X-ray driven evaporation of exoplanet atmospheres: discovery of a uniquely suited test system

The evaporation of exoplanetary atmospheres is thought to be driven by high-energy irradiation. However, the actual mass loss rates are not well constrained. Co-I Kipping has recently discovered that the star KOI-314, an M1V dwarf at 65 pc distance, is orbited by two earth-sized planets, the inner one of them rocky and the outer one gaseous (P_orb = 14d and 23d). Other recent works have shown an abundance of small rocky planets in very close orbits around their host stars, suggesting that the stellar high-energy irradiation evaporates away gaseous envelopes. KOI-314 is the first nearby system in which earth-sized planets of both types are detected, allowing us to constrain the efficiency of planetary evaporation if the stellar X-ray irradiation is measured. We therefore propose a 10 ks Chandra ACIS-S pointing to determine the stellar X-ray luminosity and hardness ratio. The accuracy of the orbital solution decreases quickly due to Transit-Timing Variations, which is why we ask for DDT.