Bivariate Sample Research Articles

Role of Virtual Monoenergetic Images in the Assessment of Vessel Enhancement in Segmental Level in Third-Generation Dual-Source Dual-Energy CT Pulmonary Angiography—A Prospective Study

Abstract Introduction Pulmonary embolism is the third most common cause of cardiovascular death worldwide and imaging plays a pivotal role in establishing the diagnosis. Computed tomography pulmonary angiography (CTPA) scores over other modalities and is the current diagnostic investigation of choice. In this study, we assessed the main pulmonary artery and its corresponding segmental artery attenuation in reconstructed virtual monoenergetic (mono plus) images (VMI-MP) and linear blended images (spectral post processing, SPP) obtained from dual-energy CTPA. The values were compared using contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR). Materials and Methods Forty patients (mean age group, 53.6 years; 26 females and 14 males) with segmental pulmonary thromboembolism were included in this prospective study. The patients underwent CTPA study using bolus tracking in the dual-source CT-SOMATOM Force, Siemens. Postcontrast datasets (90 kV, 150 kV, and SPP) were used to reconstruct the monoenergetic images using syngo.via software virtually. Comparison was done between bivariate samples using the paired sample t-test. Results The mean Hounsfield unit (HU) artery in the left lung for VMI-MP and SPP images were 886.9 ± 242 and 356.8 ± 121.3 HU, respectively. Similarly, for the right lung, it was 868.3 ± 243.5 and 336.1 ± 105.5 HU, respectively. The mean attenuation of the arteries in MP images was higher and statistically significant (p-value <0.005). Likewise, the CNR) and SNR were found to have a statistically significant p-value (<0.005). An acceptable increase in image noise was seen in VMI as compared with SPP images. Conclusion Low-keV VMIs perform more effectively than the conventional polyenergetic spectrum to evaluate vessel attenuation, which in turn increases thrombus detectability. The increased CNR in VMI enables improved lesion conspicuity.

Determinants of Water Source Choice for Irrigation in the Arkansas Delta

AbstractThe use and the share of water applied from several irrigation water sources correlate with the irrigation practices in use by the peers of Arkansan farmers. From a sample of producers from an irrigation survey in Arkansas, a bivariate sample selection model accounts for how peer use of numerous irrigation practices affects the use and the share of irrigation that comes from a water source. The bivariate sample selection model controls for the bias in the statistical estimates that occur because producers who volunteer for an irrigation survey are likely to know about and use irrigation more than the population. We find that peer influence operates through multiple irrigation practices, and peer influence through an irrigation practice depends on an irrigator's location and current farm practices. For example, peer use of a tail‐water recovery system and peer use of alternate wetting and drying both increase the probability of surface water use alone.

Fisher information in order statistics and their concomitants for Cambanis bivariate distribution

Abstract The Fisher information matrix (FIM) relevant to order statistics (OSs) and their concomitants of the shape-parameters vector of the Cambanis bivariate distribution is investigated. Singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution are used to obtain the Fisher information (FI). In addition, the FI contained in the scale and shape parameters of generalized exponential distributions in the concomitants of OSs is obtained. The cumulative residual FI in the concomitant of OSs based on the Cambanis family is theoretically and numerically studied. Finally, a bivariate real-world data set has been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.

Impact of Denture Prostheses on Cognitive Functioning in Completely Edentulous Patients: A Pilot Study.

The aim is to evaluate the impact of denture prostheses on cognitive functioning in completely edentulous patients using a novel cognitive assessment tool. Thirty (n=30) completely edentulous patients of age groups above 60 years were taken in the present study group. Pre- and post-cognitive assessments were done on the patients using a novel cognitive assessment tool, Dental Cognitive Functioning Assessment Tool (DCFAT). These assessments were done in the pre-treatment stage and after two weeks and three months of prostheses function. The mean DCFATscore of 30patients shows 10.13 recorded prior to denture fabrication and 11.5 and 14 after two weeks and three months of prosthesis function, respectively. A mean difference in the DCFATscore of 1.37 was seen between the pre-denture fabrication stage and two weeks of prosthesis function. The mean difference in DCFATscore of 3.87 was seen between the pre-denture fabrication stage and three months of prosthesis function and the mean difference score of DCFAT score 2.5 was observed after two weeks and three months of prosthesis function. One-way ANOVA was used to investigate the statistical difference between bivariate samples followed by the post hoc Tukey test. The results were statistically significant p< 0.00001. The inference obtained suggest that the replacement of missing teeth by denture prostheses enhances the cognitive functioning in the elderly population which can eventually reduce the occurrence of dementia.

Reporting Quality of the Abstracts for Randomized Controlled Trials in Pediatric Dentistry.

The purpose of this study is to systematically appraise the reporting quality of abstracts for randomized controlled trials (RCT) published in pediatric dentistry using Consolidated Standards of Reporting Trials (CONSORT) for abstracts and to analyze the relationship between the characteristics of the RCT to the quality of abstracts. RCTs published in Pediatric Dentistry were retrieved from the PubMed database from 2016 to 2021. The quality of abstracts was appraised using CONSORT for abstracts checklist by two independent reviewers. In descriptive statistics, frequency and percentage analysis were used for categorical variables, whereas mean and standard deviation were used for continuous variables. To find the significant difference between the bivariate samples in independent groups, Mann-Whitney U test was employed. Multivariate analysis was performed using Kruskal-Wallis test and Mann-Whitney U tests. Probability value of p-value less than 0.05 was considered as statistically significant. Two hundred abstracts were included in the study. All the abstracts adequately reported the "objective" item, whereas only 2 and 4% of abstracts adequately addressed "randomization" and "harms" items, respectively. A significant relationship was observed between the continent of first author/corresponding author, number of authors, impact factor, adherence to CONSORT guidelines, word count, focus of study, and a priori protocol registration to the quality of abstracts (p < 0.05). The abstracts of the RCT included in the study did not adequately follow the CONSORT for abstract guidelines. Adherence to the reporting guidelines would improve the overall reporting quality of abstracts of RCT published in Pediatric Dentistry. The overall mean score of the abstracts was 6.80 out of 15 indicating that the abstracts did not adequately follow the CONSORT for abstract reporting guidelines.

COMPARATIVE STUDY TO ASSES ANALGESIC EFFICACY AND OPIOID SPARING EFFECT OF USG GUIDED SUBCOSTAL TRANSVERSUS ABDOMINIS PLANE BLOCK WITH INTRAPERITONEAL INSTILLATION OF BUPIVACAINE IN PATIENT UNDERGOING LAPAROSCOPIC CHOLECYSTECTOMY FOR POSTOPERATIVE PAIN RELIEF.

Background- Intensity of pain in early post-operative period after laparoscopic cholecystectomy is signicant. There are several methods employed in the management of postoperative pain after laparoscopic cholecystectomy such as conventional systemic analgesics, including paracetamol, non-steroidal anti-inammatory drugs, systemic opioids, and thoracic epidural analgesia with all having its limitations and side effects. Objective- The present study aims to compare ultrasound-guided subcostal transversus abdominis (STA) block with intraperitoneal instillation of bupivacaine in reducing postoperative pain, total analgesic consumptions after elective laparoscopic cholecystectomy. Materials and methods: 60 adult patients were randomly divided into 2 groups of 30 in each. The selected patients were randomly divided into two groups Group 1, patients received USG guided tap block before surgery. Group 2 patients received 40 ml of 0.25 % bupivacaine after surgery, instillation done by surgeon intraperitoneally at gall blabber bed and under the domes of diaphragm. Statistical analysis: In all Quantitative data were expressed in mean and standard deviation. Qualitative data were expressed in proportion and percentages. To nd the signicant difference between the bivariate samples in independent groups the Unpaired sample t-test and the Mann-Whitney U test was used. Above statistical tools the probability value &gt; .05 was considered as signicant level. Results: The mean Numerical Rating Scale scores were less in Group 1 than in Group 2 from 1 hours to 24 hours and it was statistically signicant. Demand of rescue analgesia was higher in group 2 when compared to group 1 and it was statistically signicant. Conclusion: TAP block is a better modality for analgesia compared to intraperitoneal instillation in patients undergoing elective laparoscopic cholecystectomy

Medical multivariate time series imputation and forecasting based on a recurrent conditional Wasserstein GAN and attention

Objective:In the fields of medical care and research as well as hospital management, time series are an important part of the overall data basis. To ensure high quality standards and enable suitable decisions, tools for precise and generic imputations and forecasts that integrate the temporal dynamics are of great importance. Since forecasting and imputation tasks involve an inherent uncertainty, the focus of our work lay on a probabilistic multivariate generative approach that samples infillings or forecasts from an analysable distribution rather than producing deterministic results. Materials and Methods:For this task, we developed a system based on generative adversarial networks that consist of recurrent encoders and decoders with attention mechanisms and can learn the distribution of intervals from multivariate time series conditioned on the periods before and, if available, periods after the values that are to be predicted. For training, validation and testing, a data set of jointly measured blood pressure series (ABP) and electrocardiograms (ECG) (length: 1,250=ˆ10s) was generated. For the imputation tasks, one interval of fixed length was masked randomly and independently in both channels of every sample. For the forecasting task, all masks were positioned at the end. Results:The models were trained on around 65,000 bivariate samples and tested against 14,000 series of different persons. For the evaluation, 50 samples were produced for every masked interval to estimate the range of the generated infillings or forecasts. The element-wise arithmetic average of these samples served as an estimator for the mean of the learned conditional distribution. The approach showed better results than a state-of-the-art probabilistic multivariate forecasting mechanism based on Gaussian copula transformation and recurrent neural networks. On the imputation task, the proposed method reached a mean squared error (MSE) of 0.057 on the ECG channel and an MSE of 28.30 on the ABP channel, while the baseline approach reached MSEs of 0.095 (ECG) and 229.1 (ABP). Moreover, on the forecasting task, the presented system achieved MSEs of 0.069 (ECG) and 33.73 (ABP), outperforming the recurrent copula approach, which reached MSEs of 0.082 (ECG) and 196.53 (ABP). Conclusion:The presented generative probabilistic system for the imputation and forecasting of (medical) time series features the flexibility to handle masks of different sizes and positions, the ability to quantify uncertainty due to its probabilistic predictions, and an adjustable trade-off between the goals of minimising errors in individual predictions and minimising the distance between the learned and the real conditional distribution of the infillings or forecasts.

Statistical dependence and shape of Young tableau

Given two continuous random variables, X and Y, we study the relationship between their statistical dependence and the Young tableau of the permutation defined from the graph of a bivariate sample coming from (X, Y). From a sample of size n of (X, Y), we identify the Young tableau of the permutation which maps the ranks of the X observations on the ranks of the Y observations. Procedures to detect statistical dependence between pairs of random variables, based on statistics calculated on the permutation defined by the graph of a bivariate sample have been developed, see García and González-López (2020) [Symmetry 12, 9, 1415. https://doi.org/10.3390/sym12091415] and García and González-López (2014) [J Multivar Anal 127, 126–146. https://doi.org/10.1016/j.jmva.2014.02.010]. In those papers, the information used is the length of the longest increasing (decreasing) subsequence, identified as the first line (the first column) of the Young tableau of the permutation. In this paper, we expose the information captured by the shape of the Young tableau of the permutation.

Likelihood Ratio Tests for Lorenz Dominance

In testing hypotheses pertaining to Lorenz dominance (LD), researchers have examined second- and third-order stochastic dominance using empirical Lorenz processes and integrated stochastic processes with the aid of bootstrap analysis. Among these topics, analysis of third-order stochastic dominance (TSD) based on the notion of risk aversion has been examined using crossing (generalized) Lorenz curves. These facts motivated the present study to characterize distribution pairs displaying the TSD without second-order (generalized Lorenz) dominance. It further motivated the development of likelihood ratio (LR) goodness-of-fit tests for examining the respective hypotheses of the LD, crossing (generalized) Lorenz curves, and TSD through approximate Chi-squared distributions. The proposed LR tests were assessed using simulated distributions, and applied to examine the COVID-19 regional death counts of bivariate samples collected by the World Health Organization between March 2020 and February 2021.

On the Bivariate Composite Gumbel–Pareto Distribution

In this paper, we propose a bivariate extension of univariate composite (two-spliced) distributions defined by a bivariate Pareto distribution for values larger than some thresholds and by a bivariate Gumbel distribution on the complementary domain. The purpose of this distribution is to capture the behavior of bivariate data consisting of mainly small and medium values but also of some extreme values. Some properties of the proposed distribution are presented. Further, two estimation procedures are discussed and illustrated on simulated data and on a real data set consisting of a bivariate sample of claims from an auto insurance portfolio. In addition, the risk of loss in this insurance portfolio is estimated by Monte Carlo simulation.

Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

AbstractThe Sarmanov family of bivariate distributions is considered as the most flexible and efficient extended families of the traditional Farlie–Gumbel–Morgenstern family. The goal of this work is twofold. The first part focuses on revealing some novel aspects of the Sarmanov family’s dependency structure. In the second part, we study the Fisher information (FI) related to order statistics (OSs) and their concomitants about the shape-parameter of the Sarmanov family. The FI helps finding information contained in singly or multiply censored bivariate samples from the Sarmanov family. In addition, the FI about the mean and shape parameter of exponential and power distributions in concomitants of OSs is evaluated, respectively. Finally, the cumulative residual FI in the concomitants of OSs based on the Sarmanov family is derived.

Qad: An R‐package to detect asymmetric and directed dependence in bivariate samples

Abstract Correlations belong to the standard repertoire of ecologists for quantifying the strength of dependence between two random variables. Classical dependence measures are usually not capable of detecting non‐monotonic or non‐functional dependencies. Furthermore, they completely fail to detect asymmetry and direction in dependence, which exist in many situations and should not be ignored. In this paper, we present qad (short for quantification of asymmetric dependence), a nonparametric statistical method to quantify directed and asymmetric dependence of bivariate samples. Qad is applicable in general (e.g. linear, non‐linear, or non‐monotonic) situations, is sensitive to noise in data, exhibits a good small sample performance, detects asymmetry in dependence, shows high power in testing for independence, requires no assumptions regarding the underlying distribution of the data and reliably quantifies the information gain/predictability of quantity Y given knowledge of quantity X, and vice versa (i.e. q(X,Y) q(Y,X)). Here, we briefly recall the methodology underlying qad, introduce the functions of the R‐package qad, which returns estimates for the measures denoting the directed dependence of on (or, equivalently, the influence of on ), the directed dependence of on , the asymmetry in dependence. Furthermore, qad can be used to predict Y given knowledge of X, and vice versa. Additionally, we compare empirical performance of qad with that of seven other well established measures and demonstrate the applicability of qad on ecological datasets. We illustrate that direction and asymmetry in dependence are universal properties of bivariate associations. Qad thus provides additional information gain and avoids model bias and will therefore advance and facilitate the understanding of ecological systems.

Information measures for order statistics and their concomitants from Cambanis bivariate family

One of the most efficient and robust methods in estimation is to find the Fisher information matrix (FIM). In this paper, the FIM concerning order statistics (OSs) and their concomitants about the shape-parameter vector of Cambanis bivariate distribution is derived. This method contains information conveyed by singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution. In addition, we obtain and study the Fisher information (FI) about the mean and shape parameters in the concomitants of OSs for this bivariate distribution based on exponential and power function distributions. Finally, the information entropy of Shannon in the OSs and their concomitants based on the Cambanis distribution is studied. Some numerical computations were performed on the FI which lend support to the theoretical results.

Analysis of the relationship between using personal protective equipment (PPE) masks on the incidence of respiratory symptoms disorders of online motorcycle taxis drivers in Malang

ABSTRACT Health problems that are often encountered due to work are respiratory disorders that cause premature death every year. Exposure to pollution is harmful to health, and chronic exposure causes lung cancer and COPD. The use of masks is an alternative in reducing exposure to pollution. This study aimed to determine the relationship between the habit of wearing masks on the incidence of respiratory symptoms disorder of online motorcycle taxi drivers in Malang. This study was an analytic observation with a cross-sectional design. Samples were determined using the comparative bivariate analytical sample formula. The data were analyzed using a univariate test and bivariate analysis with a chi-square test. This study showed a significant relationship between the habit of wearing a mask with p score = 0.015 (p&lt;0,05), changing time with p score = 0.004 (p&lt;0,05), and the type of mask on respiratory symptoms disorders with p score = 0.006 (p&lt;0,05). The results obtained regarding the description of the habit of using masks, the results of the method of using masks were mainly in the good category. In conclusion, there is a significant relationship between the habit of wearing masks and the incidence of respiratory symptoms disorders among online motorcycle taxi drivers in Malang. Keywords : Habits, masks, symptoms of respiratory disorders, online motorcycle taxisCorrespondence : Jeremisetiawan@webmail.umm.ac.id

Ranked set sampling in finite populations with bivariate responses: An application to an osteoporosis study.

The majority of the research on rank-based sampling designs in finite populations has been concerned with univariate situations. In this article, we study design-based estimation using a bivariate ranked set sampling (BIRSS) for finite populations when we have bivariate response variables. We derive the first and second-order inclusion probabilities associated with a BIRSS design. We show that the size of a BIRSS sample is random and propose using a conditional Poisson sampling (CPS) design to rectify this problem. We then use calculated inclusion probabilities to obtain design-based estimators of correlation coefficients between the bone mineral density (BMD) levels at the baseline and followup of a longitudinal BMD study in the province of Manitoba in Canada. We also study the problem of estimating the parameters of a regression model between the followup BMD and easy to obtain auxiliary information from the underlying population. Finally, we study the problem of classifying patients as those with or without osteoporosis using BIRSS and various CPS designs. We show that BIRSS designs are very flexible and can be used to obtain more efficient design-based estimators in sample surveys when dealing with response variables that are hard to measure or expensive to obtain.

Peer Irrigators and the Choice of Field Management and Water Control Practices for Irrigation in Arkansas

We examined how irrigation techniques in use by family and friends influence the use and share of land utilizing different irrigation techniques by Arkansas producers. A bivariate sample selection model simultaneously estimated how farm characteristics determine the use and explain the share of a farm that utilizes an irrigation technique. We found that the irrigation techniques in use by family and friends do affect the irrigation techniques a producer uses and the share of acres utilizing different irrigation techniques. A producer with a family or friend that uses end-blocking irrigation is 41% more likely to use end-blocking themselves. Having a family or friend who uses pivot irrigation technology tends to decrease the share of irrigated acres that utilizes end block irrigation by 0.211. We also found that when the irrigation techniques in use by family and friends interact with variables such as location and participation in a regional conservation partnership program, the effects on the producer’s decision vary. The share of irrigated acres that use cutback irrigation decreases by 0.21 for a producer who has a peer that uses irrigation scheduling. However, if the producer lives along Crowley’s Ridge and has a peer that uses irrigation scheduling, the share of irrigated acres that use cutback irrigation decreases by an additional 0.54.

Estimation of Surface Radiation Dosage to Thyroid Gland and Lower Abdomen While Using Intraoral Periapical Radiography: A Phantom Study.

Background and objectiveEvery dose of radiation has the potential to cause biological harm. Quantitative assessment of radiation doses to radiosensitive organs can aid dental professionals in taking the appropriate protective measures against radiation. This data may also be used among the general public to alleviate fears of radiation exposure in dental radiography. This study aimed to estimate the surface radiation dose at the level of the thyroid and lower abdomen during intraoral periapical radiography (IOPAR).Materials and methodsA total of 80 calcium sulfate (CaSO4) discs were utilized in this cross-sectional in vitro study to estimate the surface radiation dose at the level of thyroid and lower abdomen on a phantom model while using an IOPAR. After exposure, the discs were submitted to the Radiation Laboratory's "Personnel Monitoring Service" to measure the surface radiation dose. Mean and standard deviations were calculated using descriptive statistics for continuous variables. The Mann-Whitney U test was used to compare bi-variate samples of independent groups. All statistical analyses were performed using SPSS Statistics version 21.0 (IBM, Armonk, NY).ResultsThe results showed a statistically significant difference in radiation exposure between the maxillary anterior and mandibular anterior regions when the thermoluminescent dosimeter (TLD) was placed in the lower abdomen (p=0.000). When the maxillary and mandibular posterior regions were compared, there was a statistically significant difference in radiation exposure when the TLD was placed in the lower abdomen (p=0.000).ConclusionWhen the cone was positioned in the maxillary region, there was an increase in surface radiation dosage to the lower abdomen and thyroid.

Understanding the Sampling Bias: A Case Study on NBA Drafts

In several real data applications a biased sample arises naturally from the selection procedure. Recently, Economou et al. (Biom J 62: 238–249, 2020) used the concept of bivariate weighted distributions and proposed four different families of weight functions to describe cases in which the bias in a bivariate sample is caused by adopting sampling schemes that result in over- or under-representation of individuals with specific properties in the sample. The current paper focuses on revealing the contribution of each variable to the bias in the bivariate sample. More specifically, under the Bayesian perspective, Approximate Bayesian Computation methods are used to sample approximately from the posterior distribution, and the Deviance Information Criterion is employed to compare the fit of the models obtained by using different weight functions. The proposed method is illustrated to a real data set concerning NBA draft players.

Estimating the national and regional prevalence of drinking or eating more than usual during childhood diarrhea in Malawi using the bivariate sample selection copula regression.

BackgroundEstimation of prevalence of feeding practices during diarrhea using conventional imputation methods may be biased as these methods apply to observed factors and in this study, feeding practice status was unobserved for those without diarrhea. The study aimed at re-estimating the prevalence of feeding practices using the bivariate sample selection model.MethodsThe study used 2015–2016 Malawi demographic health survey (MDHS) data which had 16,246 children records who had diarrhea or not. A bivariate Joe copula regression model with 90 degrees rotation was fitted to either drinking or eating more, with diarrhea as a sample selection outcome in the bivariate models. The prevalence of drinking more than usual and prevalence of eating more than usual were then estimated based on the fitted bivariate model. These prevalences were then compared to the prevalences estimated using the conventional imputation method.ResultsThere was a substantial increase in the re-estimated national prevalence of drinking more fluids (40.0%, 95% CI [31.7–50.5]) or prevalence of eating more food (20.46%, 95% CI [9.87–38.55]) using the bivariate model as compared to the prevalences estimated by the conventional imputation method, that is, (28.9%, 95% CI [27.0–30.7]) and (13.1%, 95% CI [12.0–15.0]) respectively. The maps of the regional prevalences showed similar results where the prevalences estimated by the bivariate model were relatively higher than those estimated by the standard imputation method. The presence of diarrhea was somehow weakly negatively correlated with either drinking more fluids or eating more food.ConclusionThe estimation of prevalence of drinking more fluids or eating more food during diarrhea should use bivariate modelling to model sample selection variable so as to minimize bias. The observed negative correlation between diarrhea presence and feeding practices implies that mothers should be encouraged to let their children drink more fluids or eat more food during diarrhea episode to avoid dehydration and malnutrition.

Occlusal Contact Points, Areas and Bite Force Distribution in Angle’s Class I, II and III Patients using T-scan

Introduction: Number of occlusal contacts and uniform bite force distribution during maximum intercuspation are determinants of a good functional occlusion. Distribution of posterior contacts in the three malocclusion groups along with force distribution has been a topic of research. Aim: To quantify the number of occlusal contacts and areas, bite force distribution in Angle’s Class I, II, III subjects using T-scan and to identify the centre of force trajectory. Materials and Methods: This cross-sectional, observational study was conducted in the Department of Orthodontics, SRM College, Chennai, Tamil Nadu, India, from June 2018 to December 2018. Total 45 subjects in the age group of 18 to 24 years were divided into three groups of 15 subjects each based on Angle’s classification of malocclusion with teeth in normal line of occlusion. T-Scan system sensor and software were used to record and store data. The collected data were analysed with IBM Statistical Package for the Social Sciences (SPSS) software version 23.0. The descriptive statistics were performed, followed by Analysis of Variance (ANOVA). Post hoc Tukey test was done to find the difference between the groups. Chi-square test was done for the categorical data and the Paired t-test for determining the significant difference between the bivariate samples in paired groups. Level of significance was set at p&lt;0.05. Results: Out of three study groups, mean contact points (p&lt;0.001), contact areas (p&lt;0.001) and bite forces (p=0.0032) were statistically highly significant in Angle’s class I group when compared to the other groups. Statistically, the right and the left side differences in force distribution of the three groups were significant with the forces predominantly being higher on the right side. Conclusion: Subjects with Angle’s Class I molar relation had greater contacts, contact area and better bite force distribution. There was preference to the right side in bite force distribution in all the three groups. Centre of force trajectory was concentrated between first and second molars in all the groups