Dahlberg formula: a novel approach for its evaluation

INTRODUCTION: The accurate evaluation of error of measurement (EM) is extremely important as in growth studies as in clinical research, since there are usually quantitatively small changes. In any study it is important to evaluate the EM to validate the results and, consequently, the conclusions. Because of its extreme simplicity, the Dahlberg formula is largely used worldwide, mainly in cephalometric studies. OBJECTIVES: (I) To elucidate the formula proposed by Dahlberg in 1940, evaluating it by comparison with linear regression analysis; (II) To propose a simple methodology to analyze the results, which provides statistical elements to assist researchers in obtaining a consistent evaluation of the EM. METHODS: We applied linear regression analysis, hypothesis tests on its parameters and a formula involving the standard deviation of error of measurement and the measured values. RESULTS AND CONCLUSION: we introduced an error coefficient, which is a proportion related to the scale of observed values. This provides new parameters to facilitate the evaluation of the impact of random errors in the research final results.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

Error Autocorrelation and Linear Regression for Temperature-Based Evapotranspiration Estimates Improvement

Estimates of evapotranspiration on a local scale is important information for agricultural and hydrological practices. However, equations to estimate potential evapotranspiration based only on temperature data, which are simple to use, are usually less trustworthy than the Food and Agriculture Organization (FAO)Penman-Monteith standard method. The present work describes two correction procedures for potential evapotranspiration estimates by temperature, making the results more reliable. Initially, the standard FAO-Penman-Monteith method was evaluated with a complete climatologic data set for the period between 2002 and 2006. Then temperature-based estimates by Camargo and Jensen-Haise methods have been adjusted by error autocorrelation evaluated in biweekly and monthly periods. In a second adjustment, simple linear regression was applied. The adjusted equations have been validated with climatic data available for the Year 2001. Both proposed methodologies showed good agreement with the standard method indicating that the methodology can be used for local potential evapotranspiration estimates.

U-Pb dating by zircon dissolution method using chemical abrasion

Chemical abrasion was carried out on zircons grains of the Temora II standard for U-Pb dating prior to analyses using in situ Laser Ablation-MultiCollector Ion Coupled Plasma Mass Spectrometer (LA-ICPMS) followed by the Isotope Dissolution Thermal Ionization Mass Spectrometer (ID-TIMS) method. The proposed methodology was herein applied in order to reduce primarily the effects of secondary Pb loss, the presence of common lead and/or silicate impurities. Nine Temora II zircon grains were analyzed by the laser ablation method yielding an age of 418.3±4.3 Ma. Zircon grains of a same population were separated for chemical abrasion before dissolution and mass spectrometry analyses. Six fractions of them were separated for isotope dissolution using 235U-205Pb mixed spike after we have checked and assured the laboratory conditions of low blank values for total Pb of less than 2 pg/g. The obtained U-Pb zircon age by the ID-TIMS method was 415.7±1.8 Ma (error 0.43 %) based on four successful determinations. The results are consistent with the published ages for the Temora diorite (Temora I â 416.75±1.3 Ma; Temora II â 416.78±0.33 Ma) and established as 416±0.33 Ma. The technique is thus recommended for high precision U-Pb zircon analyses (error < 1 %), mainly for high resolution stratigraphic studies of Phanerozoic sequences.