The significant figures in a numerical expression are defined as all those whose values are known with certainty with one additional digit whose value is uncertain.
Errors refer to the differences between measured and true values in measurements and experiments. It is impossible to perform analyses that are completely free of errors. Errors are caused by faulty instruments, imprecise measurements, and random variations. Methods to reduce errors include frequent calibration of instruments, analysis of known samples, and repeating measurements. Precision refers to the reproducibility of measurements and can be estimated through repeated measurements of replicate samples. Accuracy is the closeness of a measurement to the true value and is more difficult to determine than precision. There are two main types of errors: determinate errors caused by mistakes that can be avoided, and accidental errors that are difficult to control. Methods to minimize errors include calibration, using blanks, comparative analysis techniques, and repeated
This document discusses errors in measurement and analysis. It defines absolute and relative errors as the difference between experimental and true values. Errors are classified as determinate (systemic) or indeterminate (random). Determinate errors include personal, instrumental, method, additive and proportional errors. Indeterminate errors cannot be avoided and come from unknown causes. Accuracy refers to how close a measurement is to the true value, while precision describes the reproducibility of measurements. Significant figures convey the precision or accuracy of numerical values. The document provides examples and rules for determining significant figures.
Errors - pharmaceutical analysis -1, bpharm 1st semester, notes, topic errors
full details and answer about error
TN DR MGR UNIVERSITY
by Kumaran.M.pharm, professor
This document discusses various concepts related to errors and accuracy in chemical analysis. It defines different types of errors like gross errors, systematic errors, and random errors. It explains how to classify errors based on their origin and how to minimize different types of errors. The document also covers key statistical concepts like mean, median, standard deviation, normal distribution, precision and accuracy that are important for understanding errors in chemical analysis.
The document discusses various types of errors that can occur in quantitative chemical analysis, including random errors, systematic errors, determinate errors, indeterminate errors, and errors due to faulty instrumentation, impure reagents, or improper methodology. It also describes ways to minimize errors, such as calibrating apparatus, running blanks and controls, using multiple analytical techniques, and performing replicate measurements. Accuracy is defined as how close a measurement is to the true value, while precision refers to the reproducibility of measurements.
Introduction to Pharmaceutical ChemistryPriti Kokate
Chapter No. 1 from pharmaceutical chemistry , updated syllabus notes as per MSBTE
1.Introduction to pharmaceutical chemistry
Topic covers following bits
#Scope
#Objective
#Sources & Types Of Errors
#Impurities in Pharmaceuticals
#Limit Test For
*Chloride
*Sulphate
*Iron
*Heavy Metal
*Arsenic
Errors refer to the differences between measured and true values in measurements and experiments. It is impossible to perform analyses that are completely free of errors. Errors are caused by faulty instruments, imprecise measurements, and random variations. Methods to reduce errors include frequent calibration of instruments, analysis of known samples, and repeating measurements. Precision refers to the reproducibility of measurements and can be estimated through repeated measurements of replicate samples. Accuracy is the closeness of a measurement to the true value and is more difficult to determine than precision. There are two main types of errors: determinate errors caused by mistakes that can be avoided, and accidental errors that are difficult to control. Methods to minimize errors include calibration, using blanks, comparative analysis techniques, and repeated
This document discusses errors in measurement and analysis. It defines absolute and relative errors as the difference between experimental and true values. Errors are classified as determinate (systemic) or indeterminate (random). Determinate errors include personal, instrumental, method, additive and proportional errors. Indeterminate errors cannot be avoided and come from unknown causes. Accuracy refers to how close a measurement is to the true value, while precision describes the reproducibility of measurements. Significant figures convey the precision or accuracy of numerical values. The document provides examples and rules for determining significant figures.
Errors - pharmaceutical analysis -1, bpharm 1st semester, notes, topic errors
full details and answer about error
TN DR MGR UNIVERSITY
by Kumaran.M.pharm, professor
This document discusses various concepts related to errors and accuracy in chemical analysis. It defines different types of errors like gross errors, systematic errors, and random errors. It explains how to classify errors based on their origin and how to minimize different types of errors. The document also covers key statistical concepts like mean, median, standard deviation, normal distribution, precision and accuracy that are important for understanding errors in chemical analysis.
The document discusses various types of errors that can occur in quantitative chemical analysis, including random errors, systematic errors, determinate errors, indeterminate errors, and errors due to faulty instrumentation, impure reagents, or improper methodology. It also describes ways to minimize errors, such as calibrating apparatus, running blanks and controls, using multiple analytical techniques, and performing replicate measurements. Accuracy is defined as how close a measurement is to the true value, while precision refers to the reproducibility of measurements.
Introduction to Pharmaceutical ChemistryPriti Kokate
Chapter No. 1 from pharmaceutical chemistry , updated syllabus notes as per MSBTE
1.Introduction to pharmaceutical chemistry
Topic covers following bits
#Scope
#Objective
#Sources & Types Of Errors
#Impurities in Pharmaceuticals
#Limit Test For
*Chloride
*Sulphate
*Iron
*Heavy Metal
*Arsenic
The document discusses the importance of limit tests in pharmaceutical chemistry for determining impurities, describing the principle and procedure for the limit test for chlorides which involves the chemical reaction of chlorides with silver nitrate in the presence of nitric acid to form a silver chloride precipitate, comparing the test sample to a standard solution of known chloride concentration.
The document discusses analytical chemistry methods and concepts related to errors, precision, accuracy, and statistical analysis of data. It defines types of errors, describes methods to minimize errors, and explains concepts like absolute and relative error, precision, accuracy, and statistical measures including mean, median, mode, standard deviation, and t-tests and F-tests. It also provides an example of calculating average deviation and standard deviation from a set of concentration data and discusses the normal distribution curve.
This document discusses sources of errors in quantitative analysis and methods to minimize errors. It defines:
1) Systematic errors which can affect results consistently, including personal, operational, instrumental, methodical, and additive/proportional errors.
2) Random errors due to limitations of instruments or observations. These can be minimized but not eliminated.
3) Methods to reduce errors including calibration, blanks, independent methods, and standard additions.
4) Expressing errors as absolute or relative values. Precision refers to agreement of repeated measurements while accuracy reflects agreement with true values.
This document discusses different types of errors that can occur in analytical chemistry measurements and methods. It describes determinate errors, which include instrumental errors from faulty tools, methodic errors from defective experimental methods, operational errors from improper technique, and personal errors from the analyst. It also discusses indeterminate errors, which are random errors that cannot be attributed to a known cause. The document explains how errors can propagate in calculations and discusses accuracy and precision in measurements.
This document discusses measurement errors and uncertainty. It defines measurement as assigning a number and unit to a property using an instrument. Error is the difference between the measured value and true value. There are two main types of error: random error, which varies unpredictably, and systematic error, which remains constant or varies predictably. Sources of error include the measuring instrument and technique used. Uncertainty is the doubt about a measurement and is quantified with an interval and confidence level, such as 20 cm ±1 cm at 95% confidence. Uncertainty is important for tasks like calibration where it must be reported.
This document discusses errors in measurement and different types of errors. It explains that there are five main elements that can cause errors: standards, work pieces, instruments, persons, and environment. There are three types of errors: systematic errors, which occur due to imperfections and are of fixed magnitude; random errors, which occur irregularly; and statistical analysis can be used to analyze random errors through calculations of mean, range, deviation, and standard deviation. Systematic errors include instrumental errors from faulty instruments, environmental errors from external conditions, and observational errors from human factors like parallax.
- Precision refers to how closely repeated measurements are clustered together, while accuracy describes how close measurements are to the true value. There are various ways to express accuracy and precision numerically.
- Accuracy can be expressed as absolute error or relative error compared to the true value. Precision can be expressed using values like standard deviation, deviation from the mean/median, and range.
- Errors can be determinate (systematic) or indeterminate (random). Determinate errors are consistent and can be avoided, while indeterminate errors follow a normal distribution and cannot be eliminated. Statistical analysis is needed to understand random error.
- Reliability is a measure of reproducibility of a test when repeated, quantifying random error. Validity is how well a test measures what it intends to, requiring comparison to a criterion.
- Reliability is typically quantified by the typical error or intraclass correlation. Validity uses correlation and error of estimate from regression of the test on a criterion.
- Both reliability and validity should be high for a test to accurately track small individual changes over time and distinguish individuals. Ideal values are >0.96 for reliability and validity correlations and typical/estimate errors <20% of between-subject standard deviation.
1. Systematic errors affect the accuracy of results and are caused by factors like improper instrument calibration, faulty methodology, or personal biases.
2. Random errors affect precision and result from unpredictable factors that cause random scatter in measurements.
3. Various statistical analyses can be used to determine systematic and random errors in experimental data, including calculating measures of central tendency, variability, and confidence limits. Propagation of errors must also be considered.
Errors in pharmaceutical analysis can be determinate (systematic) or indeterminate (random). Determinate errors are caused by faults in procedures or instruments and cause results to consistently be too high or low. Sources include improperly calibrated equipment, impure reagents, and analyst errors. Indeterminate errors are random and unavoidable, arising from limitations of instruments. Accuracy refers to closeness to the true value, while precision refers to reproducibility. Systematic errors can be minimized by calibrating equipment, analyzing standards, using independent methods, and blank determinations.
Errors in chemical analysis can be random or systematic. Random errors cause imprecise results while systematic errors lead to inaccurate results by introducing bias. Common sources of systematic error include faulty instrumentation, non-ideal chemical behaviors in analytical methods, and personal biases of experimenters. Systematic errors can be detected through frequent calibration of instruments, analysis of reference standards, independent verification methods, blank determinations, and evaluation of results from varying sample sizes. Controlling for systematic errors is important for obtaining reliable analytical data.
Accuracy refers to how close a measurement is to the true value, while precision refers to the reproducibility of measurements. Accuracy is determined by calculating percentage error compared to the accepted value. Precision depends on the number of significant figures in a measurement as determined by the measuring tool. Random and systematic errors can affect accuracy, while random errors affect precision. The uncertainty of a measurement combines its precision and accuracy errors and is reported with the mean value and at a given confidence level, typically 95%. Propagation of error calculations allow determining the total uncertainty when a value depends on multiple measurements.
A statistical error is the difference between a sample value and the true population value. There are two main types of error - sampling error and non-sampling error. Sampling error occurs when the sample is not fully representative of the population, while non-sampling error can arise from factors like non-response, measurement issues, interviewer errors, adjustments to the data, or processing mistakes. Common ways to measure and reduce sampling error include calculating the standard error, sample size, and sample design.
This document discusses measurement errors and standards. It defines key terms related to measurement accuracy and precision. Accuracy is the closeness of a measurement to the true value, while precision refers to the consistency of repeated measurements. Errors can be absolute or relative. Systematic errors are due to instrument flaws, while random errors have unknown causes. The document also discusses limiting/guarantee errors, which specify the maximum allowed deviation from a component's rated value. Resolution refers to the smallest detectable change in a measurement. Sensitivity is the change in output per unit change in input.
This document provides an introduction to analyzing experimental errors and data. It discusses evaluating potential sources of errors before, during, and after an analysis. There are two types of experimental errors - determinate errors that affect accuracy and indeterminate errors that affect precision. Determinate errors can be constant or proportional while indeterminate errors are random. The document outlines various sources of these errors and methods to identify and minimize them, such as analyzing samples of different sizes or using reference standards.
This document discusses error analysis and significant figures in measurements. It defines absolute and relative errors, and explains that random errors can be estimated by taking multiple measurements and calculating their standard deviation. Systematic errors result from flaws in the measurement process. The document also provides rules for propagating errors through calculations based on measured values. Measurements should be reported with a number of significant figures consistent with their estimated error.
This document discusses measurement uncertainty. It defines measurement uncertainty as a parameter included with any measurement result that accounts for possible errors. It describes sources of uncertainty like sampling, storage conditions, and personal effects. The document outlines methods of calculating uncertainty using the standard deviation, and explains why assessing uncertainty is important for interpreting results and ensuring measurement quality. Measurement uncertainty is a key component of any measurement result.
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptxssuserd509321
The document discusses factors that affect sample size calculation in different study designs. It provides examples of calculating sample sizes for descriptive cross-sectional studies, case-control studies, cohort studies, comparative studies, and randomized controlled trials. The key factors discussed are the level of confidence, power, expected proportions or means in groups, margin of error, and standard deviation. Sample size is affected by the type of study design, variables being qualitative or quantitative, and the goal of establishing equivalence, superiority or non-inferiority between groups. Electronic resources are provided for calculating sample sizes.
Today's Topic Errors - Introduction, Sources of Errors, Types of Errors, Minimization of Errors, Accuracy, Precision, Significant Figures in Pharmaceutical Analysis subject in B.pharmacy 1st year as per JNTUA Syllabus...
The document discusses the importance of limit tests in pharmaceutical chemistry for determining impurities, describing the principle and procedure for the limit test for chlorides which involves the chemical reaction of chlorides with silver nitrate in the presence of nitric acid to form a silver chloride precipitate, comparing the test sample to a standard solution of known chloride concentration.
The document discusses analytical chemistry methods and concepts related to errors, precision, accuracy, and statistical analysis of data. It defines types of errors, describes methods to minimize errors, and explains concepts like absolute and relative error, precision, accuracy, and statistical measures including mean, median, mode, standard deviation, and t-tests and F-tests. It also provides an example of calculating average deviation and standard deviation from a set of concentration data and discusses the normal distribution curve.
This document discusses sources of errors in quantitative analysis and methods to minimize errors. It defines:
1) Systematic errors which can affect results consistently, including personal, operational, instrumental, methodical, and additive/proportional errors.
2) Random errors due to limitations of instruments or observations. These can be minimized but not eliminated.
3) Methods to reduce errors including calibration, blanks, independent methods, and standard additions.
4) Expressing errors as absolute or relative values. Precision refers to agreement of repeated measurements while accuracy reflects agreement with true values.
This document discusses different types of errors that can occur in analytical chemistry measurements and methods. It describes determinate errors, which include instrumental errors from faulty tools, methodic errors from defective experimental methods, operational errors from improper technique, and personal errors from the analyst. It also discusses indeterminate errors, which are random errors that cannot be attributed to a known cause. The document explains how errors can propagate in calculations and discusses accuracy and precision in measurements.
This document discusses measurement errors and uncertainty. It defines measurement as assigning a number and unit to a property using an instrument. Error is the difference between the measured value and true value. There are two main types of error: random error, which varies unpredictably, and systematic error, which remains constant or varies predictably. Sources of error include the measuring instrument and technique used. Uncertainty is the doubt about a measurement and is quantified with an interval and confidence level, such as 20 cm ±1 cm at 95% confidence. Uncertainty is important for tasks like calibration where it must be reported.
This document discusses errors in measurement and different types of errors. It explains that there are five main elements that can cause errors: standards, work pieces, instruments, persons, and environment. There are three types of errors: systematic errors, which occur due to imperfections and are of fixed magnitude; random errors, which occur irregularly; and statistical analysis can be used to analyze random errors through calculations of mean, range, deviation, and standard deviation. Systematic errors include instrumental errors from faulty instruments, environmental errors from external conditions, and observational errors from human factors like parallax.
- Precision refers to how closely repeated measurements are clustered together, while accuracy describes how close measurements are to the true value. There are various ways to express accuracy and precision numerically.
- Accuracy can be expressed as absolute error or relative error compared to the true value. Precision can be expressed using values like standard deviation, deviation from the mean/median, and range.
- Errors can be determinate (systematic) or indeterminate (random). Determinate errors are consistent and can be avoided, while indeterminate errors follow a normal distribution and cannot be eliminated. Statistical analysis is needed to understand random error.
- Reliability is a measure of reproducibility of a test when repeated, quantifying random error. Validity is how well a test measures what it intends to, requiring comparison to a criterion.
- Reliability is typically quantified by the typical error or intraclass correlation. Validity uses correlation and error of estimate from regression of the test on a criterion.
- Both reliability and validity should be high for a test to accurately track small individual changes over time and distinguish individuals. Ideal values are >0.96 for reliability and validity correlations and typical/estimate errors <20% of between-subject standard deviation.
1. Systematic errors affect the accuracy of results and are caused by factors like improper instrument calibration, faulty methodology, or personal biases.
2. Random errors affect precision and result from unpredictable factors that cause random scatter in measurements.
3. Various statistical analyses can be used to determine systematic and random errors in experimental data, including calculating measures of central tendency, variability, and confidence limits. Propagation of errors must also be considered.
Errors in pharmaceutical analysis can be determinate (systematic) or indeterminate (random). Determinate errors are caused by faults in procedures or instruments and cause results to consistently be too high or low. Sources include improperly calibrated equipment, impure reagents, and analyst errors. Indeterminate errors are random and unavoidable, arising from limitations of instruments. Accuracy refers to closeness to the true value, while precision refers to reproducibility. Systematic errors can be minimized by calibrating equipment, analyzing standards, using independent methods, and blank determinations.
Errors in chemical analysis can be random or systematic. Random errors cause imprecise results while systematic errors lead to inaccurate results by introducing bias. Common sources of systematic error include faulty instrumentation, non-ideal chemical behaviors in analytical methods, and personal biases of experimenters. Systematic errors can be detected through frequent calibration of instruments, analysis of reference standards, independent verification methods, blank determinations, and evaluation of results from varying sample sizes. Controlling for systematic errors is important for obtaining reliable analytical data.
Accuracy refers to how close a measurement is to the true value, while precision refers to the reproducibility of measurements. Accuracy is determined by calculating percentage error compared to the accepted value. Precision depends on the number of significant figures in a measurement as determined by the measuring tool. Random and systematic errors can affect accuracy, while random errors affect precision. The uncertainty of a measurement combines its precision and accuracy errors and is reported with the mean value and at a given confidence level, typically 95%. Propagation of error calculations allow determining the total uncertainty when a value depends on multiple measurements.
A statistical error is the difference between a sample value and the true population value. There are two main types of error - sampling error and non-sampling error. Sampling error occurs when the sample is not fully representative of the population, while non-sampling error can arise from factors like non-response, measurement issues, interviewer errors, adjustments to the data, or processing mistakes. Common ways to measure and reduce sampling error include calculating the standard error, sample size, and sample design.
This document discusses measurement errors and standards. It defines key terms related to measurement accuracy and precision. Accuracy is the closeness of a measurement to the true value, while precision refers to the consistency of repeated measurements. Errors can be absolute or relative. Systematic errors are due to instrument flaws, while random errors have unknown causes. The document also discusses limiting/guarantee errors, which specify the maximum allowed deviation from a component's rated value. Resolution refers to the smallest detectable change in a measurement. Sensitivity is the change in output per unit change in input.
This document provides an introduction to analyzing experimental errors and data. It discusses evaluating potential sources of errors before, during, and after an analysis. There are two types of experimental errors - determinate errors that affect accuracy and indeterminate errors that affect precision. Determinate errors can be constant or proportional while indeterminate errors are random. The document outlines various sources of these errors and methods to identify and minimize them, such as analyzing samples of different sizes or using reference standards.
This document discusses error analysis and significant figures in measurements. It defines absolute and relative errors, and explains that random errors can be estimated by taking multiple measurements and calculating their standard deviation. Systematic errors result from flaws in the measurement process. The document also provides rules for propagating errors through calculations based on measured values. Measurements should be reported with a number of significant figures consistent with their estimated error.
This document discusses measurement uncertainty. It defines measurement uncertainty as a parameter included with any measurement result that accounts for possible errors. It describes sources of uncertainty like sampling, storage conditions, and personal effects. The document outlines methods of calculating uncertainty using the standard deviation, and explains why assessing uncertainty is important for interpreting results and ensuring measurement quality. Measurement uncertainty is a key component of any measurement result.
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptxssuserd509321
The document discusses factors that affect sample size calculation in different study designs. It provides examples of calculating sample sizes for descriptive cross-sectional studies, case-control studies, cohort studies, comparative studies, and randomized controlled trials. The key factors discussed are the level of confidence, power, expected proportions or means in groups, margin of error, and standard deviation. Sample size is affected by the type of study design, variables being qualitative or quantitative, and the goal of establishing equivalence, superiority or non-inferiority between groups. Electronic resources are provided for calculating sample sizes.
Today's Topic Errors - Introduction, Sources of Errors, Types of Errors, Minimization of Errors, Accuracy, Precision, Significant Figures in Pharmaceutical Analysis subject in B.pharmacy 1st year as per JNTUA Syllabus...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
(June 12, 2024) Webinar: Development of PET theranostics targeting the molecu...Scintica Instrumentation
Targeting Hsp90 and its pathogen Orthologs with Tethered Inhibitors as a Diagnostic and Therapeutic Strategy for cancer and infectious diseases with Dr. Timothy Haystead.
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdfSelcen Ozturkcan
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.
PPT on Direct Seeded Rice presented at the three-day 'Training and Validation Workshop on Modules of Climate Smart Agriculture (CSA) Technologies in South Asia' workshop on April 22, 2024.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
2. Significant Figures
The significant figures in a numerical expression are defined as all those
whose values are known with certainty with one additional digit whose
value is uncertain.
For e.g., if the mass of a substance is reported as 2.03765 gram, then only
the first four figures are meaningful. The last digit known with certainty
is 7.
The digit 6is uncertain and indicates only that the mass is more than
2.037 but less than 2.038.
The last digit 5 is meaningless and superfluous.
By definition, the expression 2.03765 has only five significant figures, of
which four figures are certain and one figure is uncertain
3. Rules for significant figures
• All non –zero numbers are significant. The number 33.2 has three
significant figures because all of the digits present are non-zero.
• Zeros between two non0-zero digits are significant. 2051has four
significant figures. The zero is between 2 and 5.
• Leading zeros are not significant. They are nothing more than
place holders, The number 0.54 has only two significant figures.
All of the zeros are leading.
• Trailing zeros to the right of the decimal are significant.
4. • Trailing zeros in a whole number with the decimal shown are significant.
• Trailing zeros in a whole number with no decimal shown are not significant.
• For a number in scientific notation : N × 10x
5. Error is defined as the numerical difference between a
measured value and the absolute or true value of an analytical
determination.
The absolute or true value of a quantity is, however, never
unknown. All that we can use is only an accepted value.
The error in a measured quantity may be represented either as
absolute error or relative error .
Errors
6. Absolute error :The absolute error E, in a measurement is expressed
as
E = xi – xt
where xi is the measured value and xt is the true (accepted) value
for the given measurement.
Relative error : The relative error in a measurement is expressed as
Er = xi - xt
xt
Absolute error and Relative Error
7. Error
Determinate errors or
Systematic errors
Indeterminate errors or
Random errors
• Instrument errors
• Method errors
• Personal errors
Classification of errors
8. Determinate Errors
• Have a definite source
• Determinate error is generally unidirectional with respect to true
value and thus makes the measured value either low or higher
than the true value.
• Reproducible
• Predicted by an expert analyst
• These errors can be either avoided or corrected
9. Determinate errors are of three types : instrument errors, method errors and
personal errors.
Instrument Errors
• These errors arise from imperfections in measuring devices.
• For instance, measuring devices such as pipettes, burettes, measuring
cylinders, measuring flasks etc. contain volumes that are different from
those indicated by their graduations
10. The reasons for these differences are :
1. The use of glassware at a temperature which is significantly
different from the temperature at which the glassware was
calibrated.
2. Distortions in the walls of the container due to heating while
drying the glassware
3. Errors in the original calibration
4. Contamination of the inner surfaces of the containers
11. Instruments powered by electricity are very much prone to
determinate errors because of the following reasons :
• Fall in voltage of battery operated instruments.
• Increased resistance in circuits due to unclean electrical contacts.
• Effect of temperature on resistors and standard cells.
• Currents induced from 220V power lines.
These errors can be easily detected and corrected.
12. Method Errors
These errors arise from the non ideal behavior of reagents and
reactions involved in a given analysis.
The non ideality originates from :
• The slowness of the reactions
• Incompleteness of reactions.
• Instability of reactants
• Non-specificity of reagents .
• Occurrence of side reactions which interfere with the main
process of measurement.
Since theses errors are inherent in the method, they cannot be
easily detected and corrected.
13. Personal Errors
• These errors arise from erratic personal judgement, as also from
prejudice or bias.
• Many experimental measurements such as the estimation of the
position of the pointer between two scale divisions , judgement of
the color of the solution at the end point of a titration, judgement of
the level of a liquid with respect to a graduation on a burette or a
pipette, are sources of personal errors.
• These errors would vary from person to person and can be reduced
to a minimum by experience and careful physical manipulation
14. Determinate errors are further classified into constant errors
and proportional errors
Determinate Errors
Constant Errors Proportional Errors
15. Constant Errors
• The magnitude of a constant error is independent of the size of the
sample or the size of the quantity that is being measured.
• It is also independent of the concentration of the substance being
analyzed.
• For e.g. in volumetric analysis, the excess of the titrant that has to be
added to bring about a change in color at the end point remains the
same whether we titrate 10 ml or 20 ml or 25 ml of the solution.
• Constant errors would become more serious as we decrease the size of
the quantity being measured.
• The effect of a constant error can be reduced to a minimum by
increasing the size of the sample to a maximum within permissible
limits
16. Proportional Errors
• It arises due to the presence of interfering impurities in the
sample.
• The magnitude of such an error depends upon the fraction of the
impurity and is independent of the size of the sample.
17. Correction of Determinate
Errors
• The determinate instrument errors are detected and corrected by
periodic calibration of the instruments.
• The determinate personal errors can be reduced to a minimum by
care and self-discipline. The most essential requisite of avoiding
personal errors is to fight against bias.
• The determinate method errors are rather difficult to detect. The
following procedures are suggested for the identification and
compensation of method errors.
18. 1. Analysis of standard samples : Method errors can be detected by
carrying out the analysis of a standard sample prepared in such a way
that its composition is exactly the same as that of the material under
test.
2. Independent Analysis : A dependable procedure for detecting
method errors consists in carrying out parallel analysis of the sample
by another independent method of established reliability.
3. Blank determination : Blank determination in which all the steps
involved in the analysis are carried out in the absence of the sample in
exactly the same fashion is quite useful for exposing method errors
which are due to contaminations of the reagents and glass vessels
employed for the analysis.
19. Indeterminate errors
• These errors arise from uncertainties which are inevitably
associated with every physical or chemical measurement.
• These are random or accidental errors whose sources, though
many cannot be positively identified.
• As a result of these errors, the data from replicate
measurements fluctuate randomly around the mean of the set.
20. Fluctuation of data from the mean in replicate measurements
• It is evident from these curves that most frequently the deviation
from the mean is very small.
• It is also clear that there is almost equal probability of positive and
negative errors with the result that overall magnitude of the
indeterminate errors become almost insignificant.
21. Precision
• The degree of agreement between two or more replicate
measurements made on a sample in an identical manner, i.e., exactly
in the same fashion, is known as the precision of the measurement.
• If we make a large number of observations of a single quantity and
then plot the number of times a given value of the quantity itself, we
obtain a curve of the type given below. This is known as error
distribution curve.
22. • These curves have two useful qualitative features, viz., the height of
the peak of the distribution curve and the spread of the distribution
curve(dispersion)
• The precision of a set of measurements is judged from the
dispersion, i.e. the spread of the error distribution curve.
• The lesser the spread, the greater is the precision of the of the
measurements.
Error distribution curve
23. ACCURACY
• Accuracy is defined as the closeness of a measurement or a
set of measurements to the true or accepted value.
• Accuracy is expressed in terms of absolute error and relative
error.
24. Difference between
Accuracy and Precision
• Accuracy - measure of the agreement between an experimental result
and the true value of a given quantity.
• Precision - measures the agreement between several experimental
results obtained for the same quantity under identical
conditions.Precision can be determined by replicate measurements of
the same quantity.
• Accuracy can never be determined exactly because it involves the use of
absolute or true value of the quantity being measured which is never
known.
25. • Accuracy is expressed in terms of relative error or absolute
error whereas precision is expressed in terms of various
types of deviations from the mean.
• The error distribution curve for a less precise set of
measurements differs from that of a more precise set with
respect to its scatter or spread or dispersion; the spread
being more for a less precise set of measurements .
26. Error distribution curve for less accurate and
more accurate sets of results
Characteristics of less precise and more precise result