Factors Of Experimental Error
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We're using the word "wrong" to emphasize a point. All experimental data is imperfect. Scientists know that their results always contain errors. However, one of their goals is to minimize errors, and to be aware of what the errors may be. Significant
Factors That Cause Experimental Error
digits is one way of keeping track of how much error there is in a measurement. sources of error in picket fence experiment Since they know that all results contain errors, scientists almost never give definite answers. They are far more likely to say: "it is likely experimental error formula that ..." or "it is probable that ..." than to give an exact answer. As a science student you too must be careful to learn how good your results are, and to report them in a way that indicates your
Experimental Error Examples
confidence in your answers. There are two kinds of experimental errors. Random Errors These errors are unpredictable. They are chance variations in the measurements over which you as experimenter have little or no control. There is just as great a chance that the measurement is too big as that it is too small. Since the errors are equally likely to be high as low, averaging a sufficiently large number of results will, in principle, reduce their effect. Systematic Errors These
Types Of Experimental Error
are errors caused by the way in which the experiment was conducted. In other words, they are caused by the design of the system. Systematic errors can not be eliminated by averaging In principle, they can always be eliminated by changing the way in which the experiment was done. In actual fact though, you may not even know that the error exists. Which of the following are characteristics of random errors? Check all that apply. a) doing several trials and finding the average will minimize them b) the observed results will usually be consistently too high, or too low c) proper design of the experiment can eliminate them d) there is no way to know what they are It is not easy to discuss the idea of systematic and random errors without referring to the procedure of an experiment. Here is a procedure for a simple experiment to measure the density of rubbing alcohol (iso-propanol). Materials: digital electronic balance that can be read to 0.01 g 100 mL graduated cylinder, marked every 1 mL iso-propanol Procedure: Find and record the mass of the empty, dry graduated cylinder. Fill the graduated cylinder about 3/4 full of the alcohol. Record the volume of the alcohol in the cylinder. Find and record the mass of the filled graduated cylinder Some possible random errors in this experiment Some possible systematic errors in this experiment slight vari
the measurement devices (hard to read scales, etc.) - Usually caused by poorly or miscalibrated instruments. - There are usually ways to experimental error vs human error determine or estimate. - Cannot reduce by repeated measurements, but
Experimental Error Examples Chemistry
can account for in some way. 3. Indeterminate (Random) Errors
- Natural variations in measurements. experimental error physics - May be result of operator bias, variation in experimental conditions, or other factors not easily accounted for. - May be minimized by repeated measurement and using an http://www.digipac.ca/chemical/sigfigs/experimental_errors.htm average value. Experimental results may be described in terms of precision and accuracy. Precision - relatively low indeterminate error. - reproducibility. - high precision means a number of readings or trials result in values close to the same number. Accuracy - relatively low determinate error. - close to a true value. Accurate and http://www.ahsd.org/science/stroyan/hphys/stats/meas_uncert_1.htm precise Precise but not accurate Reliability- a procedure is said to be reliable if it may be completed with a high degree of accuracy and precision. For most of our investigations we will be concerned with the precision of results. Experimental Data and Measures of Uncertainty Quantities that give some measure of experimental precision are Deviation (individual values) Average deviation Average Deviation of the Mean (Standard Average Deviation) Sample standard deviation (sometimes denoted as ) Standard error It is customary to report experimental results with an uncertainty in the following form Result = Average ± uncertainty The uncertainty is one of the measures of precision given above (a.d., A.D., s, or Sx). For our present cases we will use standard error and report results as Result = Average ± Sx This information is simply preliminary to analyses we will be performing on some sample data, and data we will collect in the future. The idea here is to give you the formulae that are uMathematica Wolfram|Alpha Appliance Enterprise Solutions Corporate Consulting Technical Services Wolfram|Alpha Business Solutions Products for Education Wolfram|Alpha Wolfram|Alpha Pro Problem Generator API Data http://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html Drop Mobile Apps Wolfram Cloud App Wolfram|Alpha for Mobile Wolfram|Alpha-Powered http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html Apps Services Paid Project Support Training Summer Programs All Products & Services » Technologies Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe. Computable experimental error Document Format Computation-powered interactive documents. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Natural Language Understanding System Knowledge-based broadly deployed natural language. Wolfram Data Framework Semantic framework for real-world data. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Knowledgebase Curated computable knowledge of experimental error powering Wolfram|Alpha. All Technologies » Solutions Engineering, R&D Aerospace & Defense Chemical Engineering Control Systems Electrical Engineering Image Processing Industrial Engineering Mechanical Engineering Operations Research More... Education All Solutions for Education Web & Software Authoring & Publishing Interface Development Software Engineering Web Development Finance, Statistics & Business Analysis Actuarial Sciences Bioinformatics Data Science Econometrics Financial Risk Management Statistics More... Sciences Astronomy Biology Chemistry More... Trends Internet of Things High-Performance Computing Hackathons All Solutions » Support & Learning Learning Wolfram Language Documentation Fast Introduction for Programmers Training Videos & Screencasts Wolfram Language Introductory Book Virtual Workshops Summer Programs Books Need Help? Support FAQ Wolfram Community Contact Support Premium Support Premier Service Technical Services All Support & Learning » Company About Company Background Wolfram Blog News Events Contact Us Work with Us Careers at Wolfram Internships Other Wolfram Language Jobs Initiatives Wolfram Foundation MathWorld Computer-Bas
of causes of random errors are: electronic noise in the circuit of an electrical instrument, irregular changes in the heat loss rate from a solar collector due to changes in the wind. Random errors often have a Gaussian normal distribution (see Fig. 2). In such cases statistical methods may be used to analyze the data. The mean m of a number of measurements of the same quantity is the best estimate of that quantity, and the standard deviation s of the measurements shows the accuracy of the estimate. The standard error of the estimate m is s/sqrt(n), where n is the number of measurements. Fig. 2. The Gaussian normal distribution. m = mean of measurements. s = standard deviation of measurements. 68% of the measurements lie in the interval m - s < x < m + s; 95% lie within m - 2s < x < m + 2s; and 99.7% lie within m - 3s < x < m + 3s. The precision of a measurement is how close a number of measurements of the same quantity agree with each other. The precision is limited by the random errors. It may usually be determined by repeating the measurements. Systematic Errors Systematic errors in experimental observations usually come from the measuring instruments. They may occur because: there is something wrong with the instrument or its data handling system, or because the instrument is wrongly used by the experimenter. Two types of systematic error can occur with instruments having a linear response: Offset or zero setting error in which the instrument does not read zero when the quantity to be measured is zero. Multiplier or scale factor error in which the instrument consistently reads changes in the quantity to be measured greater or less than the actual changes. These errors are shown in Fig. 1. Systematic errors also occur with non-linear instruments when the calibration of the instrument is not known correctly. Fig. 1. Systematic errors in a linear instrument (full line). Broken line shows response of an ideal instrument without error. Examples of systematic errors caused by the wrong use of instruments are: errors in measurements of t