Quantify Experimental Error
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Overview Keeping a lab notebook Writing research papers Dimensions & units Using figures (graphs) Examples of graphs Experimental error Representing error Applying statistics Overview Principles
Experimental Error Examples
of microscopy Solutions & dilutions Protein assays Spectrophotometry Fractionation & experimental error formula centrifugation Radioisotopes and detection Error Analysis and Significant Figures Errors using inadequate data are much less
Experimental Error Examples Chemistry
than those using no data at all. C. Babbage] No measurement of a physical quantity can be entirely accurate. It is important to know, therefore, types of experimental error just how much the measured value is likely to deviate from the unknown, true, value of the quantity. The art of estimating these deviations should probably be called uncertainty analysis, but for historical reasons is referred to as error analysis. This document contains brief discussions about how errors are reported, the kinds sources of experimental error of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, concerned with the “percent error” exercises common in high school, where the student is content with calculating the deviation from some allegedly authoritative number. You might also be interested in our tutorial on using figures (Graphs). Significant figures Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.42
brothers, and 2 + 2 = 4. However, all measurements have some degree of uncertainty that may come from a variety of sources. The process of evaluating the uncertainty associated with a measurement result
Experimental Error Calculation
is often called uncertainty analysis or error analysis. The complete statement of a measured measurement and error analysis lab report value should include an estimate of the level of confidence associated with the value. Properly reporting an experimental result along
Sources Of Error In Physics
with its uncertainty allows other people to make judgments about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is http://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted. When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt http://www.webassign.net/question_assets/unccolphysmechl1/measurements/manual.html to find this ideal quantity to the best of our ability with the time and resources available. As we make measurements by different methods, or even when making multiple measurements using the same method, we may obtain slightly different results. So how do we report our findings for our best estimate of this elusive true value? The most common way to show the range of values that we believe includes the true value is: ( 1 ) measurement = (best estimate ± uncertainty) units Let's take an example. Suppose you want to find the mass of a gold ring that you would like to sell to a friend. You do not want to jeopardize your friendship, so you want to get an accurate mass of the ring in order to charge a fair market price. You estimate the mass to be between 10 and 20 grams from how heavy it feels in your hand, but this is not a very precise estimate. After some searching, you find an electronic balance that gives a mass reading of 17.43 grams. While this measurement is much more precise than the original estimate, how do you know that it is accurate, and how confident are you that
applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a https://en.wikipedia.org/wiki/Uncertainty_quantification head-on crash with another car: even if we exactly knew the speed, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense. Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are experimental error the most common approach to study problems in uncertainty quantification.[1][2][3] Contents 1 Sources of uncertainty 1.1 Aleatoric and epistemic uncertainty 2 Two types of uncertainty quantification problems 2.1 Forward uncertainty propagation 2.2 Inverse uncertainty quantification 2.2.1 Bias correction only 2.2.2 Parameter calibration only 2.2.3 Bias correction and parameter calibration 3 Selective methodologies for uncertainty quantification 3.1 Methodologies for forward uncertainty propagation 3.2 Methodologies experimental error examples for inverse uncertainty quantification 3.2.1 Frequentist 3.2.2 Bayesian 3.2.2.1 Modular Bayesian approach 3.2.2.2 Fully Bayesian approach 4 Known issues 5 See also 6 References 7 Further reading Sources of uncertainty[edit] Uncertainty can enter mathematical models and experimental measurements in various contexts. One way to categorize the sources of uncertainty is to consider:[4] Parameter uncertainty, which comes from the model parameters that are inputs to the computer model (mathematical model) but whose exact values are unknown to experimentalists and cannot be controlled in physical experiments, or whose values cannot be exactly inferred by statistical methods. Examples are the local free-fall acceleration in a falling object experiment, various material properties in a finite element analysis for engineering, and multiplier uncertainty in the context of macroeconomic policy optimization. Parametric variability, which comes from the variability of input variables of the model. For example, the dimensions of a work piece in a process of manufacture may not be exactly as designed and instructed, which would cause variability in its performance. Structural uncertainty, aka model inadequacy, model bias, or model discrepancy, which comes from the lack of knowledge of the underlying true physics.