Experimental Error Analysis
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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 of microscopy Solutions & dilutions Protein rough experiment error assays Spectrophotometry Fractionation & centrifugation Radioisotopes and detection Error Analysis and Significant measurement error analysis Figures Errors using inadequate data are much less than those using no data at all. C. experimental error definition Babbage] No measurement of a physical quantity can be entirely accurate. It is important to know, therefore, just how much the measured value is likely to deviate from the
Error Analysis Chemistry
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 of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated experimental error formula 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 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement i
purpose of this section is to explain how and why the results deviate from the expectations. Error analysis should include a calculation of how much the results vary from expectations. This can be done by calculating the percent error observed in the experiment. Percent Error = experimental error examples 100 x (Observed- Expected)/Expected Observed = Average of experimental values observed Expected = The value that
Types Of Experimental Error
was expected based on hypothesis The error analysis should then mention sources of error that explain why your results and your expectations differ.
Sources Of Experimental Error
Sources of error must be specific. "Manual error" or "human error" are not acceptable sources of error as they do not specify exactly what is causing the variations. Instead, one must discuss the systematic errors in the procedure (see http://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html below) to explain such sources of error in a more rigorous way. Once you have identified the sources of error, you must explain how they affected your results. Did they make your experimental values increase or decrease. Why? One can classify these source of error into one of two types: 1) systematic error, and 2) random error. Systematic Error Systematic errors result from flaws in the procedure. Consider the Battery testing experiment where the lifetime of a battery http://sciencefair.math.iit.edu/writing/error/ is determined by measuring the amount of time it takes for the battery to die. A flaw in the procedure would be testing the batteries on different electronic devices in repeated trials. Because different devices take in different amounts of electricity, the measured time it would take for a battery to die would be different in each trial, resulting in error. Because systematic errors result from flaws inherent in the procedure, they can be eliminated by recognizing such flaws and correcting them in the future. Random Error Random errors result from our limitations in making measurements necessary for our experiment. All measuring instruments are limited by how precise they are. The precision of an instrument refers to the smallest difference between two quantities that the instrument can recognize. For example, the smallest markings on a normal metric ruler are separated by 1mm. This means that the length of an object can be measured accurately only to within 1mm. The true length of the object might vary by almost as much as 1mm. As a result, it is not possible to determine with certainty the exact length of the object. Another source of random error relates to how easily the measurement can be made. Suppose you are trying to determine the pH of a solution using pH paper. The pH of the solution can be determined by looking at the color of the pap
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 http://www.webassign.net/question_assets/unccolphysmechl1/measurements/manual.html associated with a measurement result is often called uncertainty analysis or error analysis. The complete statement of a measured value should include an estimate of the level of confidence associated with the value. Properly reporting an experimental result along with its uncertainty allows other people to make judgments about the quality of the experiment, and it facilitates meaningful comparisons with other similar experimental error values or a theoretical prediction. Without an uncertainty estimate, it is 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 of experimental error we define what is being measured. While we may never know this true value exactly, we attempt 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 balanc
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