Error And Error Analysis
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it. In doing this it is crucial to understand that all measurements of physical quantities are subject to uncertainties. It is never possible to measure anything exactly. It is good, of course, to make error propagation the error as small as possible but it is always there. And in order
Percent Error
to draw valid conclusions the error must be indicated and dealt with properly. Take the measurement of a person's height as an error analysis equation example. Assuming that her height has been determined to be 5' 8", how accurate is our result? Well, the height of a person depends on how straight she stands, whether she just got up (most error analysis physics people are slightly taller when getting up from a long rest in horizontal position), whether she has her shoes on, and how long her hair is and how it is made up. These inaccuracies could all be called errors of definition. A quantity such as height is not exactly defined without specifying many other circumstances. Even if you could precisely specify the "circumstances," your result would still have an error associated
Error Analysis Chemistry
with it. The scale you are using is of limited accuracy; when you read the scale, you may have to estimate a fraction between the marks on the scale, etc. If the result of a measurement is to have meaning it cannot consist of the measured value alone. An indication of how accurate the result is must be included also. Indeed, typically more effort is required to determine the error or uncertainty in a measurement than to perform the measurement itself. Thus, the result of any physical measurement has two essential components: (1) A numerical value (in a specified system of units) giving the best estimate possible of the quantity measured, and (2) the degree of uncertainty associated with this estimated value. For example, a measurement of the width of a table would yield a result such as 95.3 +/- 0.1 cm. Significant Figures The significant figures of a (measured or calculated) quantity are the meaningful digits in it. There are conventions which you should learn and follow for how to express numbers so as to properly indicate their significant figures. Any digit that is not zero is significant. Thus 549 has three significant figures and 1.892 has four significant figures. Zeros between non zero digits are significant. Thus 4023 has fo
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Error Analysis Language
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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 = http://sciencefair.math.iit.edu/writing/error/ 100 x (Observed- Expected)/Expected Observed = Average of experimental values observed Expected = The value that 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 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 error analysis (see 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 error and error battery 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 co
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