Error Bars In Experimental Physics
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and Graphs phy124:error_and_uncertainty Table of Contents Uncertainty, Error and Graphs Uncertainty in measurements An inspirational message from 1600 for care in experimentation Notation Error Absolute Error Relative Error Random Error Systematic Error Propagation of Errors Obtaining error bars in experimental biology Values from Graphs An experiment with the simple pendulum: Things one
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would measure Estimate of error in the length of the string Error in the period Making a plot
Error Bars In Physics A Level
of our data Uncertainty, Error and Graphs Uncertainty in measurements In physics, as in every other experimental science, one cannot make any measurement without having some degree of uncertainty. A
How To Calculate Error Bars In Physics
proper experiment must report for each measured quantity both a “best” value and an uncertainty. Thus it is necessary to learn the techniques for estimating them. Although there are powerful formal tools for this, simple methods will suffice in this course. To a large extent, we emphasize a “common sense” approach based on asking ourselves just how much any measured uncertainty graph excel quantity in our experiments could be “off”. One could say that we occasionally use the concept of “best” value and its “uncertainty” in everyday speech, perhaps without even knowing it. Suppose a friend with a car at Stony Brook needs to pick up someone at JFK airport and doesn't know how far away it is or how long it will take to get there. You might have made this drive yourself (the “experiment”) and “measured” the distance and time, so you might respond, “Oh, it's 50 miles give or take a few, and it will take you one and a half hours give or take a half-hour or so, unless the traffic is awful, and then who knows?” What you'll learn to do in this course is to make such statements in a more precise form about real experimental data that you will collect and analyze. Semantics: It is better (and easier) to do physics when everyone taking part has the same meaning for each word being used. Words often confused, even by practicing scientists, are “uncertainty
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graphs | What to plot? | Examples ] Error and Uncertainty All readings, data, results or other numerical quantities taken from the real world by direct measurement or otherwise are subject to uncertainty. This is a consequence http://pfnicholls.com/physics/Uncertainty.html of not being able to measure anything exactly. Uncertainty cannot be avoided but it can https://en.wikipedia.org/wiki/Error_bar be reduced by using 'better' apparatus. The uncertainty on a measurement has to do with the precision or resolution of the measuring instrument. When results are analysed it is important to consider the affects of uncertainty in subsequent calculations involving the measured quantities. If you are unlucky (or careless) then your results will also be subject to errors. Errors are error bars mistakes in the readings that, had the experiment been done differently, been avoided. It is perfectly possible to take a measurement accurately and erroneously! Unfortunately it is not always possible to know when you are making an error (otherwise you wouldn't make it!) and so godd experimental technique has to able to guard against the affect of errors Types of Error: Human Error: Errors introduced by basic incompetence, mistakes in using the apparatus etc. Reduced error bars in by repeating the experiment several times and comparing results to those of other similar experiments, by ensuring results seem reasonable Systematic Error: Error introduced by poor calibration or zero point setting of instruments such as meters - this may cause instrumentation to always 'under read' or 'over read' a value by a fixed amount. Reduced by plotting graphs, the relationships between two quantities often depends on the way in which they change rather than their absolute values. A systematic error would manifest itself as an intercept on the y-axis other than that expected. In the A Level course this is most commonly experienced with micrometers (that don't read zero when nothing is between the jaws) and electrical meters that may not rest at zero Equipment Error: Error introduced by the mis-functioning of equipment. The only real check is to see if the results seem reasonable and 'make sense' ... take time to stop and think about what the instruments are telling you ... does it seem okay? Parallax Error: Error introduced by reading scales from the wrong angle i.e. any angle other than at right angles! Some meters have mirrors to help avoid parallax error but the only real way to avoid parallax error is to be aware of it Estimating uncertainty Estimating the uncertainty on a reading is an art that develops
error, or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a certain confidence interval (e.g., a 95% interval). These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text. Error bars can be used to compare visually two quantities if various other conditions hold. This can determine whether differences are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific papers in the experimental sciences are expected to include error bars on all graphs, though the practice differs somewhat between sciences, and each journal will have its own house style. It has also been shown that error bars can be used as a direct manipulation interface for controlling probabilistic algorithms for approximate computation.[1] Error bars can also be expressed in a plus-minus sign (±), plus the upper limit of the error and minus the lower limit of the error.[2] See also[edit] Box plot Confidence interval Graphs Model selection Significant figures References[edit] ^ Sarkar, A; Blackwell, A; Jamnik, M; Spott, M (2015). "Interaction with uncertainty in visualisations" (PDF). 17th Eurographics/IEEE VGTC Conference on Visualization, 2015. doi:10.2312/eurovisshort.20151138. ^ Brown, George W. (1982), "Standard Deviation, Standard Error: Which 'Standard' Should We Use?", American Journal of Diseases of Children, 136 (10): 937–941, doi:10.1001/archpedi.1982.03970460067015. This statistics-related article is a stub. You can help Wikipedia by expanding it. v t e Retrieved from "https://en.wikipedia.org/w/index.php?title=Error_bar&oldid=724045548" Categories: Statistical charts and diagramsStatistics stubsHidden categories: All stub articles Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaWikipedia sto