Experimental Error Combining
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can answer The best answers are voted up and rise to the top How to combine measurement error with statistic error up vote 10 down vote favorite 3 We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because error analysis physics of my reaction time. If I now measure, say 40, 41 and 39 seconds in three runs, I will also have standard deviation of 1. What is the total error then? Do I add them up, like so? $$\sqrt{1^2 + 0.1^2}$$ Or is it just the 1 and I discard the (systematic?) error of my reaction time? I wonder if I measure a huge number of times, the standard deviation should become tiny compared to my reaction time. Is the lower bound 0 or is it my reaction time with 0.1? measurement statistics error-analysis share|cite|improve this question edited Apr 9 '12 at 16:17 Qmechanic♦ 64.2k991242 asked Apr 9 '12 at 12:41 Martin Ueding 3,32221339 add a comment| 3 Answers 3 active oldest votes up vote 6 down vote accepted I think you're exercising an incorrect picture of statistics here - mixing the inputs and outputs. You are recording the result of a measurement, and the spread of these measurement values (we'll say they're normally distributed) is theoretically a consequence of all of the variation from all different sources. That is, every time you do it, the length of the string might
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About Us Learn more about Stack Overflow the company Business Learn more experimental error analysis about hiring developers or posting ads with us Physics Questions Tags Users Badges Unanswered Ask Question _ Physics Stack experimental error definition Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask http://physics.stackexchange.com/questions/23441/how-to-combine-measurement-error-with-statistic-error a question Anybody can answer The best answers are voted up and rise to the top How to combine the error of two independent measurements of the same quantity? up vote 4 down vote favorite 3 I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. http://physics.stackexchange.com/questions/23643/how-to-combine-the-error-of-two-independent-measurements-of-the-same-quantity $k$ is just the mean of $k_1$ and $k_2$. I thought that I would need to square-sum the errors together, like so: $$ \Delta k = \sqrt{(\Delta k_1)^2 + (\Delta k_2)^2} $$ But if I measure $k_n$ $n$ times, $\Delta k$ would become greater and greater, not smaller. So I need to divide the whole root by some power of $n$, but I am not sure whether $1/n$ or $1/\sqrt n$. Which is it? measurement statistics error-analysis share|cite|improve this question edited Apr 12 '12 at 8:20 Qmechanic♦ 64.2k991242 asked Apr 12 '12 at 8:02 Martin Ueding 3,32221339 More on measurements and errors: physics.stackexchange.com/q/23441/2451 and physics.stackexchange.com/q/23565/2451 –Qmechanic♦ Apr 12 '12 at 12:34 add a comment| 2 Answers 2 active oldest votes up vote 8 down vote accepted The formula you've specified $$ \Delta k = \sqrt{(\Delta k_1)^2 + (\Delta k_2)^2} $$ is the formula to obtain error of quantity $k$, as being dependent on $k_1$ and $k_2$ according to the following expression $$ k = k_1 + k_2.$$ Generally, to obtain experimental error of a dependent quantity (and the expression stated in your question),
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 assays Spectrophotometry Fractionation & centrifugation Radioisotopes and detection Error Analysis and Significant Figures Errors using http://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html inadequate data are much less 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, 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 experimental error 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 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). experimental error examples 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 in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero is significant,
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