Questions tagged [error-analysis]

Techniques and methods for computing, estimating, or placing bounds on the errors of expressions (formulas) based on knowledge of error distributions, error intervals or bounds of variables and parameters entering those expressions, and of methods used in the computations.

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38 views

How can I propagate uncertainties with different measurement units? [closed]

I would like to know how I should proceed to solve this problem: I measure with a caliber ($\Delta L = \pm 0.1\ \mathrm{mm}$) the dimensions of the section of a plank and result is $a = 1.2\ \...
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1answer
30 views

Significant Figures in functions

How to extend the idea of significant figures to operations like $\sin\theta$, $\log x$, $\sqrt{x}$, $\cos^{-1} x$, $e^x$ etc. Is there a general rule or method to find/define the no. of significant ...
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1answer
51 views

About significant figures and π [closed]

If I have to find 2.00*π, how many digits of pi must I take? 3 or 4? (2.00 has 3 significant figures). According to my textbook you're supposed to take a certain amount of digits of pi. I just don't ...
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Model fit error pinching

I am performing a model function fit, $f=f(x,a,b)$, with the two parameters $\left\{a,b\right\}$ to be determined from the best fit to a set of data. In my determination of the resulting $1 \sigma$ ...
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1answer
28 views

How is the root-mean-square error related to the confidence interval?

If the car's speed is calculated as V = 100 km/s, and the RMSE of V is 20 km/s. Does that mean V = 100 +/- 10 km/s, or V = 100 +/- 20 km/s?
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Bell Inequality Experimental Error Term

I'm doing an experiment using entangled photons to try and breach Bell's inequality. We're working out a I'm following this paper but am a little confused on how to calculate the error term given. ...
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1answer
66 views

How should I treat background radiation in an experiment?

I am performing an experiment to verify the inverse-square law for the intensity of a beam of $\gamma$ rays emitted by a sample of $^{60}\text{Co}$. The set-up is as follows: A Geiger-Müller tube ...
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Error Analysis due to Voltmeter Constraints [migrated]

I got a situation: at the moment I am unable to access both channels for Keithley 2182A nanovoltmeter using LabVIEW. However, for some odd reason, while I cannot access the channels at once, LabVIEW ...
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Discrepancy between upper-lower bound method and uncertainty propagation law

Let $X+\delta X$ denote a value $X$ with corresponding uncertainty in measurement of $\delta X$. According to the uncertainty propagation law, for the uncertainty concerning addition of terms, for ...
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Uncertainty of set of data

Suppose I measure the distance between two objects for three trials. The two objects then get farther away, and I measure the distance between them again for three trials. I repeat this for 3 more ...
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1answer
47 views

If a device's uncertainty for measuring time is $ 10^{-4} $, what happens to the uncertainty when the experimental value is squared?

In a case where the device's uncertainty is found to be $ 10^{-4} $. As it is a device that measures a time interval; when squaring the experimentally obtained value, what should one do with the ...
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1answer
48 views

Calculating combined errors

I am trying to learn to combine errors, but I am confused on how to calculate it once I string it all together into my equation. The equation is given by $$ y = A + (n - n_1) \cdot \frac{B - A}{n_2 - ...
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1answer
38 views

Error propagation biot savart law [closed]

How do I calculate the error in the magnetic field (B) using the error propagation techniques? The first picture is the formula and the second picture is the error calculation using the rules. I feel ...
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2answers
49 views

Calculating errors based on other variables

I am trying to calculate the mass and respective error of a star in kg. I have the numbers in units of $M_{Sun}$,in the form $M_{star}=(a\pm b)$ $M_{Sun}$. Given that I have the mass (with error) of ...
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1answer
54 views

Uncertainty propagation through a twice-weighted average

I am collecting the intensity of radiation as a function of wavelength. I want to take this data and average it so that I can have an average intensity for a spectral band. In my average, I want to ...
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2answers
49 views

Propagation of error for difference of values

I think there is a simple answer out there but I have hit a silly mental block. Say I have two values, each with their own error (precision): $845.9 \pm 0.3, 845.6 \pm 0.3$ Now, I understand that ...
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1answer
26 views

Are the measurement outcomes of an observable gaussian distributed?

Suppose in an experiment we perform $n$ independent measurements to find the true value of an observable $X$. Let the outcomes of $n$ measurement are denoted by $x_1,x_2,...x_n$. If $n$ is ...
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2answers
59 views

Propagating uncertainty in logarithmic calculation

I have a calculation using the following pseudo-formula: $ y = -ln(X/X_o)$ where both $X$ and $X_o$ have an associated error with them. I have propagated the error out simply using: $ \delta y = y\...
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2answers
42 views

Properly reporting instrument readings

As a first approximation, the uncertainty ($\delta X$) associated to a mensurand can be expressed as $\delta X= \Delta X / 2$ with $\Delta x$ being the resolution of the instrument. There is also a ...
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25 views

Error estimation for field theories

I am looking for resources on error estimation for field theories, both the error due to perturbation theory and measurement error. In other words, consider a field theory of a field $\phi$, with some ...
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1answer
21 views

Dividing absolute uncertainties for a range of values

I have a set of measurements for displacement and time. The absolute uncertainties for them are $\pm 0.005$m and $\pm 0.0167$seconds respectively. How do I correctly find the uncertainties for ...
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2answers
39 views

Calculating errors from given graphs

In a recent experiment, I have found the viscosity of glycerol by measuring the time it took for steel balls of measured density and radius to fall a certain distance in the liquid. Now, I need to ...
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27 views

Combining errors of measurements where one is a quantity the other is a percentage

I'm still very new to physics and i am a bit stuck on this one as its the first time i've seen error margins with % rather than actual quantities. Say i have two measurements with margins of errors: ...
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1answer
59 views

Should the implied uncertainty of a measurement be ±½ or ±1 of its least significant figure?

I've seen conflicting statements on whether the implied uncertainty of a measurement should be interpreted to be ±½ or ±1 of its least significant figure. Wikipedia goes with the ±½ convention: ...
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Why is $c$ and $h$ not constant in this equation? [closed]

From the equation: $$(mc^2)^2+(cp)^2 = E^2$$ When rest mass = 0 we get $p = E/c \approx E = p\cdot c$ Looking specifically at photons (zero mass): Granted that c remains constant, any change in E ...
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Why do different operations on significant digits give different values?

For example, if I add 2.50 five times, I get 12.50, keeping the number of decimals. However, if I multiply 2.50 by 5, I get 12.5. Why is this? Which rule should take precedence, and why?
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Why is a leading digit not counted as a significant figure if it is a 1?

Reading the book Schaum's Outline of Engineering Mechanics: Statics I came across something that makes no sense to me considering the subject of significant figures: I have searched and saw that ...
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1answer
26 views

Statistical and systematic error

In this paper, but in many others too, we see a result presented as $$ ... = 16.84\pm0.16(stat)\pm0.20(syst).$$ How are these two errors calculated? Is there a single algorithm to calculate these ...
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1answer
30 views

Error propagation with measured value zero

So, in our experiment, we measured the optical rotation of a compound with a polarimeter, and then we have to calculate the specific rotation and the error in calculating the specific rotation. I am ...
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1answer
83 views

Significant Figures and Uncertainty

Check the figure: As you can see from the figure, the pencil has 5.65 cm length with 0.05 cm uncertainty. We simply could say the length has 3 significant figures considering 5 and 6 are known digits ...
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1answer
43 views

Why are error bars used instead of error blobs or error rectangles?

In reporting experimental results, it is common to use error bars to communicate uncertainty in measurement of the quantity represented by the y-axis. But, usually, there would also be uncertainty in ...
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How long should I record the data of walking acceleration for FFT analysis?

Seems there is no apparent frequency of walking activity (it should be approximately close to 2 Hz) Is it because the time of the data is too short? Here is my csv file:enter link description here
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Uncertainty principle and meaning of particle's position

Suppose we have a particle and a detector. The detector will detect electron position not in a sharp peak but according Heisenberg principle in a peak with a deviation. But what that deviation ...
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1answer
37 views

Limits to the precision of quantum measurements

When measuring position the Compton wavelength is believed to be a limit on the precision of the result. If we shine light of a too high frequency on the particle then we will see particle creation ...
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2answers
40 views

Errors in measuring devices

I have a question regarding what we mean when we report the error in any measurement. Let's say I have a measuring scale which has markings in mm. Therefore any measurement I make has a limit on the ...
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1answer
36 views

Absolute Error in dB in a Measurement

I was reading this material about doing measurements and I have seen this expression for the absolute error in dB: $$a_x\text{(dB)}=20\log_{10}\left(1+\frac{a_x\text{(%)}}{100}\right) $$ My question ...
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How many significant figures should be used in an answer?

For an answer to a problem in significant figures, should the number of significant figures in the answer be based on the term with the least number of significant figures in the prompt? Just as an ...
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3answers
2k views

Better method to measure the time period of a pendulum

My physics textbook states that in measuring the time period of a pendulum it is advised to measure the time between consecutive passage though the mean position in the same direction. This results in ...
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2answers
39 views

Calculating uncertainty in a fitted model

I am working on a project that requires the measurement of the Verdet constant of a material by observing a phase shift in the cosine squared model provided by Malus's law. I have recorded the ...
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22 views

What does it mean by (±20%) in sensitivity of a pressure sensor?

Sensitivity: (±20%) 15.5 pC/psi (225 pC/bar) this the sensitivity rating of a pressure sensor. what does it mean by (±20%).
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26 views

How to find average uncertainty for a set of results?

I have determined multiple values for the refractive index of a material, each with their own uncertainty. If I find the average refractive index, how do I find its uncertainty? Would I find the ...
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1answer
107 views

Help with calculating uncertainty of refractive index for Michelson Interferometer?

I need help with calculating the uncertainty of the refractive index of air which has been obtained by the equation in this document: $$n_{\text{air,atm}}=(\frac{N}{P/P_{\text{atm}}})(\frac{\lambda}{...
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1answer
49 views

How to combine several dependent predictions and get the best estimate?

I want to predict the value of some physical quantity $P$ at a time $t$ using actual measurements of $P$ acquired before and after $t$. The formula I use for making these predictions is: $$\hat{P}_{t}...
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30 views

Clarification on error and uncertainty propagation

This is a purely fictional example: suppose I want to find the voltage drop across a resistor $R$ where a current $I$ flows. My resistance supplier established a tolerance of 5% for $R$, so I know ...
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1answer
150 views

Uncertainty in measurements with a ruler,

I am using a 30 cm ruler with a resolution of 0.1cm (1mm). I measure the length of a side of a cube with sharp edges. I keep the ruler against the side of the cube and take two readings from the ruler....
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12 views

Estimating error in measurements

Suppose I have a series of measurements $(X_i)_{i=1,\dots,n}$ and I compute the mean $\bar{X} = n^{-1} \sum X_i$. For each measurement I represent the result as the true value plus an error via $X_i = ...
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Significant number determination

Expressing magnutitudes with units and significant numbers which reflect the sensitivity of our measurement devices seems to be important in physics. When adding/ subtracting two numbers we report the ...
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21 views

Help with Uncertainties (Cassy Lab software)?

Hi I've done an experiment using this software called Cassy Lab. I have all my data and I have done all the calculations I needed to do. However I am confused about the uncertainties. All the ...
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1answer
52 views

Anomalous magnetic moment [closed]

I have the two values of the anomalous magnetic moments: $$ a_{\mu}^{SM}=(1 165 917 760 \pm 662)\cdot 10^{-12} \\ a_{\mu}^{exp}=(1 165 920 910 \pm 630) \cdot 10^{-12} $$ Where the first is the ...
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5answers
10k views

How exactly do you avoid fooling yourself?

In cargo cult science Feynman writes: "Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a ...

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