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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Propagation of incertitude - specific example [duplicate]

I am setting up an experiment, where I know the force and the incertitude (delta) of that force. However, I need to graph the logarithm of that force with the incertitude of the log. Can someone help ...
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16 views

A way to treat uncertainty in intensity measurement

I did an experiment to prove the inverse square law but don't know if my idea to calculate the error is correct. The relationship is $I=const*r^{n}$ with n=-2, we had a computer software to read the ...
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Thermistor calibration - estimation of number of reference temperature points needed

A thermistor changes resistance with the temperature in a non-linear way and follows the exponential Arrhenius equation. Two reference points, ice slush water and boiling water, are used for ...
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37 views

Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
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33 views

Simple question relating to physics prac reports

I am writing a physics practical report relating to the elasticity of materials relating to their momentum in a collision. I have values for the elasticities that are all within 2% of each other but I ...
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11 views

How to understand the uncertainty of quoted value of cosmic black body radiation?

Geiner's Quantum Mechanics - An Introduction quotes a alue of cosmic black body radiation, "$2.65 \pm 0.09 K$". How to understand this uncertainty? I have undergraduate mathematics degree and are ...
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9 views

Chi Square Minimization [migrated]

In my data analysis I've found that my $\chi^2$ is turning out to be very small $\sim10^{-3}$. But this can't be true, for the errors in the fitting variables themselves are of the order of ...
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2answers
45 views

Error calculation in parallel resistances

This is the question: There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination. According to what I've ...
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1answer
40 views

Propagation of uncertainty - which formula? [duplicate]

Can someone explain to me when do I use this formula ...and when do I use this one?
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117 views

Why is propagation of uncertainties quadratic rather than linear? [duplicate]

1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation: if $C = A+B$ or $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = ...
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2answers
58 views

How to calculate the error in measurments of derived quantities knowing the error in basic quantities?

I wonder how to calculate error of a derived quantity $z$ knowing the error of all quantities that $z$ depends on say $x$ and $y$. For example: Suppose I want to calculate the speed of a body ...
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35 views

Propagation of Error on Radius of a Circle

I need to calculate the radius of a circle and its error from the chord length $L$ and height $h$ from the chord to the circumference of the circle. I know the formula for $R$ to be $R = ...
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2answers
60 views

Significant figure rules [duplicate]

In a simple physics experiment, we take the average a few readings to reduce the random errors. I apply significant figure rules to these. Say we round off at each step: (8.0+9.0+10.0)/3 = 27.0/3 ...
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1answer
67 views

Measuring depth or height from sea level

How is the depth or height relative to sea level measured? Well, if it's near the ocean, it can be easily measured manually, but what if it is 100 km away from the sea? What method is used?
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1answer
21 views

Scale Factor on Error

I was gathering some data from the particle data group website and for many results it gives a value, an uncertainty and then a scale factor for the uncertainty. For instance, at here, where it gives ...
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1answer
146 views

Significant Figures in Physics

A string has linear density $10.0 \cdot 10^{-3} \, \mbox{kg/m}$ and is kept under a tension of 100 N. A sinusoidal transverse wave, with a wavelength of 0.30 m, is traveling in the positive direction ...
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2answers
77 views

Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How ...
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5answers
493 views

Why do the errors in a formula depend on how it's written?

Let there be an equation, let's say $V=IR$. Now when we write its error formula we write it as $$\frac{\Delta V}{V} = \frac{\Delta I}{I} + \frac{\Delta R}{R}.$$ Now let us take example values. For ...
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1answer
73 views

Combination of errors question [closed]

A resistance R is in series with an inductance L. At angular frequency ω the magnitude of the complex impedance Z of this combination is given by |Z|^2 = R^2 + (ωL)^2 . Find |Z|, and the error in |Z|, ...
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1answer
54 views

How do we find the accuracy of atomic clocks?

We say that atomic clocks are the most accurate clocks ever made, they may lose or gain $x$ seconds in $y$ years. How do we find this uncertainty because we do not have an ideal clock to compare with ...
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2answers
76 views

Weighted mean from data [closed]

Suppose we have 3 experimental groups measuring "x", they measure $$x_1=\mu_1\pm \sigma_1$$ $$x_2=\mu_2\pm \sigma_2$$ $$x_3=\mu_3\pm \sigma_3$$ In the 3 experiments, we have done N measurements of ...
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49 views

Propagation of uncertainty - proof that it is minimal

I am not really sure if this is the right SE community for this question, but, I swear, I haven't found any better. The problem is as follows: we have n distance sensors placed around a quickly ...
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1answer
153 views

What is the error in a ruler?

I'm having trouble understanding simple error analysis of a ruler. Suppose we have this ruler. There is a mark for every centimeter. The precision is half a centimeter. This should mean that the ...
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1answer
78 views

error propagation with different plus and min errors and data fitting

I am refreshing my memory on error propagation and data fitting (Levenberg-Marquadt). You have the absolute (measurement) error, the relative (measurement) error, the population/sample standard ...
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1answer
40 views

Why does the rule for multiplication/division take into consideration the no. of significant figures?

I've learned that the rule for multiplication, when taking into account the significant figures, is as follows: The final result should retain as many significant figures as there are in the original ...
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1answer
77 views

Error propagation from frequency to wavelength

I have measured a value for a frequency of $1.07 \times 10^{10} \pm 5 \times 10^7) \text{ Hz}$. Obviously it is very simple to find the wavelength from this frequency value, which I have (using ...
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27 views

Uncertainty in $T$ from measuring $nT$

Suppose I wish to obtain the period of an oscillation, $T$, so I measure the time for $n$ oscillations to obtain $nT$. Suppose I use a stopwatch, so the quantity $nT$ has an uncertainty of around 0.1 ...
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1answer
53 views

Is there uncertainity of position of the perfectly homogenous radiating body?

I heard the standard interpretation of Heisenberg Uncertainty Principle: Just the measurement affects the position of the body because always you want to see a body (=to measure the position), you ...
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1answer
40 views

Energy resolution of LHC Electromagnetic Calorimeter

So I am trying to get an estimate of the electromagnetic calorimeter resolution at LHCb, and I have found this online: But I have no idea of what it means. Can anyone explain what the last part ...
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1answer
53 views

Resolution of experiment is lower than the detector, so how to weigh the data?

I am attempting to create an atomic model based on data from a transmission electron microscope (TEM). Basically you shoot electrons at bunch of identical molecules stuck to a grid, and look at the ...
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2answers
79 views

Which error propagation equation to use for a function of 2 variables?

So I have been taught two formulas for error propagation: For $Z=A+B$, $\sigma_Z=\sqrt{(\sigma_A^2+\sigma_B^2)}$ and for Z=AB or Z=A/B ...
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1answer
62 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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1answer
80 views

How should I calculate uncertainty of measurement calculated as average of two measurements

I am measuring force with two channel transducer. Both channels (separately) of this transducer has been calibrated and I can calculate uncertainty of measurement for each of it. However I want to ...
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201 views

Percent error calculations dilemma

I have a set of experimental results for calculating g: 9.82 9.52 10.77 10.39 9.75 9.79 10.13 10.56 10.26 9.84 10.07 9.58 These were taken using a pendulum experiment. My dilemma is that, ...
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1answer
197 views

What is logical way to calculate percentage error?

I wish to know logic behind percentage error formula. Say, $A$ is measured or calculated quantity, $B$ is theoretical or known or benchmark quantity. Then, what should be the formula for percentage ...
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32 views

Maximum error of number of observations within several certain intervals – Accuracy of variable is known

I have carried out a series of measurements of different thermal comfort parameters from which I have calculated another variable called PMV. My data set consists of hourly measurements (and ...
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1answer
41 views

Numerical Error Propagation

I'm doing the common experiment of determining $ g $ by means of a simple pendulum, and I've decided to do so by measuring the period of the pendulum at variable lengths. I've had no problems ...
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1answer
308 views

Frictionless Cart on a Ramp (Experimental Design Question)

Question: Why is the calculated value for our final velocity higher than our predicted value? Since our prediction neglected air resistance and friction, shouldn't the velocity for the actual cart ...
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56 views

Uncertainty of measurement with goniometer

I got a goniometer with scale -90 to 90 degree. I use only 0 to 90 degree. One section of the scale has 1 degree. I read a value of $62^\circ$. What is the uncertainty of this measurement? I thougt ...
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27 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
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3answers
49 views

Can a piezo actuator have infinite resolution?

See here: http://www.omega.com/googlebase/product.html?pn=LD400-1&gclid=CjwKEAjw77OhBRCJ7Onfp_HNtwYSJACZqHAWVTfW1BO4RSfSVjz9P3Q4FoPTvZ2r3NIc2W1uEthVhBoCgUHw_wcB I don't think so. Do they just ...
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1answer
49 views

How can I find an error formula for density? [closed]

$${p} = \frac{4m}{πtd^2}$$ How can I find the error in this formula? I don't know where to begin. I know that I'm looking for the "partial derivative" of density to solve this, but that is a brand ...
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2answers
133 views

How should I quote errors when measurements are asymetrically clustered?

Suppose five people measure the length of a stick and report the following values 4.90cm 4.92cm 4.93cm 4.94cm 4.94cm In high school science we are told that in ...
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1answer
123 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
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1answer
34 views

Error limits when we have 4 lengths adding up and then finding its mean?

I have the following readings for length of a wire: 10.2 ± 0.1 cm 10.3 ± 0.1 cm 10.1 ± 0.1 cm 10.2 ± 0.1 cm Now, when I find out the mean value, I get: (10.2 ± 0.1 + 10.3 ± 0.1 + 10.1 ± 0.1 + ...
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44 views

What is the error on measuring the phase of a sine wave?

Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t) = 1 + A \sin(\omega t+\phi)$$ where $A < 1$. I have measured this wave N times, and we can assume these ...
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1answer
58 views

About $\chi^2_\text{adjusted}$ [closed]

I am reading "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by J. R.Taylor", and I read the following formula in an exercise: ...
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1answer
235 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
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164 views

Combining ±% with ±dB in measurement uncertainty

Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the ...
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78 views

Background subtraction for a signal ans Errors Analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...