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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Proper significant digits in terms of a characteristic scale

Suppose I have a defined quantity in a paper $$g = 20\ \mathrm{meV}$$ and I wish to express the following equivalence (where $k_{B}$ is the Boltzmann constant which easily has more than 3-digit ...
0
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0answers
18 views

error calculation with a variable error

I have to calculate the error on the following quantity: $$f(\epsilon^M,\epsilon^S)= \sqrt{ \frac{1}{N}\sum_{i=1}^N (\log{\epsilon_i^M} - \log{\epsilon_i^S})^2 } $$ Usually I would use this standard ...
2
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4answers
83 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
1
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3answers
131 views

Is it correct to calculate the propagation of error in this way? [closed]

I conducted an experiment and measured the values of $R$ and $H$ to calculate $v_i$. The equation used is: $$v_i=\sqrt{{gR^2}\over{2H}}$$. My average values ($v_i$ is calculated only for the average ...
0
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1answer
62 views

What does error order $O(t^2)$ mean? [closed]

What does it mean if something is $O(t^2)$? And more importantly, how would I check for this relationship? I thought it meant error proportional to $t^2$, and that this could be tested by plotting a ...
2
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1answer
102 views

Why do length measurements apparently have zero uncertainty?

In order to estimate the length $L$ of an object the distance from its edges to the $0$ of a graded ruler are measured. Assume this object has its edges at $x$ and $y$ (mean values) with standard ...
3
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3answers
76 views

Why are significant figure rules in Multiplication/Division different than in Addition/Subtraction?

I've never understood specifically why this is. Here's what I mean. In Addition/Subtraction, what matters are the digits after the decimal point. So for example: 1.689 + 4.3 = ...
0
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1answer
43 views

Precision of the edge of a cube versus the volume of a cube [closed]

The edge of a cube was measured with 1% precision. How is the precision of the volume of same cube calculated on the basis this measurement? Is it true that precision of the measurement would be 3%?
0
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1answer
48 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
0
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1answer
45 views

The confusion of fractional error calculation

I need to find the focal length of a lens by using equation 1/u + 1/v=1/f I have: u= 50+-3 mm v= 200+-5 mm I calculate the value of f as 40mm. Now i need to find the uncertainty in this value. ...
6
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1answer
1k views

The uncertainty of a metre ruler?

I have been taught that the uncertainty in the measurement of a metre ruler is +-1 mm. However , I was also taught that the uncertainty is half of the smallest division in the measuring instrument. ...
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2answers
46 views

Error propagation without analytical expression

I have an algorithm $f$ that takes two inputs $x,y$ and gives one output. I say algorithm because I don't have the analytical expression for $f(x,y)$ (it's a black box in a computer, surely a ...
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votes
1answer
84 views

error propagation of a quantity [closed]

I have $e =$ 0.015 $\pm$ 0.005. How would I use error of propagation to calculate the uncertainty on $$ \frac{1}{( 1 - e^2)^{\frac{1}{8}} } $$ EDIT Since the question was put on hold then I will ...
0
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0answers
26 views

Systematic error of constant speed

Given a constant unknown speed $m$ and $n$ data samples of (position, time). Performing a linear regression yields $y = mx + c$, and a statistical error on $m$ and $c$. I already have this values. ...
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0answers
19 views

Calculating the error with Cramer's Rule

I am trying to calculate the error in the function $A=\frac{\det{A_1}}{det{A}}=\frac{y_1^{'}\alpha_2-y_2^{'}\alpha_1}{y_1\alpha_2-y_2\alpha_1}$ but unfortunately every method I attempt is giving me an ...
2
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4answers
61 views

Propagation of uncertainties

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...
3
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1answer
97 views

Elementary graphical error analysis

Suppose you analyze experimantal data with pencil and piece of paper, one simple method is to plot the data in a linearized way with error bars. Suppose you are interested in the slope of this linear ...
0
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1answer
62 views

How can we calculate statistical uncertainty on number between 0 and 1? [closed]

Lets suppose I have zero events in data. And Monte Carlo predicts 0.5 events. If I take square root of 0.5 to report statistical uncertainty on MC prediction, it comes out to be $\pm0.707$. This means ...
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0answers
34 views

Position from acceleration, or acceleration from position, to track an object moving the speed of sound

I'm working on a project that involves tracing the motion of a fast-moving object (approx the speed of sound) through a fairly defined trajectory. Would it be more accurate to measure the position of ...
0
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1answer
47 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
1
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1answer
30 views

Error propagation rounding [duplicate]

hope I am right in this section. I am unsure with error propagation. When calculation the error in a titration, many errors has to be taken into account: Error in Glassware/ Error in Balance/ Error ...
1
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2answers
110 views

Use of normal distribution in measurement error theory

When you study an experimental results you assume that normal distribution describe random error, specially in lab courses in K12. Is this true for every random component error treatment in physics? ...
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1answer
88 views

Error propagation with dependent variables

Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra where each channel with $f(y)$ counts has error $\sqrt{f(y)}$. ...
1
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1answer
27 views

Residuals are normally distributed

I did not know whether to post this question in the Physics or Statistics section of StackExchange, but the question involves the application of statistics to the analysis of experimental results. I ...
2
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1answer
36 views

Confirmation of Uncertainty in Indices New Formula? [closed]

I am experimenting relations with regards of the value with uncertainty raised to the $n$th power. I came up with this formula: $$(A\pm\alpha)^n=A^n\pm(A^{n-1}n\alpha)$$ Anyone here able to ...
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0answers
118 views

Calculating accuracy, error, full scale error, relative error and more in a specific case

I recently bought a O2(oxygen) sensor and I am trying to figure out the error in the percentage O2 (O2pct, unitless but in %) output value that it gives out. This error is not stated in its data ...
1
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1answer
46 views

Error in total counts

I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t. Later on I take the total count rate. (Number of counts/time: $N/t$) I'm supposed to find ...
3
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1answer
104 views

Inaccuracy at measuring gravity constant with Cavendish experiment

For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment. I set up a structure like the one suggested on this website: ...
5
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3answers
741 views

What does it mean to “bin” in a spectroscopy context

In the following online article http://www.star.le.ac.uk/~sav2/stats/a.html I see the word "bin" used, in relation to x-ray spectroscopy, both as a verb and as a noun (people both "bin" things and ...
0
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2answers
30 views

Filament lamp $(V,i)$ behavior between 0 and 1V

I was wondering why the behavior is more "chaotic" at 0~1V when compared to 2V+ (which is when it starts to glow).
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1answer
38 views

Error Propagation for Bound Variables

Say I'm trying to calculate the energy term Pressure*Volume based on measurement of P and V over many different trials. Given a constant temperature, pressure and volume are bound variables as PV=nRT ...
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1answer
115 views

Mass loss for Fusion energy? [closed]

I am thinking how you can estimate the mass loss of the fusion energy for 1 kWh. I think you cannot use Einstein's $E=mc^2$ to calculate the mass loss in the fusion reaction of the Sun. How can ...
0
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1answer
64 views

Why is drag neglected while dealing with kinematic problems?

Why is drag neglected while dealing with kinematic problems? While dealing with problems related to finding velocity, acceleration and other kinematic problems, it is mentioned to "neglect drag". ...
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0answers
45 views

Error propagation for products [duplicate]

Suppose you have two measured (independent) physical quantities $x$ and $y$ with relative errors $r_x := \frac{\delta x}{x}$ and $r_y := \frac{\delta y}{y}$, where $\delta x$ and $\delta y$ are the ...
1
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1answer
104 views

Error propagation for exponents

I was told that since $x^n = x\cdot x\cdot x \cdot \ldots \cdot x$ that the error is $$\delta f = f_{\text{best}} |n|\lbrace \frac {\delta_x}{f_{\text{best}}} \rbrace$$ where $f$ is a function of ...
0
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2answers
38 views

Which 'error' to choose random or absolute?

WIn the experiment, to measure the distance I used a ruler (the least digit is 0.5 cm) For each idep. variable step I repeated the experiment 10 times, and then calculated the standard deviation ...
0
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0answers
35 views

Basics of experimental error 'bookkeeping'

In scientific experiment, I know that it is very important to know the exact level of error contained in a result, but I am not sure what the correct procedure is to 'keep book' of these errors. I ...
2
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1answer
43 views

Measurements and errors

I've measured several values of $V$ and $I$ in a simple circuit to determine de value of a resistance $R$: $$R=\frac{V}{I}$$ I have a list of points $(V,I)$ with their corresponging error (from the ...
8
votes
3answers
321 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...
2
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3answers
70 views

Why aren't calculation results in error propagation at the center of the range?

We have two copper rods, with $L_1$ and $L_2$ as their lengths respectively, and we want to glue the two bars together, with glue that's infinitesimally thin. $$\begin{align} L_1 &= 20 ± 0.2\ ...
2
votes
2answers
560 views

error propagation with an integral

My question here is about how to determine the error of an integral given individual uncertainties in two parameters defining the function being integrated. I used a curve fitting function to ...
0
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3answers
69 views

Significant figures

How to calculate significant figures of a number? I got confuse as the number 28600 has 3 significant figure instead of 5. Anyone can explain?
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64 views

how to handle errors in this high-school experiment?

I'd like to conduct some measurements with my pupils in the high-school I'm teaching in, but I ran into some conceptual problems. I'd like to measure the (approximately constant) speed $v$ of an ...
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0answers
35 views

Error propagation log2

I have a quick question to report some numbers on an experiment. I made measurements of fluorescence in a titration of a chemical. The titrations were 1:2 serial dilutions so I report each ...
4
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2answers
381 views

Physical experiments - False positives

How is it made sure that something has been discovered, and not just noise? Is one discovery of something that is predicted considered to be enough (Higgs-particle)? What are the probabilities of a ...
6
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5answers
1k views

Number of significant figures

I am looking for an intuitive answer that will explain me why there are only two significant figures in say the number 1500. Also definition from wikipedia: The significant figures of a number ...
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4answers
65 views

Is there a maximum accuracy for positions in the universe?

I was thinking how, since an object in our universe can move from one position to another, it must have passed through all the positions between those two positions. (I am thinking it moved it a ...
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0answers
54 views

How can we calculate the standard deviation of multiple values with different uncertainties each?

For example, if I have a set of readings, like: 13.4 +/- 0.5 14.5 +/- 0.7 12.8 +/- 0.6 13.9 +/- 0.4 14.8 +/- 0.5 How do I calculate the standard deviation of ...
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1answer
75 views

Not direct/inverse proportion implies systematic error

We were doing error-analysis and my physics teacher said: A relationship between physical constants is either direct proportion or inverse proportion. If these are not true then there is a systematic ...
1
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1answer
66 views

# significant figures in calculations?

I was taught to use the same number of significant figures in my answer as the piece of data with the lowest number of significant figures, so I was a bit confused when the solutions manual for this ...