New answers tagged error-analysis
1
It depends a lot on the precision that you want to achieve on your measurement. As standard, it is considered that with 10 times that you run the operation it should be enough. But to know clearly the times that you need to run the operation, just check the standard deviation. With a few times, say 5, it is large but it goes down as you add more runs to the ...
3
Take its differential form :
$$\mathrm{d} \rho = \frac{1}{4/3 \pi r^3} \mathrm{d}m - \frac{m}{4\pi r^4}\mathrm{d}r$$
The greatest variation in $\rho$ will be achieved when all the terms add positively
$$\delta \rho =\frac{1}{4/3 \pi r^3} \delta m + \frac{m}{4\pi r^4}\delta r$$
Factor of $-3$ appears as matter of integration. Which you can recast into
...
0
You have to be careful to differentiate between uncorrelated and correlated (systematic) errors. Your first analysis is for uncorrelated errors in $h_1$ and $h_2$, e.g. measurement noise. The effects of uncorrelated errors add in quadrature as you have written since the resulting errors in $\Delta PE$ can either add or subtract. For the correlated error ...
1
The purpose of rounding your sig figs is so that you don't miscommunicate to other people the precision of your result. Intermediate results aren't going to be communicated to anyone else, so that reason for rounding doesn't apply to them. You don't want to round too much at intermediate steps, because rounding errors can accumulate.
Sometimes people will ...
3
Significant digits is a convention that only affects how you write numbers, not what the numbers actually are. So you only round when you are asked to drop down to a given number of significant digits - that is, at the end.
Think of it like this: there's a difference between a number, which is an abstract idea, and a written representation of a number. Some ...
0
For a linear regression fit of the form: $y=ax+b$, with $S_{yi}=S_i\neq const.$, then:
$$
a=\frac{\sum{\frac{1}{S_i^2}} \sum{\frac{x_iy_i}{S_i^2}} - \sum{\frac{x_i}{S_i^2}} \sum{\frac{y_i}{S_i^2}}} {\sum{\frac{1}{S_i^2}} \sum{\frac{x_i^2}{S_i^2}} - \left(\sum{\frac{x_i}{S_i^2}}\right)^2}
$$
with:
$$
S_a=\sqrt{\frac{\sum{\frac{1}{S_i^2}}} ...
1
You will want to first convert your current uncertainties $\delta i_c$ into uncertainties in $\log{i_c}$, $\delta(\log{i_c})$. You will need the uncertainties in the $x$ and $y$ values that you use in the fit in order to get the uncertainties in the fit parameters. Note that the uncertainty of the $\log$is not simply the $\log$ of the uncertainties.
Taylor ...
1
If your data has error bars for the $y$-axis, you could use a least-squares/$\chi^2$ technique to fit your model:
You have $\{x_i,y_i\pm\epsilon_i\}$ for $i=1,\ldots,N$ data. You want
to find $K_B$ and $I_c$ such that $y=f(k_B,I_C,x)$. Construct the function,
$$
\chi^2 = \sum_{i=1}^N\frac{(f(k_B,I_c,x_i)-y_i)^2}{\epsilon_i^2},
$$ and
minimize this ...
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