Questions tagged [measurement-error]
Measurement error is the difference between a measured value of a quantity and its true value.
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Where are the difeferences between: ATE, MAE, SEM and TEM? [closed]
Where are the differences between Absolute Typical Error (ATE), Mean Absolute Error (MAE), Standard error of measurement (SEM), and Typical error of measurement (TEM)?
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Is there a standard measurement of 2-dimensional precision?
Suppose a gun is fired at the bullseye of a target a specific number of times.
Ignoring the accuracy (e.g. all the shots are well to the left and above the bullseye), is there a standard way of ...
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Bias results for mismeasurement of continuous confounders
Consider data generated from a model $Y = \alpha A + \beta U$, where $U$ is a confounder, i.e. $\langle A,U\rangle \neq 0$. We don't measure U, but rather a noisy version of it, $U' = U+\epsilon$, ...
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Gradient descent residual
I've implemented the gradient descent method for finding roots of a system of nonlinear equations and I am wondering how the residual is determined? Is the residual simply the Euclidean norm (2-norm) ...
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Occam's Razor: Commit to a hypothesis before vs. commit after seeing the data
In the section on Occam's Razor of the book "Understanding Machine Learning, S. Ben David et al." (its free online version here), the authors wrote:
if we commit to any hypothesis before ...
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Normalize data with a variance-shift in measurement-error to achieve high correlation with true underlying process?
I am discussing the question whether to normalize the data or not in the following setting:
I have a true time series
$$s_t = iid(0,\sigma_s^2)$$
however I only observe different $$\hat{s}_{t,i} = s_t ...
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Sampling error for proportion with finite population - which correction to use?
I am trying to calculate sampling error for a questionnaire that was answered by some of the participants in a program (say about . I want to calculate the sampling error for the proportion of the ...
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Classification error when estimating population size of rare phenomena
I need to understand how a particular statistical challenge has been formally recognised or is commonly described in literature, and what the best academic resources are that discuss it. Here's the ...
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Weighted least squares with measurment errors: how to get proper standard errors for coefficients?
If we have outcome variable as measurements with associated SD as form of measurement uncertainty and we want to incorporate the uncertainty information in linear regression model, what is the proper ...
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What is the optimal measuring time split for limited measuring time between signal+background and background in a Poisson counting experiment?
I’m trying to figure out the best split of time between measuring either background or signal+background in a counting experiment in the case where we have prior estimates for the signal and ...
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Estimating error rates from inter-rater reliability values
I have been tasked to approximate the error rate of a research procedure.
The only data I have available are reports which specify the number of targets (n), the number of raters (k) and give pairwise ...
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Scaling of Error Bars in Paired Measurements with an Unknown Signal
I'm grappling with a statistics problem related to the scaling of error bars, and I'm hoping to gain a clearer understanding.
Scenario:
I'm attempting to measure the spectrum of a sample. For the sake ...
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How to estimate the number of erroneous entries in a dataset?
Two researchers are tasked to independently collect a same set of data ($N$ observations) from a same set of subjects. For simplicity, let us assume they observe only one variable. After comparing ...
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Determine direction of bias with measurement error
We want to estimate the following population model:
$$y_i=\beta x_i+\epsilon_i$$
with $E[y_i]=E[x_i]=$ and $E[x_i\epsilon_i]=0$. We cannot observe $x_i$ directly, but we observe two variables $x_i^a$ ...
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How to model observation error of multiple entries on a single Likert-type item?
This is a hypothetical problem for me at the moment because (1) I have no such data and (2) often software provides a forced choice in these cases so I doubt it would be a problem if I conducted a ...
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Definition of Uncertainity
I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
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heteroscedastic uncertainty
I am majoring in economics and I am reading this paper by Crossley & Kennedy (2002). It discusses the reliability of self-assessed health status (that is "In general, would you say that your ...
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Understanding the Difference between Bernoulli Distribution and Binomial Distribution
In my recent study, I conducted 67 measurements and recorded 11 successful outcomes. Now, I am seeking clarification on the appropriate formulas to calculate the measurement error. Should I use the ...
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Is ceiling effect mitigated by standardisation, renorming or combining with other indicators?
I have a psychological test that consist of a set of binary items. It has a noticeable ceiling effect in the sum scores (essentially, a majority of participants get most items correct).
I also see ...
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Regression models with uncertainty as T-Distribution [duplicate]
Are there any distributions which represent uncertainty about $\hat y$ as a $t$ distribution.
In other words: $ p(y\mid x, ~\text{model}) \sim \mathbf T(\hat y, \text{df}, \sigma)$ where $\bf T$ is a ...
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BMI is calculated from two other measurements, so does it need adjusting for multiple comparisons?
If BMI is calculated from measures of patient height as well has weight, do statistical tests and resulting p values around BMI changes need adjusting for multiple comparisons? I.e. Two tests were ...
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Calculate the average of absolute values of a measurement with a measurement error
I have a few parameters; each is measured imprecisely with a known but unique random
measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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Understanding tensorflow calculation of MSE for output vector of N dimensions
Here is the code example with variable names guiding the process:
...
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Combining GUM Type A and Type B uncertainties
Assume $N$ measurements of the same parameter, i.e. a surface temperature $\vartheta_\mathrm{surf}$, were obtained using one single measuring chain (temperature sensor, cables, ADC ...).
Furthermore, ...
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Noise cancels but variance sums - contradiction?
I have been told both things with regard to e.g. summing noisy time series, to justify opposing expectations.
On the one hand, I have been told to expect that summing multiple noisy inputs should lead ...
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Types of measurement error and their implications in SEM
An often cited advantage of Structural Equation Modeling (SEM) is that it is able to account for measurement error in the observed indicator variables, therefore allowing for consistent estimates in ...
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The standard error of precision from the standard error of intermediate precision and repeatability of a analytical chemical method
A validation report of an analytical method (to determine the assay of a product) is given and the goal is to try to determinate the overall uncertainty of it. I started with calculating the standard ...
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Regression with a sum of variables and a proxy [closed]
I want to estimate the coefficient $a$ in the regression
$$ P = c + aX + bY + u $$
However, I only have the variables $T = X+Y$ and $\tilde{Y} = \mu_1 + \mu_2 Y + e$. If I had the variable $Y$, then I ...
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What methods (if any) are available for differentiating between true population variance and variance caused by measurement error?
This may be a question of philosophy or metrology, but I'd like to know if there are any methods that are available to differentiate between variance that is caused by a true spread in the population ...
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How to estimate Mean with Uncertainty of a selected sample from variable A, that occured when variable B met some condition?
I am trying to find the mean of a sample from time-series of variable 'A', consisting of all 'A' values that occured when the concurrent Variable 'B' met some condition.
I know that the A measurments ...
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How to calculate the variance of fixed effects Panel data model with measurement error ( attenuation bias)
Consider the following model
\begin{align}
y_{i t}& =\beta x_{i t}+\varepsilon_{i t} \\\\
\Delta y_{i t}&=\beta \Delta x_{i t}+\Delta \varepsilon_{i t} \\\\
\tilde{x}_{it} &= x _{i t} + ...
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Estimating uncertainties in parameters from minimization of an expression
I was curious if they are anything in the literature about estimating or propagating uncertainties when the desired result is from the minimization of an expression. I have several books on ...
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The distribution of biased and inconsistent OLS estimator under CEV assumption
We know the result that the OLS estimator with measurement error under the Classical Measurement Error (CEV) assumption is biased and inconsistent, and you can write down the probability limit of $\...
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MAD/Mean Ratio - advantages/disadvantages of using average or sum
The calculation the MAD (Mean Absolute Deviation)/Mean ratio is this, according to the title:
$$
\frac{\overline{\left | Forecast - Demand \right |}}{\overline{Demand}}$$
However, the calculation is ...
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Estimate how many wrong measures there is in a sample
This study shows that the average penis mean is 13.24cm and the standard deviation is 1.89cm. Let's suppose we have a population with this mean and standard deviation for penis length.
Suppose we ask ...
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How to model a combination of measurement error and missing data in R and Stan
The data
Consider some simulated data:
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How to propagate errors from two sources
Suppose I performed 10 measurements, and have the dataset:
...
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Fitting data taking into account for the spread in data, which are zero for some data points
I'm trying to use scipy to fit a $\tanh$ function to some data. The data is of the form $(x_i, y_i)$ for $i=1,\cdots,N$, where $0\leq y_i \leq 1$. I choose $x_i$ to be linearly spaced, such that $x_0=...
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Error analysis of a measured physical quantity
I have a set of 100 data point pairs, representing the estimated $(x_{\mathrm{est}},y_{\mathrm{est}})$ position coordinates of a physical object, calculated based on sensor range measurements. Knowing ...
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How to estimate variance when measuring fluctuating variable that never settles?
I am supposed the investigate viscosity related phenomena in water flow through a horizontal pipe, connected to a water tank at one end, and with clear opening on the other. Mounted in the middle is ...
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Error in measurement from two correlated devices
I'll provide physical context just to be able to write my question clearly. In an experiment, we're trying to measure the electric field using a device called an electrofield meter $EFM$. The way it ...
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Treating multiple observed differences as a latent variable vs. difference in multiple latent variables
Suppose I want to model the change in some outcome before and after treatment. The outcome of interest is the change in a latent variable measured with error before and after treatment by 3 observed ...
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Evaluation metric which is able to handle cases where actual value is 0, different units and isn't disproportionately affected by outliers
Just as the title imply, I am searching for an error evaluation metric with the following characteristics:
able to handle cases where actual value is 0
can evaluate different units/scales
isn't ...
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ROC analysis with a fuzzy reference standard with estimates of its reliability
I‘m conducting ROC analyses in order to assess the diagnostic accuracy (AUC, sensitivity and specificity for certain cut-offs) of multiple index tests (ordinal scaled measures). The goal is to compare ...
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What are correlated errors and why are they important?
I am looking for help on correlated systematic errors, and their meaning. I have some quantities $x,y,z$ which determine a function I need to calculate. These 3 quantities are determined by a ...
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Predict colours [closed]
I have very basic knowledge in statistical science and appreciate your patience. My problem is if you have a bag with seven differently coloured balls, you are allowed to blindly pick 3 balls every ...
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Bayesian inference for simple gaussian model with measurement error
I'm having trouble understanding how to specify a model for Bayesian inference.
I have a set of measurements, each with known uncertainty, and I would like to infer the mean of the measurements with ...
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How to model discretised values of a continuous variable?
I have some measurements--tissue swelling in response to an injury--with limited precision (mm). Thus, although the underlying phenomenon is continuous, my values are discrete. The values range ...
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What is a principle of least perturbations?
Background
In BPF Performance Tools by Brendan Gregg, there is a section describing a series of 18 experiments measuring the overhead of tracing with eBPF on Linux.
In the description of the ...
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Understanding the GRS test of the Capital Asset Pricing Model
I posted a similar question on Quantitative Finance Stack Exchange a while ago. It has not received any answers, thus I am reposting a version of it here in the hope of finding a larger pool of ...
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