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Questions tagged [measurement-error]

Measurement error is the difference between a measured value of a quantity and its true value.

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How to use posterior predictions from one model (standard curve) as an outcome variable in another model?

I'm working with a dataset concerning the concentration of a large number of different chemical compounds in a mixture, using a Bayesian approach (with brms in R). The instrument that measures the ...
Jacob Weverka's user avatar
3 votes
1 answer
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What is a good introduction to errors-in-variables models?

I'm aware of this resource https://en.wikipedia.org/wiki/Errors-in-variables_models, but I don't put a lot of faith into wikipedia articles on stats, so I'm looking for some reliable references on the ...
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Calculate the propagated uncertainty by measurement error in linear fit coefficients

I am currently taking a physic experiment class and am required to analyse the uncertainty of data caused by measurement error. They have provided me the standard way to propagate the error, namely by ...
Monolitho's user avatar
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How can I find the margin of error of the extrema point?

I create a 4th or 5th degree fit curve to find the extrema point of distribution. However, how will I calculate the margin of error of the extrema on x values? Is there any statistical method or ...
Erkan Güler's user avatar
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Measurement error R in Kalman Filter [duplicate]

I want to calculate the measurement error R for Kalman filter if I have such data: True value of the golden bar is 18 g. A tool was used to measure the weight of the bar: 17.7, 17.8, 18.1, 17.8. How ...
Max Heron's user avatar
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Uncertainty of mean

Assume I have $N$ measurements, each with error estimate $\delta$, i.e., $x_1\pm\delta,x_2\pm\delta,\dots,x_N\pm\delta$. What is the best way to estimate the error of the mean value $(x_1+x_2+\dots +...
lamw's user avatar
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1 answer
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What statistical method for assessing the effect of a known measurement error variable?

I have lots of repeated measures data for a dataset of 95 subjects. The data concerns medical-imaging measures of morphology. medical-imaging is a tricky kind of data - the same body part imaged on ...
Maks Hall's user avatar
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Fitting a model with multiple inputs, multiple outputs, multiple parameters, and covariance matrices for each data point

This question is the theoretical counterpart to another question posted on StackOverflow, where I asked about the implementation of the fitting algorithm using Scipy or lmfit libraries for Python. ...
Swike's user avatar
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Instrumental variable with measurement error

I have a question related to measurement error bias and the use of instrumental variables. Assume I have a continuous outcome variable $Y$ which is observed with no error and an endogenous (continuous)...
Panagiotis's user avatar
2 votes
2 answers
39 views

How to measure the error between modeled and observed data?

Consider a scenario where observed data is represented in grey and modelled data in red, as below Here, the x-axis is a position, and the y-axis is an expected time, so that the slope defines, in a ...
sam wolfe's user avatar
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potential measurement errors

I am working on a dataset for a practice problem and was given a dataset containing information on food items such as kcal (kilocalories), Potassium, Protein, etc. We were asked to analyze the dataset ...
Harry Lofi's user avatar
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Density of $X$ from observed density of $Z$ and $Y$ when $Z=X+Y$ (and $Y \perp X$)

I have $Z = X + Y$, with $Y \perp X$ and $\mathbb{E}[Y] = \mathbb{E}[Y|X] = 0$ ($Y$ is basically an error term). I observe the distribution of $Z$ and I know the distribution of $Y$. I want a formula ...
G. Ander's user avatar
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Binomial Test for data with normally distributed messurement error

I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
Adrian 's user avatar
1 vote
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Standard Deviation and Standard Mean Error of measurement with uncertainties

It is well known that, given a set of $n$ values $Y_1, \cdots, Y_n$, its Sample Standard Deviation is $\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^n (X_i - \bar{X})}$ and its Standard Mean Error is $\...
Bml's user avatar
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Error bars on average for discrete limited values close to edge of range

Let's say I have discrete data that can only fall into a limited range - for example rating a product with a score from 1 to 10. How would I go about assigning error bars to the average value of the ...
Ann Nika's user avatar
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Errors-in-variables regression with sample size weighting?

Very belated follow-up to a previous question: I have some pretty simple linear models predicting a rate (continuous response var) from certain features of the distribution of some measured value. The ...
TY Lim's user avatar
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Should I normalise my dependent variable by a measured variable that I want to be constant?

This is a question about the validity of applying the results of a statistical test, and unfortunately will require some explanation of the experiment in question. Essentially, I want to measure how ...
Rachel Jones's user avatar
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Determining number of repeat measures needed to deal with measurement error through bootstrapping?

I have a performance test with a high degree of inherent measurement error. I have some data from a pilot study where I took 30 repeat measures with a single device and I want to figure out how many ...
CBRF23's user avatar
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Include error on the predictor from mean and asymetric credible interval

I am doing non-linear models with brms. My model is : ...
user avatar
2 votes
2 answers
97 views

Effectiveness of Using Moving Averages in Timeseries Regression Analysis with Noisy Data

I am working with a dataset where I suspect there is significant noise in both the dependent variable ($y_t^*$) and the independent variable ($x_t^*$). I am considering using moving averages to ...
The One's user avatar
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4 answers
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What is the difference between sampling error and measurement error?

The terms sampling error and measurement error in statistics field are very relevant and have a paramount importance for data analysis and reporting.
Dr. Subhash Chander's user avatar
4 votes
1 answer
140 views

What is the standard error of a binomial process with a false-positive rate

I have a question that must be common, but after searching, I can't find an explanation. Suppose we wish to estimate the percentage of people, p, who have a disease. We test n people. The test has ...
Gary S's user avatar
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1 answer
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Calculate mean and standard deviation of the ratio of two dependent variables

I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
s.cerioli's user avatar
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Estimating the error bounds for a derivative chart of data

I have collected position (S) versus time (t) data. A typical result is shown in the following chart: As can be seen all three regression models provide excellent fits to the mean values of the data ...
rdemyan's user avatar
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2 votes
1 answer
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Estimating hazard ratios for values of a continuous predictor without catagorizing

I have a dataset where I am looking at time to diagnosis as a continuous predictor of mortality. Using a Cox model, I want to estimate HRs for values of this continuous predictor to be able to say ...
user405452's user avatar
1 vote
1 answer
35 views

Cartesian precisions from spherical standard deviations

I have to simulate a simple sensor, which has 3 standard deviations defined in spherical frame : sigma-azimuth, sigma-elevation, sigma-distance. When I simulate a detection, I compute a noisy position ...
ConanLord's user avatar
1 vote
0 answers
27 views

Evaluating and comparing forecasting methods through errors in multi dimensional time series data

I have a fairly complicated problem and I would like some advice on how to properly assess the results. I have a series of 12 connected 'zones' that have a specific numerical value at any given point ...
Tom's user avatar
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4 votes
2 answers
71 views

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 ...
Ray Butterworth's user avatar
5 votes
1 answer
63 views

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, $U' = U+\epsilon$, ...
user310374's user avatar
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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) ...
blov's user avatar
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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 ...
marc's user avatar
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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 ...
eli-k's user avatar
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5 votes
2 answers
85 views

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 ...
geotheory's user avatar
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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 ...
NeuroPanda's user avatar
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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 ...
Physicist_285's user avatar
2 votes
2 answers
41 views

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 ...
cactuslover's user avatar
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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 ...
OneSickDisease's user avatar
6 votes
0 answers
45 views

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 ...
Igor F.'s user avatar
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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 $x_i^a$ ...
manifold's user avatar
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1 vote
1 answer
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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 ...
Galen's user avatar
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1 vote
2 answers
163 views

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 ...
Govind Prajapat's user avatar
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31 views

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 ...
Alonso Quijano's user avatar
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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 ...
DmitriBolt's user avatar
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1 answer
76 views

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 ...
FredrikH-R's user avatar
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0 answers
25 views

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 ...
Snowy Baboon's user avatar
2 votes
1 answer
91 views

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 ...
holmes's user avatar
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0 answers
41 views

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 ...
rep_ho's user avatar
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12 votes
7 answers
2k views

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 ...
benxyzzy's user avatar
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1 vote
1 answer
239 views

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 ...
user321797's user avatar
1 vote
0 answers
89 views

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 ...
user218912's user avatar

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