Questions tagged [measurement-error]

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

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What is the name for an explanatory item response model where the predictors include latent variables?

Explanatory item response models add predictors of the $\theta$ "ability" parameter. However, these predictors are always observed covariates. Sometimes, one may want to include latent ...
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Basic questions about the best way to report precision in quantitative assay validation study

This feels like a very basic question, but I'm feeling stuck on it. I'm writing up a biological assay development/validation study for a method of quantitating multiple organisms from a mixture ...
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How to include observed, exogenous variables in regressions on endogenous latent variables in structural equation models?

Background I'm working with longitudinal survey data collected at two time points. Pre-treatment data were collected, subjects were randomly assigned to a treatment/control group, then post-treatment ...
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Noise model of best fit by comparing data distributions with and without noise

I can't find a way to express this problem as a familiar, solved problem, but I feel as though it is one. I want to characterize some noise behavior in a system that aims to measure $T$, but since ...
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When to use standard deviation versus standard error in linear error propagation

I have a question about linear error propagation. Let's say that I want to use an equation to calculate n, where n = (PV)/(RT) (eq.1) I only take one measurement of P, and one measurement of T, but I ...
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Converting uncertain labels to probabilities for training data

I am devising a data collection effort to measure audio perceptual discrimination, and then model it using machine learning. What I am trying to model is: "Can a typical human hear the difference ...
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Improve Gradient Boosting Regressor

In this my code I am trying to use GradientBoostingRegressor -I am confused because I am getting a large Root Mean Squared Error but I am not sure how to evaluate if it is too high. -How can get on ...
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How to calculate difference from a reference instrument?

I have a cheap thermometer and I would like to calculate its difference from a high-quality reference thermometer when measuring the same quantity, say the temperature in an oven. Is the recommended ...
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What are the rules of thumb for interpreting correlation coefficients corrected for unreliability?

I performed a series of meta-analyses in which we corrected correlation coefficients for measurement unreliability. A reviewer is asking us to define the magnitude of the meta-analytically-produced ...
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Geostatistics with different measurement errors

I'm having a hard time identifying the subject and possible resources of my problem. I have spatio-temporal data (Z) coming from environmental sensors that travel around a city. We have the spatial ...
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Adjust results for a systematic error

My model identifies objects with a specific quality in a large population. I tested it on a sample of 500 and found that it fails to identify about 7% of the objects (false negatives) due to some ...
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If $Y$ is lognormally distributed, what is $E|Y - 1|$?

Let $Y$ be lognormal with parameters $\mu$ and $\sigma$, such that $\log(Y)$ is Gaussian with mean $\mu$ and variance $\sigma^2$. I know $0 < Y < \infty$, $E(Y) = \exp(\mu+\frac{1}{2}\sigma^2)$, ...
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Population studies - interpreting confidence intervals, should they even be included?

I work with administrative ('routinely collected') data in situations where the data capture the entire population, e.g. hospital records, prison records, etc. When reporting statistics the question ...
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How do measurement errors propagate into Percentiles?

I have a measurement systems that outputs $X_i + dX_i$ measurements. I'm trying to figure out the most correct way of estimating quality of measured device. The relative error $dX_i/X_i$ is normally ...
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Range based GRR versus ANOVA

In my company we want to assess suitability of a gauge system to measure a certain quantity. The variance of that quantity when repeatedly measured on the same piece should not exceed a certain ...
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How to Calculate the Variance of the Aggregate of a Bernoulli Process Given Known False Positive and False Negative Rates

I have $n$ sensors which output either $0$ or $1$. These sensors have known measurement error reflected by a false positive rate, $fpr$ and false negative rate, $fnr$. In my case, $fnr > fpr$. ...
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Binary Variable Measurement Error in Diff-in-Diffs

I have a Difference in Differences (DiD) model with a special kind of measurement error. The true $2\times2$ DiD model is given by: $$ y_{it} = \beta_0 T_i + \beta_1 P_t + \delta P_t \times T_i + x^*_{...
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Distribution of true value when measurement imprecision is non-constant

What I believe to have understood so far (I am not a mathematician or a statistician, so please correct me if I'm wrong.) Say we are making measurements of some phenomenon $X$, and we have a normally ...
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Bayesian model comparison with systematic error

Two parameters $(x,y)$ were measured for 3 different objects, wielding the following results: $$\{ (x,y) \}= \{ (1,3), (3,5), (5,9) \}$$ Knowing that the error in the estimation of the values $y$ is ...
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What is the error of the mean of data that have uncertainty values attached to them?

Given a set of $n$ values, the error associated with their average will be $$\text{standard deviation}/\sqrt{n}.$$ But if the values themselves have an uncertainty attached to them, such as $100\pm 1,$...
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2 votes
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GAM interactions to predict deaths (with measurement error) from weather with distributed lag

I am trying to model the effect of heat (in particular of its constituent components air temperature, humidity, solar radiation and wind speed) on daily number of deaths using a generalized additive ...
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Why is ignoring prediction error not a concern in instrumental variables?

In his book, Statistical Rethinking (2nd edition, p. 137), Richard McElreath states that including parameters with unobserved values, such as residuals, and treating them as if they were perfectly ...
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Estimate of an observable and its uncertainty from two inconsistent measurments

Suppose two independent experiments are set up to measure the same observable $\mathcal{O}$ in the same way and report two results $$ o_1 \pm \delta o_1^{stat}\pm \delta o_1^{sys}, \quad \quad o_2 \pm ...
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Scale-independent error metric for data with many zeros

I've been working on a time series forecasting model. I can't use a scale-dependent error measurement. And my target outputs also occasionally have zeros, meaning I can't use MAPE either. What is the ...
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Dummy variables vs deleting observations

I am trying to figure out whether a general (simple rule) exists for my problem. Specifically, if I have a dataset where some variables (independent/control; not the dependent one) may be measured ...
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How to express the agreement between experiment and theoretical observation?

Let us suppose I have a value measured from experiment and given by $$V_{\text{exp}} \pm \sigma_{V_{\text{exp}}}$$ and a theoretical value given as $$V_{\text{the}} \pm \sigma_{V_{\text{the}}}$$ Is ...
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Finding average error

Consider the following data: 20 +- 2, 25+-1, 30+- 3, 40+-1 If I have to find the average error, I can follow two methods: (2 + 1 + 3 + 1)/4 = 1.75 Sqrt (4 + 1+ 9 + 1 )= 3.9 Since, (20 + 25 + 30 + ...
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Simplifying probability involving two independent normally distributed variables

Given independent normally distributed random variables $X$ and $Y$ with means $\mu_X = \mu_Y = 0$ and a tolerance $u > 0$, what is $p = P(X+Y\le u\,\text{and}\,X>u)$? Can it be expressed in ...
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Mean of Relative Error Vs. Coefficient of Determination

Consider we have a method that estimates a specific parameter. We want to find the accuracy of this method and we have 10 samples (these samples include the true values of the parameters and their ...
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95 % CI for ratio of variables subject to measurement imprecision

An instrument used for measurements has a known measurement imprecision of $CV = 10 \%$. Thus, if the variable to be measured has a true value $x_{true}$, the range of possible measured values will be ...
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Bayesian data combination?

I have $N$ sensors, where $N$ is typically of order 10. An object comes in, and each sensor activates. Each sensor measures up to $M$ properties of a given object (the same set of possible ...
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Convergence of Percentile in Power Law

I have a probability distribution, that in its tail follows a power law. I've noticed, while I was simulating samples, and determining parameters experimentally, that as I increase the value of a ...
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Representation of error values for large and small raw values

Assume a population where the numbers are in the range of [0:200]. Assuming the numbers represent the performance of a program, e.g. seconds, the numbers look like ...
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Error "propagation" under base change

Imagine you have fitted a curve to data in $x$-$y$-space and obtained errors $\sigma_x$ and $\sigma_y$ for each data point. But now you rotate the coordinate system by $45^\circ$ for example. Can you ...
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Measurement system analysis

Let's say I'm responsible for checking the length of shoes on a production line. Our production system isn't great, so a shoe that should be 25 cm long might actually be a slightly different length (...
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Determining Error Bars on Normal Data from Sensor with Rated Error

You are using a sensor to take temperature measurements at 10 Hz. You sample for 100 seconds and end up with 1000 samples. Upon analyzing a histogram of the data, you see that it appears normal with a ...
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Is this a viable means of diagnosing errors in measurements from data sources?

I recently started a project that involves taking measurements at hundreds of different sources. These measurements, in theory, should all cancel out at each point in time to 0 but that's never the ...
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Multivariate forecast error metrics

I'm working with multivariate models (VAR, VECM, GARCH-M) and I want to measure the forecast error size of each model. An alternative is take individually the forecast of each univariate time series ...
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Is this a reasonable way to determine the reliability of a fit?

Background I have measurements of a trajectory that is parameterized by time. The data consists of points with two spacial coordinates $(\tilde{x}_i, \tilde{y}_i)$ and a time stamp $(t_i)$. I'm using <...
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Error Models beyond Additive/Multiplicative for Observables on Bounded Intervals

Arguably, the two most common error models are Error Model Support Formula Assumptions Constraints Additive $(-∞, +∞)$ $y_\text{obs} = y + ε$ $𝐄[ε]=0$ $𝐕[ε]=σ²$ Multiplicative $(0, +∞)$ $y_\text{...
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Why does regression dilution always bias the slope toward zero?

Regression dilution, in the case of linear regression, is supposed to be what happens when there is noise in the independent variables, namely the slope of the fitted linear regression model becomes ...
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Estimating the error in 3D phase fraction calculations

I am trying to estimate the error of a 3D volume fraction measurement (from X-Ray Microtomography experiments). Kind of like a CT-scan of a small inorganic material with embedded particles. ...
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How to compare two quantities with uncertainties?

I've got two instruments that measure one quantity. One of them is regarded to be more precise, therefore, I use this measurement as a reference. Then, I take two measurements of the same quantity ...
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How to calculate RMSE for two regression lines

I'm struggling on how can I calculate the RMSE for two regressions. Consider the following scenario: I have two linear regressions, and Id like to calculate the joint RMSE for this model. Any hint on ...
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(Co)variance interpretation in Kalman filter

Let's say I have a device which uses Kalman filter to fuse sensor data and produce an optimal estimate of the system parameters. As it should, it also estimates parameter covariance matrices at each ...
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Measurement error and type I. and type II. error [closed]

Is there a relationship between measurement error (1.) both systematic and random, (2.) systematic only and (3.) random only in terms of tendency of results of statistical tests to be biased towards ...
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Linear regression with double error bars

I am trying to perform linear regression between $y'$ and $x'$ (independent) for some experimental data. Each of the variables has a non-constant random measurement uncertainty, and the error bars do ...
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How can using standardized residuals as an outcome be a valid approach? And how do results differ from doing one regression only?

The residual approach uses standardized residuals SR from regression of Y on X1 as an outcome, and then regress them on X2 (here is a literature review: https://www.ncbi.nlm.nih.gov/pmc/articles/...
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How to deal with an imperfect reference standard in a comparison of two diagnostic methods?

Summary We discovered after performing our experiment that the method for determining our reference standard was not perfect: it may have a false-negative rate of up to 20%. With no way to confirm ...
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RMSE estimation from model accuracy and RMSE of dependent variable

Given the two variables/measurements, which were used for building up the model (Random forest regressor), I would like to estimate an RMSE of the predictor variable/measurement against the "real&...

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