# 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 ...
1 vote
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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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1 vote
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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 ...
1 vote
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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, $fnr > fpr$. ...
1 vote
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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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1 vote
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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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1 vote
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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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1 vote
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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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### 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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