# 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
1 vote
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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 ...
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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 ...
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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 ...
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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 : ...
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### 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 ...
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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.
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### 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 ...
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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 ...
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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 ...
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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 ...
1 vote
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### 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 ...
1 vote
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### 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 ...
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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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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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### 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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1 vote
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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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### 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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