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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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3 views

How to extract systematic errors from data

I am a bit confused about estimating the systematic error (I think it is systematic) from an experiment. Here is a (simplified) description of it. Assume that 2 groups measure the length of a cube ...
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Parametric (p = a +vt) version of a model into betas interpretation [on hold]

I am working on an error-in-error model (McLean 2014), where it is possible to include the correlations between uncertainties in the model. This model is formulated in a parametric form as follows: ...
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WMAPE / WAPE for the evaluation of time series with positive and negative values

I have a time series y that has both positive and negative that I want to predict. For the prediction I normalize the values to a range between 0 and 1. If I give ...
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Error weighting in two point regression analysis [closed]

I have following problem: I do measurements of the formation of a product at two time points (t=0 and t=15), each in triplicates. Afterwards I calculate the mean value + the standart deviation of ...
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Comparing the precision of two sources of estimates, about things in two different categories

Suppose we have two machines. Each machine measures things in a particular category. For example, one measures the weight of cars, and the other measures the weight of butterflies. We have available ...
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17 views

Errors on the mean

I have some data points from a measurement of a given quantity, and each point has an error associated to it. I want to report as the final value the mean of the measurements, but I am not sure what ...
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1answer
42 views

Weighting data based on the errors

I have some data (counts) with a Poisson error associated with them and I want to fit the data. I am trying to weight the data inversely proportional to the errors, such that the data points with high ...
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How do I correctly estimate the size of a subpopulation using noisy observations?

To preface this question: please comment on whether my description of the problem is missing details or the problem itself is not well-posed as I'm seeing a lot of views but no activity. I am trying ...
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1answer
70 views

Retrodiction / Specific filter to obtain initial state

Problem I have a system that is measured at regular intervals. The state of the system at those times is given by the vector $\vec x=(x_0, x_1, x_2,\cdots)$. In between each measurement, a random ...
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1answer
25 views

Bootstrapping mean of measurements when measurements have error

I have two small data sets (n < 15) that are not normally distributed. Each measurement in the two datasets was experimentally determined and has an uncertainty associated with it. I'd like to use ...
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26 views

How can I model this?

I have a question about whether I can model in a way that solves this problem: Suppose a swimming coach has 100 athletes and only cares about the distance they can each swim in 5 minutes. From this, ...
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If measurement error is only for a specific group do you avoid bias by controlling for that group?

I am running regressions to estimate the impact of health conditions on life satisfaction. I have read a paper that showed that there is likely to be measurement error in the self-reported health ...
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1answer
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How to compare two, time based, measurements of the same object

I have 2 rounds of measurements from a set of 10 capacitors. The measurements are with respect to frequency and are all measured at the same 200 frequencies between 1 kHz and 5 MHz. The data is not ...
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Standard error of correlated time series with observational error

I've got a some time series for which all data points have some measurement error. I want to compute a confidence interval of the standard error of the mean. I know how to compute and approximate the ...
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1answer
19 views

have many error likelihoods, how to combine to get a confidence or p value?

I'm working in bioinformatics and its been a long time since I dusted on my statistics. Basically I'm working on variant calling which amounts to sequencing a large number of sequence reads and ...
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how to evaluate or fulfill required accuracy for regression aka precision of estimation?

Maybe there is already a question similar to mine but there are so many involving the term accuracy and at least none, except of How to evaluate instrumentation accuracy? , didn't seem "very" similar. ...
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Identify difficult parameter to measure [closed]

I am using different tools to measure x on some objects. The tools were tested on a small set of objects for which the true x is known. And so the predicted values were found to not be accurate for ...
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Error-in-variables - Consistent estimator with lagged variable

my Econometrics teacher gave us an exercise and I can't get it, could someone help me, please? Suppose all assumptions of the classical regression model are satisfied. Suppose $y_t^*$ = $\beta$$x_t^*$+...
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How to describe accuracy/error without ground truth?

I am using machine learning regression models to predict motor scores among a population with spinal cord injury using features derived from their actual movements. Although the clinical measure we ...
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Formula for calculating the gap between expected errors [train and test]

In the famous paper of LeNet5 the authors state the following: The gap between the expected error rate on the test set $E_{test}$ and the error rate on the training set $E_{train}$ decreases with......
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Error margin calculated from individual errors/residuals

Say I run a model and then calculate the residuals or the errors between what my model predicted and the real-world results. For example: ...
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Comparing Gaussian and Poisson GLM when applied to count data; “Chi-Squared Error”

I have a fixed set of predictors ($[x_1,x_2,...,x_p]$), which I'm using to fit a GLM for univariate responses ($y_1$, $y_2$,...) of various types. E.g. I fit a GLM for $y_1 \sim [x_1,x_2,\dots,x_p]$, ...
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1answer
51 views

If I take mean of uncertain observations what happens to SD of the observations?

I have some observations, each with an accompanying standard deviation (shown here as error bars): I want to make a summarised plot of this data by taking mean of all observations for a given X value,...
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27 views

error in measured quantity times exact number

I'm working through "An introduction to error analysis" by John R. Taylor. It states, If the quantity $x$ is measured with uncertainty $\delta x$ and is used to compute the product $$q=Bx,$$ ...
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measurements with gaussian error

I'm reading a printed document(learning material) which says "Person A made measurements of a quantity, with Gaussian errors". To me this expression seems odd and the meaning is unclear. Is that a ...
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25 views

How do I tell if the sensors that feed a Kalman filter has diverged?

I have a time varying variable $x$ that I want to estimate. I have two sensors A and B that measure $x$. I feed their measurements to a Kalman filter. Sometimes, one of the sensors degrades for a ...
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Measure effectiveness of algorithm (plot included for clarification)

I have written a short algorithm that computes the "comovement" of a time series. My problem is what method to use to measure how accurate this algorithm is. Ideally it should only have negative lines ...
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1answer
74 views

Performance Imbalance Dataset Decision Tree

I have a imbalance dataset for a classification task, with the minority class accounting for about 21% of the total. When I use a decision tree based model for prediction, let's say a classification ...
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39 views

Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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Deterioration of the accuracy of a system over time

I have a system that compares the predicted variable with the true variable by calculating the absolute error percentages. . Where $\pi$ is the predicted variable and P is the true variable. And you ...
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How to find the standard error of a sample of measurements each with their own uncertainity

I have a scale that has a resolution of +-0.01 grams. I have assumed that it has a standard error of +-0.005 grams. I would like to measure the mass of an Samsung INR18650-30Q battery. I would like to ...
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1answer
40 views

Which approach should be used to compare two different measurement techniques of same samples?

I have individually measured failure forces of 8 materials and those recorded with A method and B method in same time: 8 results in each method, A=8 and B=8. The range of data of both measurement ...
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1answer
65 views

Uncertainty in measurement error

Imagine having a list of positions $\mathbf{x}$ and two different systems trying to estimate $\mathbf{x}$. One system is more precise than the other, and it will be used as ground truth. When ...
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1answer
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Correction for measurement error

Let's suppose that the true model is: $$ y_t^* = x_t^* \beta + e_t^* $$ and suppose that data on $x_t^*$ is observed with error: $$ x_t = x_t^* + u_t $$ If we consider the regression $y_t^* = x_t \...
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3answers
71 views

Does the RMSE formula have a $k$ in the denominator?

In what circumstances does the RMSE formula have a $k$ in the denominator? StackOverflow's What does RMS stand for? shows this formula for RMSE: $$RMSE=\sqrt{\frac1{n-k}\sum_i(y_i-\hat{y}_i)^2}$$ ...
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Berkson versus classical measurement error: how to choose?

When discussing the consequences of mis-measured variables, an important distinction is to be made whether the measurement error is of the classical, or Berkson type: Classical: $x=a^C + b^Cx^{*}+e$, ...
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Corrected Standard Deviation for Differences in Means

In the published work of Altman and Bland: Statistical Methods For Assessing Agreement Between Two Methods of Clinical Measurement, Lancet 1986 (https://www-users.york.ac.uk/~mb55/meas/ba.pdf) , page ...
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Covariance of measurement uncertainties

So I have a sample of data points call them $X_1$ and $X_2$, these are derived quantities based on measured values and each has a mean $\mu_{X_{1,2}}$ and variance $\sigma^2_{X_{1,2}}$ which can be ...
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111 views

Determination of MPE (maximum permissible error) in CMM

Which approach should I use for evaluation of MPE (defined in ISO 103600)? MPE is a characterization stated by the manufacturer of a length measuring device (coordinate measuring machines). It says, ...
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How to account for experimental errors when computing the derivative of a Gaussian process?

When applying Gaussian process regression upon training data, the covariance function can be generally given in the form: $\Sigma_{i,j} = k(x_i, x_j) + \sigma(x_i) \delta_{i,j}$, where $k$ is a ...
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1answer
49 views

Linear regression where some known records have a measurement error in dependent variable

I am modelling data where the dependent variable is the number of units of a certain product sold each month in each area. In all areas, the product is sold by a chain of shops 'A' and we have exact ...
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2answers
158 views

Median Absolute Deviation

How median Absolute deviation is immune to outliers? R2 or coefficient of determination is affected by outliers. And how this MAD is going to remove that constraint?
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Combined uncertainity given probability measurement belongs to one of two classes

I have two classes of measurements $A$ and $B$ characterized by different uncertainty distributions. I also have a probability $P_A$ that a given measurement belongs to class A and not B ($P_A = 1 - ...
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1answer
27 views

Is non-sampling error included in hypothesis testing assumptions?

I understand that, in hypothesis testing, we are dealing with sampling error. We calculate the statistic from the sample data and test what the probability of getting that result is when the null ...
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33 views

Which correction do I need to get a measurement uncertainty from the sample standard deviation?

I'm an experimental physicist who mainly needs statistics for the calculation of measurement uncertainties and confidence intervals. Since my results are usually normally distributed, I simply take $N$...
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When making a fit to data without weights, how reliable are the fit errors?

I often need to fit data which is a spectrum. And it isn't possible to have many identical spectrum from which to produce error bars on the individual points in an averaged spectrum. So my question ...
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24 views

Does this mean my model is useless?

Long story short, I have a random forest I've created. It's mean absolute error is .209 for the test set. The (scaled) standard deviation of the y column is .201 (for all the y column data, not just ...
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277 views

Using regression weights when $Y$ might be measured with bias

Suppose we observe data $Y, X$ and would like to fit a regression model for $\mathbf{E}[Y \,|\, X]$. Unfortunately, $Y$ is sometimes measured with a systematic bias (i.e. errors whose mean is nonzero)....
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1answer
56 views

Asymmetric error measure for forecasts

I am building a model for forecasting some number of activations. My data set has a panel structure. Now, I want to come up with a forecast performance measure to assess the performance of my model ...
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1answer
78 views

What is the error of my regression? [closed]

I'm conducting a polynomial of a third degree upon a diode measurement where Amplification was measured against Voltage. It's a very exponential behavior. However, I used the ...