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

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How to integrate observational errors in goodness of fit tests?

I have an astrophysical non-linear curve, specifically a power spectrum. I need to fit this curve with a model and obtain the goodness-of-fit (GOF). This gives me expected and observed values. The ...
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16 views

How to compare forecasting methods: based on ARIMA and curve fitting?

I'm making a project connected with identifying the dynamics of sales. My database concerns 26 weeks (so equally in 26 time-series observations) after launching the product. I want to make forecast ...
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18 views

Using aggregated data from a database with data from another

Let's say I have two databases, in the first (DB1) there is individual data on how much people trust in the government ($X_{j,r}$), and on the second (DB2) there is individual data on how much people ...
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132 views

Defining precision in a mechanical movement

I have a device which rotates on a stepper motor through a belt and pulley system. I would like to know both the positional accuracy and precision of this movement. It is of my opinion that this ...
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5 views

Weighted averages of a subset using fractions vs a frequency

So I have a bunch of scores 0-100 and a two sets of weights, the frequency which is the number of people in the sample with an average score among those people. Then I have another value that is the ...
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19 views

Logistic regression when a covariate is measured with known but heterogenous measurement error

Let $y$ be a binary variable and $x$ be a covariate measured with known heterogeneous measurement error: $x_{i}$ ~ $\operatorname{Normal}(x^{*}_{i},\sigma_{i}^{2})$. Now suppose the relationship ...
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61 views

Error in variables problem and maximum likelihood estimation in R

I am estimating cross-sectional regressions - fragment: lm(rate~liqamih.log+cap.log+F1+F2, data=x) of the R code listed below. F1 and F2 are the coefficients estimates of time series model. In ...
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282 views

How to compare measurements and uncertainties made with different measuring instruments?

I have two different measuring instruments, A and B, both measure the same physical property $x$ of an object but with different "quality": B gives measurements with a known uncertainty while I do not ...
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1answer
65 views

How to calculate relative error when the true value is zero?

How do I calculate relative error when the true value is zero? Say I have $x_{true} = 0$ and $x_{test}$. If I define relative error as: $\text{relative error} = \frac{x_{true}-x_{test}}{x_{true}}$ ...
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4answers
130 views

Can the use of dummy variables reduce measurement error?

If the continuous variables are measured with error, can the use of dummy variables mitigate the problem? For instance, IQ measures intelligence with error. So will using a dummy of high, medium, low ...
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0answers
20 views

Measurement error in nonlinear models, when can one ignore it? and what can one do about it?

Suppose you know there is measurement error in your system but you don't have any idea what the variance is. In my specific case I have a nonlinear model \begin{align} y_i&=\epsilon_i ...
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1answer
54 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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3answers
121 views

Importance of optimizing the correct loss function

I want to understand the importance of optimizing the correct loss function. Say that I am building a linear regression model $p$ for predicting some values $y_1,\ldots,y_n$. I choose to fit my ...
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1answer
58 views

Recovering true data from multiple noisy versions

I am trying to find if there is any way to get the true data from multiple noisy versions, but the true data has a peculiar property. Problem Statement Consider a matrix $F=[f_1, f_2, ... , f_n]$ ...
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22 views

Does measurement error include effects of moderator variables?

I am not very sure how to interpret measurement error correctly: as a constant, as a bias, or as a moderator factor? Is it presumed that measurement error includes moderator effects? Let it be in ...
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0answers
26 views

Is it always necessary to correct the sample correlations for a meta-analysis?

Some authors eg Hunter et al (1982) propose that we must correct sample correlations for the measurement error.It seems measurement error need not be corrected for when we take a recourse to the ...
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0answers
36 views

Regression with error in covariates

I am looking for some advice for a colleague who is dealing with regression models for which it is know, that the continuous covariate of interest $X_1$ was measured with error. More precisely, we ...
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26 views

Does true correlation in statistics represent validity coefficent as used in psychometrics? [duplicate]

The statistics appears to have borrowed certain concepts and models from psychometric theories and models. Is it a correct to presume that the two terms are equivalent?
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23 views

How to analyze within and between observer error, with count data?

I have a data set that consists of counts of striae (lines) on fish teeth. I want to assess within observer and between observer error for my data, and compare values to published counts of the same ...
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1answer
82 views

How to adjust measured values depending on control values?

I have taken 20 photographs. Each photograph contained a museum specimen of a bird and a colour chart. In each photograph, I measured the brightness of a specific part of the bird's plumage and the ...
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0answers
43 views

Prediction interval with measurement error

My data is $(Y,X)_i,i=1...N$ and i want to fit a regression model to relate $Y$ and $X$. It is known that $X$ and $Y$ are erroneous measurement of true variable $(U,V)$, but the standard errors ...
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1answer
90 views

Is there a computationally less expensive way to calculate RMS error between two signals?

Root-mean-square error (RMS error) between two signals can be calculated as given: ${\text{RMS}(x_\textrm{ actual}(t)-x_\textrm{ reference}(t))}$ When you want to calculate within a sliding window, ...
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97 views

What's the best way to measure accuracy/significance of a Stock Prediction Model?

I'm looking for insights on how to test the accuracy of a model I built to predict next days stock price - Open, High, Low and Close next day prices. Is there a unique indicator of accuracy or ...
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30 views

error of the mean in presence of background

Suppose I have a normal distribution, $N[\mu,\sigma]$, and I have a sample of size $n$. It is well know that the error (std deviation) of the mean is $\sigma/\sqrt{n}$. Now suppose that my ...
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113 views

Does sampling error include measurement error?

Gross sampling error (MSE) appears to be a composite of two errors sampling and measurement error. How do we assess measurement error ? can we find out net sampling error ?
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79 views

What is the difference between the concept and treatment of measurement error in psychometry and in statistics?

There is some confusion with respect to the measurement error. What is the definition in statistics and definition in psychometry ? The statistics does not seem to recognize the measurement error ...
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1answer
77 views

What conditions ensure that the standard deviation is a good measure of error?

While attempting to analyze error incurred in certain optics experiments, I am only able to make statements about the standard deviation of a suitable distance measure between the actual and expected ...
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138 views

Average over two variables: Why do standard error of mean and error propagation differ and what does that mean?

I'm doing an experiment with a cryostat to determine the critical temperature for lead. To avoid asymmetries, I determine the critical temperature both through heating (going from 2 K to 10 K) and ...
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1answer
73 views

How do sampling error, measurement error and specification error affect regression coefficients

Can anyone answer the question or direct me to the proper resources - ESPECIALLY for sampling error effect on the coefficients? How would the coefficients be affected if the independent variables came ...
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55 views

Regression analysis with special cost function

I want to do regression analysis using a special cost function that penalizes the sign error more than the square of the error. For example, I have a number of monthly change observations that can ...
2
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1answer
62 views

How does this trick for estimating bit error rate break down?

Imagine you are receiving a message over and over via a lossy data path. The path causes bit errors but does not affect the length of the message (or shift any bits). You don't know the actual ...
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1answer
69 views

Non-overlapping state and measurement covariances in Kalman Filter

I have implemented an EKF to track the state of a moving vehicle in 3D. My question is twofold: What happens if a measurement (e.g., for $y$ velocity) has a covariance that does not overlap with the ...
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1answer
154 views

Regression and variable with errors modelling problem

Wikipedia says that almost all Measurment error models can be formulated as follows: Usually measurement error models are described using the latent variable model latent variables approach. If ...
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48 views

How to compare the accuracy of predictive algorithms when the predicted value contains measurement error

I am conducting (somewhat casual) research on the accuracy of several algorithms meant to compute a value when given a set of experimentally gathered variables, including time. The issue is, the true ...
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17 views

Should I use variance or standard deviation as weights to combine independent measurements? [duplicate]

I've got a set of N independent measurements that I'd like to do a weighted average on to get one, hopefully better, measurement. I've got a variance measure for each measurement, would it be more ...
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1answer
75 views

What is the proper way to measure error in collected data for calibration purposes?

I got into a discussion with a colleague today about some of our data sensors. Our sensors weigh objects anywhere from 10 to 100 tonnes. currently we calculate the error as: $$ error = \frac{\left ...
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86 views

Intra-rater reliability (measurement error) with linear data - 1 rater, video performances scored 3 times

Background: I am an occupational therapist doing a PhD in clinical left hemispheric stroke assessment and intra- individual (patient) variability. I'm in my feasibility phase and I need to calculate ...
2
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1answer
159 views

Taking equipment precision into standard deviation

I have a set of $n$ measurements, $x_i$, representing distance to a point, and want to find the mean and the standard deviation of the distance, the problem is, I don't know how to take the precision ...
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1answer
64 views

Error estimation of a small dataset of counts

I am pretty sure it will take a few goes for me to phrase this question correctly but hopefully somebody with relevant knowledge will understand. I also hope this question actually has an answer(s) so ...
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0answers
94 views

Regression model where errors are not normally distributed

From a Physics equation I have the following model: $$W=\beta_0+\beta_1Z$$ $\beta_0$, $\beta_1$ are fixed values for which I want to find a $1-\alpha$ confidence region. I have ...
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129 views

Error propagation with linear regression

I'm trying to obtain an estimation of the uncertainty related to an analytical method: my function is just a linear regression $f: y=ax+b+ \epsilon$ with $y_i=\frac{R_i}{C}$, both $R$ and $C$ are ...
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39 views

Choosing a distribution in the presence of multiplicative observation errors

Suppose I have a large sample from some distribution the form of which I do not know with certainty, though it would appear to be continuous and reasonably well-behaved (e.g. unimodal, differentiable) ...
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18 views

Choosing an appropriate part of an unreliable dataset

I have a dataset with $\approx2000$ entries (for example, model of car). For each car model I know the weight of the car, and the power output. I don't know the price or age, which is likely to ...
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1answer
1k views

Normalized root mean squared error (NRMSE) vs root mean squared error (RMSE)

The response values in my data set (100 data points) are all positive integers (should not be either negative or zero values). I have developed two statistical models: Linear Regression (LR) and K ...
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1answer
74 views

High level interpretation of Cramer-Rao bound and Fisher information matrix

I am reviewing a manuscript and am struggling to understand why some statistical techniques were chosen, i.e. what information they can give. The paper looks at the effect of predicting a variable ...
2
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1answer
332 views

Propagation of uncertainty through a linear system of equations

If I have a system of equations, $Ax=B$ where the elements of $B$ have been experimentally determined and as such each element has some uncertainty, how would I propagate this to the elements of $x$? ...
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1answer
795 views

How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?

I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
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2answers
133 views

Trends in noisy data and the applicability of the 95% confidence interval

I am performing simulations while measuring a quantity A which depends on the parameter B. I make N independent measurements of A for given values of B. I can then calculate the mean to get an ...
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1answer
159 views

Errors in Variables and Deming's multivariate regression: Assumptions

There has been extensive literature that puts forth a standard set of assumptions for the Ordinary Least Squares (OLS) estimator. I am very interested in working around the two classical problems of ...
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39 views

About finding testing Errors

I have 63 rows and 17 columns in the cocomo81 dataset (see the information here). The first 16 columns are the inputs to the network and the 17th column is the estimated outputs. I took 2/3rd of the ...