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

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Evaluating mean-squared error

Hello I am running a Regression Tree experiment. I am new to Regression Trees, and I am using Mean Squared error to test my tree. I am confused because I am getting a large Mean Squared Error but I ...
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27 views

Implication of mutual information

EDIT For two signals or random variables to be independent, the mutual information (MI) must be zero. Let, $error = X -Y$ where X is the desired signal and Y is the measured signal. It is desired ...
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36 views

Are significance tests only about sampling error or other forms of variation also?

When we study differences between a treatment and control group in an experimental setting, we want to test whether those differences are big enough that we can conclude they are not simply due to ...
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120 views

Estimate average percentage error based on another gaussian measurement

I have a model where the error is proportional to the throughput. This is, the observations I got come from a measurement instrument that has some error and it measures material going through in ...
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45 views

using Root Mean Squared Error (RMSE) to compare models with different sample size

I'm using k-fold cross-validation to compare different models. I splitted my dataset in 6 chunks and used 4 random chunks as training set and the remaining 2 as a test set. Now I fitted n-different ...
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24 views

Performance of hierarchical clustering for binary data in R

I am trying to use Hierarchical clustering to see how well it performs in classifying a dataset which I previously know its true classification. I am new to clustering in general. I was able to draw ...
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25 views

What's the sample size required to confirm that two treatments are identical?

Goal: Determine if a machine is defective Say I am going to give the same treatment to a group of people. I have a machine that will randomly split them into $2$ groups before giving the same ...
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2answers
98 views

Standard deviation for a measurement that has two causes of uncertainty

I would like to know how to calculate the standard deviation for a measurement value $x$ when there are two separate sources of uncertainty, 1 and 2, each with known standard deviation, $\sigma_1$ and ...
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1answer
48 views

larger sample size or more accurate measurement?

This question is completely theoretical in the sense that I don't have any real data. Suppose I am designing a study, in which I will go measure N pairs of (X,Y), then the goal is to build a ...
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24 views

Significant digit 354 rule from Particle Data Group

The particle data group (PDG) has a particular rule to round the value of a measurement. You can find the complete description at this link (page 13). Summarizing: ... if the three highest order ...
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159 views

Linear regression model that best suit for data with errors

I'm looking for linear regression algorithm that is most suitable for a data whose independent variable (x) has a constant measurement error and the dependent variable (y) has signal dependent error. ...
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12 views

Parameter estimation of LMM with multiplicative measurement error in fixed co-variate - How?

I have a linear mixed model, with multiplicative measurement error on the fixed co-variate only (i.e. the random part is assumed to be measured without error). How could I best estimate the ...
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1answer
15 views

How to perform power analysis for repeated measures with observation error?

I am interested in producing two raster maps of the same areas but separated in time. I would like to take the average value of all pixels in each map and test if there is a difference in that mean ...
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36 views

Estimating the Marginal Effect of a Misclassified Binary Regressor Without Instruments

In ordinary least squares, we can use an errors-in-variables model when one or more of the regressors are measured with additive noise to ameliorate the effects of attenuation bias. We just need to ...
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1answer
37 views

Measurment error for two variables

I am interested in estimating the effect of security S on crime C in a given city over time (eight quarters) for twenty cities, so it's panel data. The problem is, instead of actual security spending ...
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24 views

Measure of accuracy or measure of agreement for continuous data with true values

I have two continuous variables. Variable $X$ represents the true values (basically it is atmospheric pressure measured via a barometer). Variable $Y$ represents a way to approximate the atmospheric ...
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29 views

Upper Bound of Measured Data

HW question I am having trouble on: My attempt at solving it: I thought part (a) was pretty straight forward until I worked it out and got the same value of K for K_upperbound which I assume is ...
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1answer
17 views

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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34 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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20 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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3answers
143 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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7 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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22 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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75 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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322 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
169 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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151 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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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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91 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
173 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
76 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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56 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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37 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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37 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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30 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
83 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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49 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
122 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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136 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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31 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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115 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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87 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
90 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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166 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
83 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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69 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 ...
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1answer
73 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 ...
2
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1answer
104 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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160 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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60 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 ...