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Statistical measure
The root mean square deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and
Root_mean_square_deviation
Square root of the mean square
defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the
Root_mean_square
Measure of the error of an estimator
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures
Mean_squared_error
Measure of distance between atoms of superimposed proteins
In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance
Root mean square deviation of atomic positions
Root_mean_square_deviation_of_atomic_positions
Calculations in probability theory
Squared deviations from the mean (SDM) result from squaring deviations. In probability theory and statistics, the definition of variance is either the
Squared deviations from the mean
Squared_deviations_from_the_mean
Measure of the deviation of position over time
variation of the square root of MSD versus downwind distance are commonly used in studying the dispersion phenomenon. Root-mean-square deviation of atomic positions:
Mean_squared_displacement
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard deviation (RSD), is a standardized measure of dispersion
Coefficient_of_variation
Type of algorithm
calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful for point-set
Kabsch_algorithm
Measure of variation in statistics
computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample
Standard_deviation
Measure of forecasting quality
the Mean absolute error divided by the Mean Absolute Deviation. Mean squared error Mean absolute error Mean absolute percentage error Root-mean-square deviation
Mean_absolute_scaled_error
Concept in signal processing
_{n=0}^{N-1}\left|x[m,n]\right|^{2}}}} Root-mean-square deviation is derived from MSE by taking the square root of the MSE. It downscale the MSE, providing
Similarity (signal processing)
Similarity_(signal_processing)
Test statistic
the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic
Reduced_chi-squared_statistic
Measure of statistical error
mean-square error Squared deviations Peak signal-to-noise ratio Root mean square deviation Errors and residuals in statistics Khan, Aman U.; Hildreth, W
Mean_percentage_error
Indicator for how well data points fit a line or curve
coefficient Proportional reduction in loss Regression model validation Root mean square deviation Stepwise regression Steel, R. G. D.; Torrie, J. H. (14 July 2008)
Coefficient_of_determination
Statistical measure of how far values spread from their average
the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance. Technically
Variance
Procedure to estimate standard deviation from a sample
positive values then the estimate of the variance (and its square root, the standard deviation) will be biased low. That is, the actual variability of the
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Number whose square is a given number
mathematics, a square root of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of
Square_root
Average of squared values of a sample
mean square. The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation
Mean_square
Statistical error measure
related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE)
Mean_absolute_error
Measure of similarity between two protein structures
structural alignment. An often used structural similarity measure is root-mean-square deviation (RMSD). Because RMSD = ∑ i = 1 L d i 2 / L {\displaystyle ={\sqrt
Template_modeling_score
Summary statistic of variability
need for squaring) and easier to understand. For the normal distribution, the ratio of mean absolute deviation from the mean to standard deviation is 2 /
Average_absolute_deviation
Measure of similarity between two protein structures
It is intended as a more accurate measurement than the common root-mean-square deviation (RMSD) metric - which is sensitive to outlier regions created
Global_distance_test
Value that appears most often in a set of data
standard deviations of the mean, and the root mean square deviation about the mode is between the standard deviation and twice the standard deviation. An example
Mode_(statistics)
Artificial intelligence program by DeepMind
achieved a median score of 87.[citation needed] Measured by the root-mean-square deviation (RMS-D) of the placement of the alpha-carbon atoms of the protein
AlphaFold
Specific probability distribution function, important in physics
The mean square speed ⟨ v 2 ⟩ {\displaystyle \langle v^{2}\rangle } is the second-order raw moment of the speed distribution. The "root mean square speed"
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Measurement in communication theory
Another method of specifying spectral width is a special case of root-mean-square deviation where the independent variable is wavelength, λ, and f (λ) is
Spectral_width
Statistical property
error of the mean equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure
Standard_error
Proportion of observed intensity to ideal intensity, in astronomical imaging
{\displaystyle S\approx {e^{-\sigma ^{2}}}} where sigma (σ) is the root mean square deviation over the aperture of the wavefront phase: σ 2 = ⟨ ( ϕ − ϕ ¯ )
Strehl_ratio
Aligning molecular sequences using sequence and structural information
are a superposition of the atomic coordinate sets and a minimal root mean square deviation (RMSD) between the structures. The RMSD of two aligned structures
Structural_alignment
Correction for sample variance bias
population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e., using
Bessel's_correction
Statistics concept
observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the
Errors_and_residuals
Property of having a unique mode or maximum value
the mean is μ and ω is the root mean square deviation from the mode. It can be shown for a unimodal distribution that the median ν and the mean μ lie
Unimodality
Prediction method in molecular modeling
a ligand. Fitness is typically quantified by calculating the root-mean-square deviation (RMSD) of the non-hydrogen atoms between the docked pose and the
Docking_(molecular)
Chain molecule which folds in predictable ways while in solution
conditions. The change in structure is measured by calculating the root mean square deviation from the backbone atomic position of the favored structure. The
Foldamer
Statistical value representing the center or average of a distribution
different rescaling of the different dimensions. Quadratic mean (often known as the root mean square) useful in engineering, but not often used in statistics
Central_tendency
Ballistics measure of a weapon system's precision
DRMS (distance root mean square), calculates the square root of the average squared distance error, a form of the standard deviation. Another is the
Circular_error_probable
Type of biological prediction
experimentally determined protein structures using metrics such as root-mean-square deviation (RMSD). The median RMSD between different experimental structures
Protein_structure_prediction
points that are 1 standard deviation away from the mean of x {\displaystyle x} and also 1 standard deviation away from the mean of y {\displaystyle y} are
Standard_deviation_line
Product of a number by itself
These deviations are squared, then a mean is taken of the new set of numbers (each of which is positive). This mean is the variance, and its square root is
Square_(algebra)
Bound on probability of a random variable being far from its mean
standard deviation (the square root of the variance). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in
Chebyshev's_inequality
regression Robust statistics Root mean square Root-mean-square deviation Root mean square deviation (bioinformatics) Root mean square fluctuation Ross's conjecture
List_of_statistics_articles
Statistical distance measure
\mathbf {S} } is the symmetric square root of Σ {\displaystyle \mathbf {\Sigma } } , which is the standard deviation matrix. This gives us the equivalent
Mahalanobis_distance
model these complex physicochemical bindings at the target site. Root Mean Square Deviation is the standard method of evaluating various software performance
Protein–ligand_docking
Algorithm for analyzing noisy data streams
signal. In cases that are most computationally straightforward, root mean square deviation can be used as the decision criterion for the lowest error probability
Maximum likelihood sequence estimation
Maximum_likelihood_sequence_estimation
Accuracy of light source in showing color of objects
spectral band that is important for the application. Use the root-mean-square deviation instead. The metric is not perceptual; all errors are equally
Color_rendering_index
Method of protein structure prediction using other known proteins
with decreasing sequence identity; a typical model has ~1–2 Å root mean square deviation between the matched Cα atoms at 70% sequence identity but only
Homology_modeling
Concept in quantum mechanics
^{2}}},} where Δ H ¯ {\displaystyle \Delta {\bar {H}}} is the root mean square deviation of the system Hamiltonian averaged over the interval of interest
Adiabatic_theorem
Concept that permeates much of inferential statistics and descriptive statistics
of the overall sum of squares. The distance from any point in a collection of data, to the mean of the data, is the deviation. This can be written as
Partition_of_sums_of_squares
Rule for calculating an estimate of a given quantity based on observed data
error. The standard deviation of an estimator θ ^ {\displaystyle {\widehat {\theta }}} of θ {\displaystyle \theta } (the square root of the variance), or
Estimator
Type of average of a collection of numbers
\dotsc ,x_{n}} , then the arithmetic mean of the numbers does this best since it minimizes the sum of squared deviations from the typical value: the sum of
Arithmetic_mean
Basic structural unit of DNA packaging in eukaryotes
yeast histones results in electron density maps with an overall root mean square deviation of only 1.6Å. The nucleosome core particle (shown in the figure)
Nucleosome
Statistical amount
variance vary accordingly from N − 1 down to 0. The standard deviation is simply the square root of the variance above. As a side note, other approaches have
Weighted_arithmetic_mean
Measure of statistical dispersion
whereas the standard deviation is defined in terms of the deviation from the arithmetic mean. Because the standard deviation squares its differences, it
Mean_absolute_difference
Geometric condition for workpieces and tools
flatness measures: least squares reference plane minimum zone reference planes local flatness deviation root-mean-square flatness deviation The two-dimensional
Flatness_(manufacturing)
Statistical measure of the magnitude of a phenomenon
population mean within the jth group of the total K groups, and σ the equivalent population standard deviations within each groups. SS is the sum of squares in
Effect_size
Crystallography and inorganic chemistry software
of the faces of octahedron Jahn–Teller distortion parameters Root-mean-square deviation of atomic positions Simple and flexible processes of use Cross-platform
OctaDist
Software for protein modeling and analysis
(unnormalized-GDT) for absolute global quality of a 3D model and per-position root mean square deviation (RMSD) for absolute local quality at each residue of a 3D model
RaptorX
Distributed computing project simulating protein folding
native state of the villin protein to within 1.8 angstrom (Å) root mean square deviation (RMSD) from the crystalline structure experimentally determined
Folding@home
N-th root of the product of n numbers
numbers is the square root of their product, for example with numbers 2 {\displaystyle 2} and 8 {\displaystyle 8} the geometric mean is 2 ⋅ 8 = {\displaystyle
Geometric_mean
case) is minimized. The “SuperPose” web server uses “RMSD” or Root-Mean-Square Deviation as a difference measure to find the optimal pairwise or multiple
SuperPose
Bioinformatics subfield
Cα). Usually, the alignment quality is evaluated based on the root-mean-square deviation (RMSD) of atomic positions, i.e., the average distance between
Structural_bioinformatics
Unit for the arithmetic difference of two percentages
ejection fraction, statistical deviations and related descriptive statistics, including the standard deviation and root-mean-square error, the result should
Percentage_point
Feature of some stochastic processes
non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over
Unit_root
Approximation method in statistics
function Root mean square Squared deviations from the mean Charnes, A.; Frome, E. L.; Yu, P. L. (1976). "The Equivalence of Generalized Least Squares and Maximum
Least_squares
Mathematical diagram
statistics: the Pearson correlation coefficient, the root-mean-square error (RMSE) error, and the standard deviation. Although Taylor diagrams have primarily been
Taylor_diagram
optimal alignment of two sets of points in order to compute the root mean squared deviation between two protein structures. Maximum parsimony (phylogenetics):
List_of_algorithms
Method to detect power-law scaling in time series
,Y_{N,n}} be the resulting piecewise-linear fit. Compute the root-mean-square deviation from the local trend (local fluctuation): F ( n , i ) = 1 n ∑
Detrended fluctuation analysis
Detrended_fluctuation_analysis
level/basis set/solvent model, accuracy of prediction (linear correlation factor and root mean square deviation), calculation time on personal computer (blue).
Nuclear magnetic resonance spectroscopy of carbohydrates
Nuclear_magnetic_resonance_spectroscopy_of_carbohydrates
Estimation method that minimizes the mean square error
signal processing, a minimum mean square error estimator (MMSE estimator) is an estimation method which minimizes the mean square error (MSE), which is a common
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Measure of linear correlation
slope of the regression line Geometric mean of the two regression slopes Square root of the ratio of two variances Mean cross-product of standardized variables
Pearson correlation coefficient
Pearson_correlation_coefficient
Probability distribution
certain ambiguity in terminology; its square root s {\displaystyle s} is called the sample standard deviation. The estimator s 2 {\textstyle s^{2}}
Normal_distribution
Method in computational chemistry
charge errors as compared to PCM. The approximations lead to a root mean square deviation in the order of 0.07 kcal/mol to the exact solutions. Explicit
Solvent_model
which is the second moment about the mean (or the standard deviation, which is the square root of the variance). The most well-known two-moment decision
Two-moment_decision_model
BOINC based volunteer computing project researching protein folding
as the accepted model changes. A graph of the accepted model's root-mean-square deviation (RMSD), which measures how structurally similar the accepted model
Rosetta@home
Statistical concept
introduces undesired bias to the estimate of the mean m {\displaystyle m} , because the forward square-root transform is not linear. Sometimes using the asymptotically
Anscombe_transform
Ratio of the desired signal to the background noise
{A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},} where A is root mean square (RMS) amplitude (for example, RMS voltage). Because many signals have
Signal-to-noise_ratio
Method for estimating variance of several different populations
t-test. The square root of a pooled variance estimator is known as a pooled standard deviation (also known as combined standard deviation, composite standard
Pooled_variance
Statistics concept
is called sum squared prediction error. The root mean squared prediction error is the square root of MSPE: RMSPE=√MSPE. The mean squared prediction error
Mean_squared_prediction_error
Theory in computational chemistry
NBO 7.0 version of their program. In this program, the matrix root-mean square deviation (Frobenius norm) of the resonance weights is calculated. Δ ω =
Natural_resonance_theory
comparison C-Map Pair No site D. Pelta et al. 2008 Structal Least Squares Root Mean Square deviation minimization by dynamic programming Cα Pair No server download
Structural_alignment_software
Probability distribution
linear (absolute) deviations rather than the square deviations from the mean. Therefore, the effect of very large deviations from the mean are not as overly
Beta_distribution
Statistical property
of the population variance is not a mean-unbiased estimator of the population standard deviation: the square root of the unbiased sample variance, the
Bias_of_an_estimator
Probability distribution
by taking the ratio of variables from the normal distribution and the square-root of the χ² distribution. If we use instead of the normal distribution
Student's_t-distribution
Statistical indicators in signal processing
parameter represents the mean frequency or the proportion of standard deviation of the power spectrum. This is defined as the square root of variance of the
Hjorth_parameters
Measurement in finance
{\displaystyle DR} is the target semi-deviation (the square root of target semi-variance), termed downside deviation. D R {\displaystyle DR} is expressed
Sortino_ratio
Graphical representation of the distribution of numerical data
less sensitive than the standard deviation to outliers in data. This approach of minimizing integrated mean squared error from Scott's rule can be generalized
Histogram
Estimate of an interval in which future observations will fall
credible intervals may be used to estimate the population mean μ and population standard deviation σ of the underlying population, while prediction intervals
Prediction_interval
Degree of variation of a trading price series over time
with the square-root of time as time increases, because some fluctuations are expected to cancel each other out, so the most likely deviation after twice
Volatility_(finance)
Ratio in statistics
small or the population standard deviation is unknown. For example, the t-statistic is used in estimating the population mean from a sampling distribution
T-statistic
{f} }={\mathrm {RMS} \over \mathrm {ARV} }.} Average absolute deviation Root mean square Form factor (electronics) True RMS converter Blackburn, James
Average_rectified_value
Probability distribution
k} independent, normally distributed random variables with mean 0 and standard deviation 1, then the statistic Y = ∑ i = 1 k Z i 2 {\displaystyle Y={\sqrt
Chi_distribution
Middle quantile of a data set or probability distribution
variability: the range, the interquartile range, the mean absolute deviation, and the median absolute deviation. For practical purposes, different measures of
Median
Numeric quantity representing the center of a collection of numbers
Heronian mean Identric mean Lehmer mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root mean square (quadratic mean) Rényi's
Mean
Statistic used in signal detection theory
Σ {\displaystyle \mathbf {\Sigma } } , (whose symmetric square-root, the standard deviation matrix, is S {\displaystyle \mathbf {S} } ), this generalizes
Sensitivity_index
harmonic mean, G is geometric mean, L is the logarithmic mean, A is the arithmetic mean, R is the root mean square and C is the contraharmonic mean. Unless
Contraharmonic_mean
Statistical model validation technique
predicted is continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize the errors.
Cross-validation_(statistics)
Method for model fitting in statistics
given by M i j β {\displaystyle M_{ij}^{\beta }} . The standard deviation is the square root of variance, σ i = M i i β {\displaystyle \sigma _{i}={\sqrt
Weighted_least_squares
Generalization of means
f mean corresponds to the power mean with exponent p {\displaystyle \ p\ } (e.g., for p = 2 {\displaystyle \ p=2\ } one gets the root mean square
Quasi-arithmetic_mean
Measure of frequency stability in clocks and oscillators
{\displaystyle \sigma _{y}^{2}(\tau )} . The Allan deviation (ADEV), also known as sigma-tau, is the square root of the Allan variance, σ y ( τ ) {\displaystyle
Allan_variance
Statistical measure
Gini's mean difference introduced in 1912 (but Gini did not work with centered distances). The distance standard deviation is the square root of the distance
Distance_correlation
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
Boy/Male
Hindu, Indian, Indonesian, Kenyan
Root
Surname or Lastname
Dutch (also de Roos) and Swiss German
Dutch (also de Roos) and Swiss German : habitational name for someone living at a house distinguished by the sign of a rose.Dutch (also de Roos) : metonymic occupational name for someone who grew roses, from roos ‘rose’.Dutch : from the female personal name Rosa (Latin rosa ‘rose’).Dutch : nickname from roos ‘erysipelas’, an infection which causes reddening of the skin and scalp, applied presumably to someone with a ruddy complexion.Swiss German : from a personal name formed with hrÅd ‘renown’.Swedish and Danish (of German origin) : as 1.Swedish : variant of Ros.English and Scottish : variant of Ross 2.
Male
English
 English occupational surname transferred to forename use, from the Latin word decanus, DEAN means "dean; ecclesiastical supervisor."
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Surname or Lastname
English
English : variant of Squire.
Female
English
Scottish form of French Jeanne, JEAN means "God is gracious." Compare with masculine Jean.
Boy/Male
Egyptian
Root.
Boy/Male
English American
Shieldbearer.
Male
English
Anglicized form of Irish Gaelic Cian, KEAN means "ancient, distant."
Surname or Lastname
English
English : patronymic from Squire.
Male
French
A derivative of Anglo-Norman French Jehan, JEAN means "God is gracious." Compare with feminine Jean.
Surname or Lastname
English
English : nickname for a cheerful person, from Middle English rote ‘glad’ (Old English rÅt).English : metonymic occupational name for a player on the rote, an early medieval stringed instrument (Middle English, Old French rote, of uncertain origin but apparently ultimately akin to Welsh crwth).Dutch : topographic name for someone who lived by a retting place (Dutch root, a derivative of ro(o)ten ‘to ret’, akin to modern English rot), a place where flax is soaked in tubs of water until the stems rot to release the linen fibers.
Surname or Lastname
English
English : patronymic from Root 1.
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Surname or Lastname
English
English : metonymic occupational name for a maker or seller of boots, from Middle English, Old French bote (of unknown origin).Dutch and North German : metonymic occupational name for a boatman, from Dutch boot ‘boat’.
Female
English
Pet form of Welsh Mared, MEGAN means "pearl."Â
Boy/Male
British, English
Spear-man
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
Male
English
Anglicized form of Irish Gaelic Seán, SEAN means "God is gracious."
Male
English
French form of English Stewart, STUART means "house guard; steward." In use by the English and Scottish.
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
Girl/Female
Muslim/Islamic
Little light rain
Boy/Male
Hindu, Indian, Islamic
Fighter; Cute
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu, Traditional
Peacock Feather
Girl/Female
Hebrew
Joyous song.
Boy/Male
American, British, English
Rich and Powerful Ruler; Strong Ruler
Boy/Male
Indian, Punjabi, Sikh
Lordship
Biblical
rebellion (but probably an unknown Assyrian word)
Male
Native American
Native American Miwok name MISU means "rippling brook."
Surname or Lastname
English (mainly northern)
English (mainly northern) : topographic name for someone who lived on a hill or at the rear of a settlement, from Middle English bakke ‘back’, ‘spine’ + man ‘man’. Compare Backer.Swedish : ornamental name composed of the elements back(e) ‘hill’ + man ‘man’.Swedish (Bäck(man)) : ornamental name composed of the elements bäck ‘stream’ + man ‘man’.German : variant of Bachmann.German : occupational name for a baker or employee of a master baker, from backen ‘to bake’ + man(n) ‘man’. Compare Beckmann.
Boy/Male
English
From the Old English 'cuth' meaning famous, and 'beorth' meaning bright.
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
ROOT MEAN-SQUARE-DEVIATION
n.
To place at right angles with the keel; as, to square the yards.
a.
Rendering equal justice; exact; fair; honest, as square dealing.
n.
An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop.
a.
Forming a right angle; as, a square corner.
n.
To multiply by itself; as, to square a number or a quantity.
a.
Full of roots; as, rooty ground.
n.
A square. See 1st Squire.
n.
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
n.
A square piece or fragment.
imp. & p. p.
of Square
n.
Having the toe square.
a.
Having four equal sides and four right angles; as, a square figure.
n.
A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean. A geometrical mean is the square root of the product of the quantities.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
n.
A square; a measure; a rule.
v. i.
To fix the root; to enter the earth, as roots; to take root and begin to grow.
n.
Hence, anything which is square, or nearly so
a.
Having a shape broad for the height, with rectilineal and angular rather than curving outlines; as, a man of a square frame.
a.
Even; leaving no balance; as, to make or leave the accounts square.
superl.
Of poor quality; as, mean fare.