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Statistical property
The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution
Standard_error
Statistical measure
Clustered standard errors (or Liang-Zeger standard errors) are measurements that estimate the standard error of a regression parameter in settings where
Clustered_standard_errors
Connected input and output streams for computer programs
input/output (I/O) connections are called standard input (stdin), standard output (stdout) and standard error (stderr). Originally I/O happened via a physically
Standard_streams
Asymptotic variances under heteroskedasticity
standard errors (or simply robust standard errors), Eicker–Huber–White standard errors (also Huber–White standard errors or White standard errors),
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Statistic expressing the amount of random sampling error in a survey's results
The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence
Margin_of_error
Measure of variation in statistics
unit as the data. Standard deviation can also be used to calculate standard error for a finite sample, and to determine statistical significance. When
Standard_deviation
Incorrect or inaccurate action
An error (from the Latin errāre, meaning 'to wander') is an inaccurate or incorrect action, thought, or judgement. In statistics, "error" refers to the
Error
Test statistic
squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see Ordinary least squares
Reduced_chi-squared_statistic
specified by an IETF standard. Microsoft's Internet Information Services (IIS) web server expands the 4xx error space to signal errors with the client's
List_of_HTTP_status_codes
Statistical amount
random variables with variance σ 2 {\displaystyle \sigma ^{2}} , the standard error of the weighted mean, σ x ¯ {\displaystyle \sigma _{\bar {x}}} , can
Weighted_arithmetic_mean
Measure of the error of an estimator
being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE
Mean_squared_error
Middle quantile of a data set or probability distribution
relative standard error of the median will be ( π / 2 ) 1 2 ≈ 1.25 {\displaystyle (\pi /2)^{\frac {1}{2}}\approx 1.25} , or 25% greater than the standard error
Median
Statistics concept
Observational error Propagation of error Probable error Random and systematic errors Reduced chi-squared statistic Regression dilution Sampling error Standard error
Errors_and_residuals
Concepts from statistical hypothesis testing
Type I error, or a false positive, is the incorrect rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false
Type_I_and_type_II_errors
Method for estimating the unknown parameters in a linear regression model
square root of s2 is called the regression standard error, standard error of the regression, or standard error of the equation. It is common to assess the
Ordinary_least_squares
Statistical confidence interval for success counts
1-{\tfrac {\alpha }{2}}\ } quantile of a standard normal distribution (i.e., the probit) corresponding to the target error rate α . {\displaystyle \ \alpha
Binomial proportion confidence interval
Binomial_proportion_confidence_interval
Graphical representations of the variability of data
reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence
Error_bar
Effect of variables' uncertainties on the uncertainty of a function based on them
quantified in terms of the standard deviation, σ, which is the positive square root of the variance. The value of a quantity and its error are then expressed
Propagation_of_uncertainty
Information describing a problematic situation
(CLI), an error message may be printed to a standard stream. A program may write an error message to a log file. The proper design of error messages is
Error_message
How many standard deviations apart from the mean an observed datum is
deviation of 1. Coefficient of variation Error function Mahalanobis distance Normalization (statistics) Omega ratio Standard normal deviate Studentized residual
Standard_score
Measure of statistical dispersion
error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation. The probable error can
Probable_error
Internet error message
retrieve the requested page. Some websites report a "not found" error by returning a standard web page with a "200 OK" response code, falsely reporting that
HTTP_404
Probability distribution
quantile function of the standard normal distribution is called the probit function, and can be expressed in terms of the inverse error function: Φ − 1 ( p
Normal_distribution
Probability distribution of the possible sample outcomes
distribution theory. The standard deviation of the sampling distribution of a statistic is referred to as the standard error of the statistic. For the
Sampling_distribution
Statistical error
resulting sample statistics can be used to estimate the standard error on the sample. The term "sampling error" has also been used in a related but fundamentally
Sampling_error
Statistical error measure
mean absolute error is a common measure of forecast error in time series analysis, sometimes used in confusion with the more standard definition of mean
Mean_absolute_error
Measure of linear correlation
and standard error = SE = 1 n − 3 , {\displaystyle ={\text{SE}}={\frac {1}{\sqrt {n-3}}},} where n is the sample size. The approximation error is lowest
Pearson correlation coefficient
Pearson_correlation_coefficient
Measure of inequality of a statistical distribution
calculation of the jackknife estimate for the standard error. Economist David Giles argued that the standard error of the estimate of A can be used to derive
Gini_coefficient
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
when the number of replicates varies across samples − in this case standard error in percent is suggested to be superior. If measurements do not have
Coefficient_of_variation
Table of probabilities related to the normal distribution
from some population in which the mean is μ and the standard deviation is σ, the standard error is σ n : {\displaystyle {\tfrac {\sigma }{\sqrt {n}}}:}
Standard_normal_table
Sampling from a population which can be partitioned into subpopulations
have a lower standard deviation (as compared to the overall standard deviation in the population), stratification gives a smaller error in estimation
Stratified_sampling
Sigmoid shape special function
error function has the following interpretation: for a real random variable Y {\displaystyle Y} that is normally distributed with mean 0 and standard
Error_function
Reliable digital data delivery methods on unreliable channels
applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery
Error detection and correction
Error_detection_and_correction
Decision, action, or inaction by an aircraft pilot
Maraba Airport Belem Airport In aviation, pilot error generally refers to an action or decision made by a pilot that is a substantial contributing factor
Pilot_error
Type of average of a collection of numbers
arithmetic and geometric means Sample mean and covariance Standard deviation Standard error of the mean Summary statistics If NM = a and PM = b. AM =
Arithmetic_mean
GNU replacement for the Bourne shell
expansion syntax for this purpose. Redirections of Standard Input, Standard Output and Standard Error data streams are performed, including File writing
Bash_(Unix_shell)
Computer programming error
Compilation error or compile error refers to a state when a compiler fails to compile a piece of computer program source code, either due to errors in the
Compilation_error
Scheme for controlling errors in data over noisy communication channels
theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable
Error_correction_code
Measures of observational error
averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided
Accuracy_and_precision
Statistical methods for comparing samples
converted to a standardized z-statistic (using a pooled standard error) and compared to the standard normal distribution to obtain p-values or form confidence
Two-proportion_Z-test
Difference between a measured value of a quantity and its true value
Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent
Observational_error
Symbol combining both + and - signs
uncertainty bounding a range of possible errors in a measurement, often the standard deviation or standard error. The sign may also represent an inclusive
Plus–minus_sign
Statistical hypothesis test
is the sample mean from a sample X1, X2, …, Xn, of size n, s is the standard error of the mean, σ ^ = 1 n − 1 ∑ i ( X i − X ¯ ) 2 {\displaystyle {\hat
Student's_t-test
Statistical test
population standard deviation. Next calculate the z-score, which is the distance from the sample mean to the population mean in units of the standard error: z
Z-test
Statistical indicators of the deviation of a sample
identically zero, but the standard deviation should be somewhat smaller (around 75 to 85% of σ). Heteroscedasticity-consistent standard errors Interquartile Range
Robust_measures_of_scale
Ratio in statistics
difference in a number’s estimated value from its assumed value to its standard error. It is used in hypothesis testing via Student's t-test. The t-statistic
T-statistic
Statistical property
used in the past. Nowadays, standard practice in econometrics is to include heteroskedasticity-consistent standard errors instead of using GLS, as GLS
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Computer-controlled phototypesetter
output stream standard error (stderr), a standard on many systems for over 40 years, was first created because of this device. Initially, error messages from
CAT_(phototypesetter)
Header file for C programs
is a header file in the standard library of the C programming language. It defines macros for reporting and retrieving error conditions using the symbol
Errno.h
Statistical modeling method
model to allow the predictor variables X to be observed with error. This error causes standard estimators of β to become biased. Generally, the form of bias
Linear_regression
Estimation procedure for correlated data
effects) with Liang-Zeger standard errors, and in individuals using Huber-White standard errors, also known as "robust standard error" or "sandwich variance"
Generalized estimating equation
Generalized_estimating_equation
Ballistics measure of a weapon system's precision
calculates the square root of the average squared distance error, a form of the standard deviation. Another is the R95, which is the radius of the circle
Circular_error_probable
Study of collection and analysis of data
or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling
Statistics
Statistical model for a binary dependent variable
standard logistic distribution of errors and the second a standard normal distribution of errors. Other sigmoid functions or error distributions can be used instead
Logistic_regression
Statistical tool
a time-series dataset produces Newey–West standard errors. In SAS, the Newey–West corrected standard errors can be obtained in PROC AUTOREG and PROC MODEL
Newey–West_estimator
Amount of discretion an appellate court applies to overturning a lower court's decision
A low standard of review means that the decision under review will be varied or overturned if the reviewing court considers there is any error at all
Standard_of_review
Set of statistical processes for estimating the relationships among variables
)+e_{i}} In the standard regression model, the independent variables X i {\displaystyle X_{i}} are assumed to be free of error. The errors-in-variables model
Regression_analysis
Statistical method
impossible or requires complicated formulas for the calculation of standard errors. The bootstrap was first described by Bradley Efron in "Bootstrap methods:
Bootstrapping_(statistics)
Study of health and disease within a population
typographical error during coding. Random error affects measurement in a transient, inconsistent manner and it is impossible to correct for random error. There
Epidemiology
Code that indicates the nature of an error
several different standards for error code values, depending on the specific API being used. The usage of error codes as an error handling strategy is
Error_code
Statistical measure in mathematical model
The standard error of the estimate of βj is the square root of the j + 1 diagonal element of s2(X′X)−1, where s is the root mean squared error (RMSE)
Variance_inflation_factor
Paradigm for the design, analysis, and scoring of tests
standard error of person estimate gives an estimate of the variance of the errors, ϵ n {\displaystyle \epsilon _{n}} , across persons. The standard errors
Item_response_theory
Statistical measure of how far values spread from their average
({\bar {X}})={\sqrt {{({S_{x}}^{2}+{\bar {X}}^{2})}/{n}}}} (see Standard error § Standard error of the sample mean). The scaling property and the Bienaymé
Variance
Score from a test designed to assess intelligence
approximately 10 points and reported standard error of measurement can be as low as about three points. Reported standard error may be an underestimate, as it
Intelligence_quotient
Approximate distinct counting algorithm
is able to estimate cardinalities of > 109 with a typical accuracy (standard error) of 2%, using 1.5 kB of memory. HyperLogLog is an extension of the earlier
HyperLogLog
Any of a set of standard configurations of Redundant Arrays of Independent Disks
sectors/read errors (hard errors), they do not provide any protection against data loss due to catastrophic failures (fire, water) or soft errors such as user
Standard_RAID_levels
Method of data analysis
variables and often on binary allele markers. The lack of any measures of standard error in PCA are also an impediment to more consistent usage. In August 2022
Principal_component_analysis
Mechanism for inter-process communication using message passing
the standard error stream should also be merged with the standard output and fed to the next process. The Bash shell can also merge standard error with
Pipeline_(Unix)
Statistical measure of variability
form is used in, e.g., the probable error. In the case of complex values (X+iY), the relation of MAD to the standard deviation is unchanged for normally
Median_absolute_deviation
Range to estimate an unknown parameter
(December 2005). "Researchers misunderstand confidence intervals and standard error bars". Psychological Methods. 10 (4): 389–396. doi:10.1037/1082-989X
Confidence_interval
Form of interprocess communication
to redirect one standard file handle to another. The most popular variation is to merge standard error into standard output so error messages can be processed
Redirection_(computing)
Linear regression model with a single explanatory variable
{\displaystyle \varepsilon _{i}} . This assumption is used when deriving the standard error of the slope and showing that it is unbiased. In this framing, when
Simple_linear_regression
Statistic measuring inter-rater agreement for categorical items
but not of sufficient magnitude to satisfy investigators. Still, its standard error has been described and is computed by various computer programs. Confidence
Cohen's_kappa
Programming language for statistics
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.055 on 4 degrees of freedom Multiple R-squared: 0.9583, Adjusted
R_(programming_language)
Measure of investment risk
e., the standard deviation of the residuals) is called "tracking error" in the investment field. The latter way to compute the tracking error complements
Tracking_error
Theory and technique of psychological measurement
the location of a test-taker on a given latent trait as well as the standard error of measurement of that location. For example, a university student's
Psychometrics
Approximation method in statistics
relationship". In standard regression analysis that leads to fitting by least squares there is an implicit assumption that errors in the independent
Least_squares
Statistical test
) {\displaystyle \operatorname {se} ({\widehat {\theta }})} is the standard error (SE) of the maximum likelihood estimate (MLE), the square root of the
Wald_test
Graphical representation of the distribution of numerical data
is 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
Statistical considerations on how many observations to make
(iid) sample of size n, where each data value has variance σ2, the standard error of the sample mean is: σ n . {\displaystyle {\frac {\sigma }{\sqrt {n}}}
Sample_size_determination
Number of values in the final calculation of a statistic that are free to vary
realistic estimate for, e.g., the error variance σ2, which in its turn scales the unknown parameters' a posteriori standard deviation; the degree of freedom
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Reciprocal of the statistical variance
standard deviation; as well as the standard error and the confidence interval (or its half-width, the margin of error). One particular use of the precision
Precision_(statistics)
Diagnostic plot of binary classifier ability
thought of as a plot of the statistical power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample
Receiver operating characteristic
Receiver_operating_characteristic
Selection of data points in statistics
Estimate, With a Specified Tolerable Error, the Average for Characteristic of a Lot or Process ASTM E141 Standard Practice for Acceptance of Evidence Based
Sampling_(statistics)
ASCII-compatible variable-width encoding of Unicode
error. This is not a good idea as a search for a space character would find the one hidden in the error. Since Unicode 6 (October 2010) the standard (chapter 3)
UTF-8
Statistical procedure
estimated value of a parameter from its hypothesized value divided by its standard error, popularized through Fisher’s publishment titled Applications of “Student’s”
Normalization_(statistics)
Mathematical relation assigning a probability event to a cost
decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables
Loss_function
Regression models accounting for possible errors in independent variables
variables. In contrast, standard regression models assume that those regressors have been measured exactly, or observed without error; as such, those models
Errors-in-variables_model
Diagnostic test or benchmark
bias induced by the study itself. Calibration errors can lead to misdiagnosis. Sometimes "gold standard test" refers to the best-performing test available
Gold_standard_(test)
Measure of the joint variability
"observation error covariance matrix" is constructed to represent the magnitude of combined observational errors (on the diagonal) and the correlated errors between
Covariance
Test statistic
ordinary least squares (OLS) standard errors for the regression coefficients to underestimate the true standard errors. As a consequence, if positive
Durbin–Watson_statistic
Output option in some software programs
in the command line, verbose output is typically output in standard output or standard error. Many command line programs, such as cURL or Bash, can be
Verbose_mode
Statistical relationship
{\displaystyle y} are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but
Correlation
Procedure to estimate standard deviation from a sample
c_{4}(n)} is that the standard error of s is σ 1 − c 4 2 {\displaystyle \sigma {\sqrt {1-c_{4}^{2}}}} , while the standard error of the unbiased estimator
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Branch of statistics
Kaplan–Meier product-limit estimate. std.err is the standard error of the estimated survival. The standard error of the Kaplan–Meier product-limit estimate it
Survival_analysis
Shell command for copying and converting file data
Ctrl+Z (the usual for Windows) On completion, dd writes statistics to standard error. The format is standardized in POSIX. The manual page for GNU dd does
Dd_(Unix)
Statistical hypothesis test
also distributed as χ2 distribution with k − 1 degrees of freedom, the error in this approximation would not affect practical decisions. This conclusion
Chi-squared_test
benefited from the error may need to prove the error was harmless beyond a reasonable doubt. Standard of review "Federal Rules Of Evidence (2015) | Federal
Harmless_error
Error that causes a program to abort
IEEE floating point standard, this creates an infinity instead). In some systems, such as macOS and Microsoft Windows, a fatal error causes the operating
Fatal_exception_error
Statistic which divides a data set into 100 parts and analyzes it as a percentage
1 {\displaystyle {\frac {1}{N+1}}} is also excluded and would cause an error.) x = f ( p , N ) = { 1 , p ∈ [ 0 , 1 N + 1 ] p ( N + 1 ) , p ∈ ( 1 N
Percentile
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