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Exact statistical hypothesis test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more
Permutation_test
Statistical test of whether two populations have equal means
where one could possibly perform Welch's t-test. A permutation and bootstrapped version of the Welch t-test has also been developed to address distributional
Welch's_t-test
Family of statistical methods based on sampling of available data
are: Permutation tests (also re-randomization tests) for generating counterfactual samples Bootstrapping Cross validation Jackknife Permutation tests rely
Resampling_(statistics)
Experiment methodology
A/B testing (also known as bucket testing, split-run testing or split testing) is a user-experience research method. A/B tests consist of a randomized
A/B_testing
Measure of linear correlation
discussed below. Permutation tests provide a direct approach to performing hypothesis tests and constructing confidence intervals. A permutation test for Pearson's
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical hypothesis test
Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It
Student's_t-test
Statistical test comparing two probability distributions
and Kuiper tests". Journal of Statistical Computation and Simulation. doi:10.1080/00949655.2026.2721410. Præstgaard, J. T. (1995). "Permutation and bootstrap
Kolmogorov–Smirnov_test
Statistical hypothesis test
A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large
Chi-squared_test
Method of statistical inference
statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical
Statistical_hypothesis_test
Statistical test
Permutational multivariate analysis of variance (PERMANOVA), is a non-parametric multivariate statistical permutation test. PERMANOVA is used to compare
Permutational analysis of variance
Permutational_analysis_of_variance
Statistical test
mind that all permutation tests are exact tests, but not all exact tests are permutation tests. The basic equation underlying exact tests is Pr ( exact
Exact_test
Nonparametric test of the null hypothesis
good. Alternatively, the null distribution can be approximated using permutation tests and Monte Carlo simulations. Some books tabulate statistics equivalent
Mann–Whitney_U_test
Statistical test
testing its statistical significance. The Mantel test deals with this problem. The procedure adopted is a kind of randomization or permutation test.
Mantel_test
Nonparametric measure of rank correlation
or equal to the observed r, given the null hypothesis, by using a permutation test. An advantage of this approach is that it automatically takes into
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Statistical hypothesis test for forecasting
The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in
Granger_causality
Statistical test used on paired nominal data
McNemar's test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs
McNemar's_test
Test of normality in frequentist statistics
Shapiro–Wilk test is a test of normality. It was published in 1965 by Samuel Sanford Shapiro and Martin Wilk. The Shapiro–Wilk test tests the null hypothesis
Shapiro–Wilk_test
Probabilistic problem-solving algorithm
approximate randomization and permutation tests. An approximate randomization test is based on a specified subset of all permutations (which entails potentially
Monte_Carlo_method
Statistical hypothesis test
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based
Wilcoxon_signed-rank_test
Theory and technique of psychological measurement
generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. Psychometrics is concerned
Psychometrics
Statistical hypothesis test
An F-test is a statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple
F-test
Evaluates how likely it is that any difference between data sets arose by chance
Pearson's chi-squared test or Pearson's χ 2 {\displaystyle \chi ^{2}} test is a statistical test applied to sets of categorical data to evaluate how likely
Pearson's_chi-squared_test
Statistical test that compares goodness of fit
In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically
Likelihood-ratio_test
Statistical interpretation with many tests
multiplicity or multiple testing problem occurs when many statistical tests are performed on the same dataset. Each test has its own chance of a Type
Multiple_comparisons_problem
Metric for fit of statistical models
Anderson–Darling test Berk-Jones tests Shapiro–Wilk test Chi-squared test Akaike information criterion Hosmer–Lemeshow test Kuiper's test Kernelized Stein
Goodness_of_fit
Statistical measure of association
coefficient. χ 2 {\displaystyle \chi ^{2}} is derived from Pearson's chi-squared test n {\displaystyle n} is the grand total of observations and k {\displaystyle
Cramér's_V
Generalization of the one-dimensional normal distribution to higher dimensions
data. Multivariate normality tests include the Cox–Small test and Smith and Jain's adaptation of the Friedman–Rafsky test created by Larry Rafsky and Jerome
Multivariate normal distribution
Multivariate_normal_distribution
Non-parametric method for testing whether samples originate from the same distribution
The Kruskal–Wallis test by ranks, Kruskal–Wallis H {\displaystyle H} test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks
Kruskal–Wallis_test
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
comparing CV values, for example the modified signed-likelihood ratio (MSLR) test for equality of CVs. Comparing coefficients of variation between parameters
Coefficient_of_variation
Statistical test
A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution
Z-test
Type of statistical test
In statistics, a rank test is any test involving ranks. Rank tests are related to permutation tests. The motivation to test differences between samples
Rank_test
Term in statistical hypothesis testing
using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and
Power_(statistics)
Statistical measure of how far values spread from their average
parametric tests have been proposed: these include the Barton–David–Ansari–Freund–Siegel–Tukey test, the Capon test, Mood test, the Klotz test and the Sukhatme
Variance
Statistical method for handling multiple comparisons
method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed
False_discovery_rate
Statistical methods for comparing samples
The two-proportion Z-test (also called the two-sample proportion Z-test) is a statistical hypothesis test for assessing whether two groups differ in the
Two-proportion_Z-test
How many standard deviations apart from the mean an observed datum is
made. The z-score is often used in the z-test in standardized testing – the analog of the Student's t-test for a population whose parameters are known
Standard_score
Diagnostic plot of binary classifier ability
values. ROC analysis is commonly applied in the assessment of diagnostic test performance in clinical epidemiology. The ROC curve is the plot of the true
Receiver operating characteristic
Receiver_operating_characteristic
Statistical test
multiplier test and the likelihood-ratio test, the Wald test is one of three classical approaches to hypothesis testing. An advantage of the Wald test over
Wald_test
Concept in inferential statistics
In statistical hypothesis testing, a result has statistical significance when a result at least as extreme would be very infrequent if the null hypothesis
Statistical_significance
Range to estimate an unknown parameter
significance testing: as F becomes so small that the group means are much closer together than we would expect by chance, a significance test might indicate
Confidence_interval
Sequence where any order is equally likely
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a set
Random_permutation
Fourth standardized moment in statistics
K-squared test is a goodness-of-fit normality test based on a combination of the sample skewness and sample kurtosis, as is the Jarque–Bera test for normality
Kurtosis
Class of statistical tests
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random
Normality_test
Collection of statistical models
to test the hypothesis that various medical treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values:
Analysis_of_variance
Measure of variation in statistics
may or not need to be corrected. Statistical tests such as these are particularly important when the testing is relatively expensive. For example, if the
Standard_deviation
Measure of statistical dispersion
67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as Q–Q plot would be indicated
Interquartile_range
Statistical method
Monaghan S, Clipson A, Epstein R (2005). "Bootstrap methods and permutation tests" (PDF). In David S. Moore, George McCabe (eds.). Introduction to the
Bootstrapping_(statistics)
Statistical model validation technique
Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how
Cross-validation_(statistics)
Statistical phenomenon
to consider when designing any scientific experiment, data analysis, or test, which intentionally selects the most extreme events - it indicates that
Regression_toward_the_mean
Statistical test with teststatistic the number of signs of one type
The sign test is a statistical test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment
Sign_test
results. Tests for paired data include McNemar's test and the paired permutation test. Tests for unpaired data include Pearson's chi-squared test and Fisher's
Paired_data
Type of average of a collection of numbers
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Arithmetic_mean
Data visualization
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Box_plot
Statistical model for a binary dependent variable
the proposed model to every permutation of the yk and it can be shown that the maximum log-likelihood of these permutation fits will never be smaller than
Logistic_regression
Fundamental theorem in probability theory and statistics
valid justification, and can lead to seriously flawed inferences. See Z-test for where the approximation holds. The law of large numbers as well as the
Central_limit_theorem
Statistical measure of variability
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Median_absolute_deviation
criterion Pensim2 – an econometric model Percentage point Permutation code Permutation test – redirects to Resampling (statistics) Pharmaceutical statistics
List_of_statistics_articles
Scientific procedure performed to validate a hypothesis
Berry, Kenneth; Johnston, Janis; Mielke Jr, Paul (2014). A Chronicle of Permutation Statistical Methods 1920–2000, and Beyond (PDF). Springer International
Experiment
Study of collection and analysis of data
of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made
Statistics
Concept in machine learning
and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases
Double_descent
mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus
List_of_permutation_topics
Dividing things between two categories
number of classes. Typical binary classification problems include: Medical testing to determine if a patient has a certain disease or not; Quality control
Binary_classification
Statistic for rank correlation
is a permutation sampled uniformly at random from S n {\textstyle S_{n}} , the permutation group on 1 : n {\textstyle 1:n} . For each permutation, its
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Unit of information
Database Datasheet Data-driven programming Data-driven journalism Data-driven testing Data-driven learning Data-driven science Data-driven control system Data-driven
Data
Numerical measure of a statistical relationship between variables
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Correlation_coefficient
Function of the observed sample results
In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed
P-value
Diagnostic plot in multivariate statistics
significant factors or components using a scree plot is also known as a scree test. Raymond B. Cattell introduced the scree plot in 1966. A scree plot always
Scree_plot
tests are used to test the fit between a hypothesis and the data. Choosing the right statistical test is not a trivial task. The choice of the test depends
List_of_statistical_tests
Set of statistical processes for estimating the relationships among variables
residuals and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters
Regression_analysis
Table that displays the frequency of variables
variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, Boschloo's test, and Barnard's test, provided the entries
Contingency_table
Estimator for quality of a statistical model
example of a hypothesis test, consider the t-test to compare the means of two normally-distributed populations. The input to the t-test comprises a random
Akaike_information_criterion
Statistic measuring inter-rater agreement for categorical items
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Cohen's_kappa
Measure of the asymmetry of random variables
going to be positive or negative. D'Agostino's K-squared test is a goodness-of-fit normality test based on sample skewness and sample kurtosis. Other measures
Skewness
Statistical model allowing for frequent zero values
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Zero-inflated_model
Bias in causal inference
ways in which results may depend on confounding. Similarly, replication can test for the robustness of findings from one study under alternative study conditions
Confounding
Model for generating observable data in probability and statistics
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Generative_model
Approximation method in statistics
necessary to make assumptions about the nature of the experimental errors to test the results statistically. A common assumption is that the errors belong
Least_squares
Statistical considerations on how many observations to make
wide confidence intervals and risk of errors in statistical hypothesis testing. using a target variance for an estimate to be derived from the sample
Sample_size_determination
Measure of the joint variability
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Covariance
Non-parametric statistical test
The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to
Friedman_test
Statistical measure of association for two binary variables
positive cases in the data A test result that correctly indicates the presence of a condition or characteristic Type II error: A test result which wrongly indicates
Phi_coefficient
Middle quantile of a data set or probability distribution
are ranked but not numerical (e.g. working out a median grade when student test scores are graded from F to A). The result might be halfway between grades
Median
Statistic which divides a data set into 100 parts and analyzes it as a percentage
and percentile ranks are often used in the reporting of test scores from norm-referenced tests, but, as just noted, they are not the same. For percentile
Percentile
Apparent lack of pattern or predictability in events
Rainer; Paterek, Tomasz; Gröblacher, Simon (April 2007). "An experimental test of non-local realism". Nature. 446 (7138): 871–875. arXiv:0704.2529. Bibcode:2007Natur
Randomness
Time series model
_{i}\sigma _{t-i}^{2}} Generally, when testing for heteroskedasticity in econometric models, the best test is the White test. However, when dealing with time
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Sequence of data points over time
similarity index State space dissimilarity measures Lyapunov exponent Permutation methods Local flow Other univariate measures Algorithmic complexity Kolmogorov
Time_series
Statistical matching technique
(r_{0},r_{1})} . Judea Pearl has shown that there exists a simple graphical test, called the back-door criterion, which detects the presence of confounding
Propensity_score_matching
Value that appears most often in a set of data
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Mode_(statistics)
Complete set of items that share at least one property in common
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Statistical_population
Function related to statistics and probability theory
is the basis for a test statistic, the so-called likelihood-ratio test. By the Neyman–Pearson lemma, this is the most powerful test for comparing two simple
Likelihood_function
Distinction between nominal, ordinal, interval and ratio variables
added] in our view, the only sensible meaning for 'rule' is empirically testable laws about the attribute. A nominal scale consists only of a number of
Level_of_measurement
Probability distribution
role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two
Student's_t-distribution
Class of statistical models
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Generalized_linear_model
Methods employed to reduce error in science tests
that causes the effect. To control for the effect of the dilutant, the same test is run twice; once with the artificial sweetener in the dilutant, and another
Scientific_control
Graphical representation of the distribution of numerical data
of bins is motivated by maximizing the power of a Pearson chi-squared test testing whether the bins do contain equal numbers of samples. More specifically
Histogram
Form of scientific experiment
the gold standard for clinical trials. Blinded RCTs are commonly used to test the efficacy of medical interventions and may additionally provide information
Randomized_controlled_trial
Statistical property
case. Tests in regression Goldfeld–Quandt test Park test Glejser test Harrison–McCabe test Breusch–Pagan test White test Cook–Weisberg test Tests for grouped
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistical method
impossible to definitively test for validity if agents are able to determine their treatment status perfectly. However, some tests can provide evidence that
Regression discontinuity design
Regression_discontinuity_design
Canadian-American mathematical statistician
powerful unbiased (UMPU) permutation test for Type I censored data, an exact test for comparing variances, and an exact test for cross-over designs. The
Phillip_Good
Concepts from statistical hypothesis testing
incorrect rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the incorrect acceptance of a
Type_I_and_type_II_errors
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