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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
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
Experiment methodology
bandit Multivariate testing Randomized controlled trial Scientific control Stochastic dominance Test statistic Two-proportion Z-test Young, Scott W. H.
A/B_testing
Statistic used in statistical hypothesis testing
50% proportion). Chi-squared tests use the same calculations and the same probability distribution for different applications: Chi-squared tests for variance
Test_statistic
Statistical testing method
t-test#Two-sample_t-tests Welch's t-test Tukey–Duckworth test Mann–Whitney U test Two-proportion Z-test Classifier Two-sample test (C2ST) Plug in statistics using empirical
Two-sample_hypothesis_testing
Statistical test used on paired nominal data
are used for matched pairs binary data. Pearson's chi-squared test Two-proportion Z-test Chi-squared distribution McNemar, Quinn (June 18, 1947). "Note
McNemar's_test
Statistical test
Cochran–Mantel–Haenzel test is a score test. Z test Chow test Sequential probability ratio test Sup-Wald test Student's t-test Welch's t-test Two-proportion Z-test Fahrmeir
Wald_test
Index that describes the performance of a dichotomous diagnostic test
directly to inference for the difference of two proportions, and the standard machinery of the two-proportion Z-test applies. In particular, the Wald (1 − α)
Youden's_J_statistic
Statistical confidence interval for success counts
function proportion_confint() Binomial distribution Estimation theory pseudocount CDF-based nonparametric confidence interval § Pointwise band Z-test § Comparing
Binomial proportion confidence interval
Binomial_proportion_confidence_interval
Evaluates how likely it is that any difference between data sets arose by chance
test Minimum chi-square estimation Reduced chi-squared statistic Two-proportion Z-test Pearson, Karl (1900). "On the criterion that a given system of deviations
Pearson's_chi-squared_test
Statistical test based on the gradient of the likelihood function
Pearson's chi-squared test. Fisher information Uniformly most powerful test Score (statistics) Sup-LM test Two-proportion Z-test Rao, C. Radhakrishna (1948)
Score_test
Test of statistical significance
binomial test is a statistical hypothesis test used to determine whether the proportion of successes in a sample differs from an expected proportion in a
Binomial_test
Quantitative measurement of accuracy
known and calculated from data, an accuracy comparison test could be made using "Two-proportion z-test, pooled for Ho: p1 = p2". Not used very much is the
Evaluation of binary classifiers
Evaluation_of_binary_classifiers
Exact statistical hypothesis test
permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more samples
Permutation_test
Statistical method for handling multiple comparisons
hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the FDR, which is the expected proportion of "discoveries"
False_discovery_rate
Hypothesis test to compare the survival distributions of two samples
The logrank test, or log-rank test, is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate
Logrank_test
Measure of variation in statistics
the proportion of data values within z standard deviations of the mean is defined by: Proportion = erf ( z 2 ) {\displaystyle {\text{Proportion}}=\operatorname
Standard_deviation
Nonparametric test of the null hypothesis
the test wilcox.test in its "stats" package. The R function wilcoxonZ from the rcompanion package will calculate the z statistic for a Wilcoxon two-sample
Mann–Whitney_U_test
Rendering issue in 3D modeling
by the precision of the z-buffer. It can also vary as the scene or camera is changed, causing one polygon to "win" the z test, then another, and so on
Z-fighting
Statistical considerations on how many observations to make
estimate of the proportion. (Note: W/2 = margin of error.) Otherwise, the formula would be Z p ( 1 − p ) n = W / 2 , {\displaystyle Z{\sqrt {\frac {p(1-p)}{n}}}=W/2
Sample_size_determination
Statistical hypothesis test
If the test statistic T is reported, an equivalent way to compute the rank correlation is with the difference in proportion between the two rank sums
Wilcoxon_signed-rank_test
Biological test for adaptive evolution
the proportion of substitutions that resulted from positive selection (also known as directional selection). To do this, the McDonald–Kreitman test compares
McDonald–Kreitman_test
Probabilistic primality test
The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number
Miller–Rabin_primality_test
Number, approximately 1.618
ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli; it also goes by other names. Mathematicians have studied
Golden_ratio
Shorthand used in statistics
z 2 2 d z ≈ 0.6826894921 Pr ( μ − 2 σ ≤ X ≤ μ + 2 σ ) = 1 2 π ∫ − 2 2 e − z 2 2 d z ≈ 0.9544997361 Pr ( μ − 3 σ ≤ X ≤ μ + 3 σ ) = 1 2 π ∫ − 3 3 e − z
68–95–99.7_rule
Test of a machine's ability to imitate human intelligence
Socio-Technological Interpretation of the Turing Test", Philosophy & Technology, 35 (3) 68, doi:10.1007/s13347-022-00561-z, S2CID 251000575 Descartes, René (1996)
Turing_test
Statistical hypothesis test
test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in influencing the test
Chi-squared_test
Measure of linear correlation
a normal probability table. For example, if z = 2.2 is observed and a two-sided p-value is desired to test the null hypothesis that ρ = 0 {\displaystyle
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical significance test
Fisher's exact test (also the Fisher–Irwin test) is a statistical significance test used in the analysis of contingency tables. Although in practice it
Fisher's_exact_test
Statistical measure of a binary classification
statistics, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals
Sensitivity_and_specificity
Diagnostic testing for SARS-CoV-2 virus infection
pandemic. The two main types of tests detect either the presence of the virus or antibodies produced in response to infection. Molecular tests for viral presence
COVID-19_testing
Probability distribution
of a hypothesis test, a "proportion z-test", for the value of p using x / n, the sample proportion and estimator of p, in a common test statistic. For
Binomial_distribution
Function of the observed sample results
distribution of the appropriate test statistic. In this example, that would be the Z-statistic belonging to the one-sided one-sample Z-test. For each possible value
P-value
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
2018 survival video game
the player's machine. This is in contrast to the DayZ mod in Arma 2, which had a large proportion of these tasks performed on the client. By doing so
DayZ_(video_game)
Middle quantile of a data set or probability distribution
simply described as the "average") is that it is not skewed by a small proportion of extreme values, and therefore provides a better representation of the
Median
Dividing things between two categories
precision) (TP/(TP+FP)). These are the proportion of the population with a given test result for which the test is correct. with complement the false discovery
Binary_classification
Radioactive isotope of caesium
radiation from Cold War nuclear tests". Yle News. 5 April 2017. Archived from the original on 2 July 2024. "Nuclear tests in the atmosphere - Säteilyturvakeskus
Caesium-137
Table that displays the frequency of variables
between the two proportions can be assessed with a variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, Boschloo's
Contingency_table
Problem in statistics
toss)? E = Z 2 n {\displaystyle E={\frac {Z}{2\,{\sqrt {n}}}}} E = Z 2 10000 = Z 200 {\displaystyle E={\frac {Z}{2\,{\sqrt {10000}}}}={\frac {Z}{200}}} E
Checking whether a coin is fair
Checking_whether_a_coin_is_fair
Statistical measure of the magnitude of a phenomenon
Cohen's g are more intuitive (proportion) than in some other effect sizes. It is sometime used in combination with Binomial test. Confidence intervals of standardized
Effect_size
Statistical model allowing for frequent zero values
z ) = ∑ n = 0 ∞ P ( Y = n ) z n = exp ( ∑ k = 1 ∞ α k λ ( z k − 1 ) ) , ( | z | ≤ 1 ) {\displaystyle G_{Y}(z)=\sum \limits _{n=0}^{\infty }P(Y=n)z^{n}=\exp
Zero-inflated_model
Branch of statistics
Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that
Survival_analysis
Indicator for how well data points fit a line or curve
of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the
Coefficient_of_determination
Bias in causal inference
independent variable, MPG is the dependent variable, and route type (or proportion of city driving) is the confounder. Because route type affects MPG and
Confounding
Mathematical rule for inverting probabilities
the proportion with property B. P(B|A) is the proportion of outcomes with property B out of outcomes with property A, and P(A|B) is the proportion of those
Bayes'_theorem
Statistical model for a binary dependent variable
predictor into two, one for each of the two outcomes: ln Pr ( Y i = 0 ) = β 0 ⋅ X i − ln Z ln Pr ( Y i = 1 ) = β 1 ⋅ X i − ln Z {\displaystyle
Logistic_regression
Statistical measure of a test's accuracy
predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the
F-score
Chart used in statistical quality control
of control chart used to monitor the proportion of nonconforming units in a sample, where the sample proportion nonconforming is defined as the ratio
P-chart
Type of statistical probability
interval actually includes the specified proportion of the population. For a normally distributed population, a z-score can be transformed into a "k factor"
Tolerance_interval
Term in statistical hypothesis testing
in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis
Power_(statistics)
Test for the presence for occult blood
whether to stop warfarin before a guaiac test. Even when using anticoagulants a high proportion of positive guaiac tests were found to be due to diagnosable
Stool_guaiac_test
Low-yield thermonuclear weapon
an early device was tested underground in early 1962. Designs for a "weaponized" version were developed in 1963. Development of two production designs
Neutron_bomb
Measure of the joint variability
between two complex random variables Z , W {\displaystyle Z,W} is defined as cov ( Z , W ) = E [ ( Z − E [ Z ] ) ( W − E [ W ] ) ¯ ] = E [ Z W ¯
Covariance
Type of statistics
clinical characteristics such as the average age, the proportion of subjects of each sex, the proportion of subjects with related co-morbidities, etc. Some
Descriptive_statistics
Generalization of the binomial distribution
confidence interval of the difference of the proportion of the matched events. For example, we might have a test for some disease, and we may want to check
Multinomial_distribution
Proportion of variance that two traits share due to genetic causes
{\displaystyle r_{g}} or r a {\displaystyle r_{a}} ) is the proportion of variance that two traits share due to genetic causes, the correlation between
Genetic_correlation
20th-century rise in intelligence test scores
and long-sustained increase in both fluid and crystallized intelligence test scores that were measured in many parts of the world over the 20th century
Flynn_effect
Statistical measure of association for two binary variables
measures. Other measures, such as the proportion of correct predictions (also termed accuracy), are not useful when the two classes are of very different sizes
Phi_coefficient
across two articles: Glossary of geography terms (A–M) lists terms beginning with the letters A through M. This page, Glossary of geography terms (N–Z), lists
Glossary of geography terms (N–Z)
Glossary_of_geography_terms_(N–Z)
ICC president & Pakistani cricketer (born 1947)
mid-stroke, and thread gaps to score a high proportion of boundaries. His 274 at Edgbaston in only his second Test is cited as a breakthrough that dispelled
Zaheer_Abbas
Multivalued function in mathematics
relationship W n ( z e z ) = z {\displaystyle \ W_{n}(z\ e^{z})=z\ } is true. f = z e z {\displaystyle \ f=z\ e^{z}\ } implies that there
Lambert_W_function
Probability distribution with more than one mode
between two distributions. To test if a distribution is other than unimodal, several additional tests have been devised: the bandwidth test, the dip test, the
Multimodal_distribution
Statistical measures of whether a finding is likely to be true
condition. In the above example, if the group of people tested had included a higher proportion of people with bowel cancer, then the PPV would probably
Positive and negative predictive values
Positive_and_negative_predictive_values
Colour space defined by the CIE in 1931
CIEXYZ colorspace is that a mixture of two colors in some proportion lies on the straight line between those two colors. One disadvantage is that it is
CIE_1931_color_space
0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also External links 1.96 2SLS (two-stage least squares) – redirects to instrumental variable
List_of_statistics_articles
introduced by Cureton as an effect size for the Mann–Whitney U test. That is, there are two groups, and scores for the groups have been converted to ranks
Probability_of_superiority
Multilingual neural machine translation service
in May 2024. Its more than 200,000 business customers include a large proportion of the Fortune 500. The translating system was first developed within
DeepL_Translator
Signals agency of the German Foreign Office
Pers Z S was the signals intelligence agency of the German Foreign Office (German: Auswärtiges Amt) before and during World War II. It consisted of two cryptologic
Pers_Z_S
Probability distribution
distribution is commonly denoted as z p {\displaystyle z_{p}} . These values are used in hypothesis testing, construction of confidence intervals and
Normal_distribution
as was the case in the Castle Bravo test. Replacing the fissionable material in the tamper with another high-Z material (lead) is essential to producing
Nuclear_weapon_design
Form of pre-employment screening
work behavior. These tests may impact on the final personnel decisions. There are two types of test related to integrity testing, overt and personality-based
Employment_integrity_testing
Alphanumeric code that uniquely identifies a bank account in any participating country
(shifts of the whole string to the left or right) High proportion of double substitution errors (two separate single substitution errors in the same string
International Bank Account Number
International_Bank_Account_Number
Sampling from a population which can be partitioned into subpopulations
= n), then the relative size of the two samples (x1 = m/n males, x2 = f/n females) should reflect this proportion. Optimum allocation (or disproportionate
Stratified_sampling
Measures of observational error
well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true
Accuracy_and_precision
Diagnostic tool for examining breasts
The triple test score is a diagnostic tool for examining potentially cancerous breasts. Diagnostic accuracy of the triple test score is nearly 100%. Scoring
Triple_test_score
Statistical property
versions will be small when sampling fraction is small (e.g. a small proportion of a finite population is studied). In this case people often do not correct
Standard_error
Australian cricketer (1851–1930)
of Australia's total of 245, is still the highest proportion (67.35%) of a completed innings in a Test match. No other Australian exceeded 20 in either
Charles_Bannerman
Statistical procedure of testing by group
{\displaystyle n} soldiers, this method of testing leads to n {\displaystyle n} separate tests. If a large proportion of the people are infected then this method
Group_testing
Principle in genetics
Thompson, Elizabeth A. (June 1992). "Performing the exact test of Hardy–Weinberg proportion for multiple alleles". Biometrics. 48 (2): 361–72. doi:10
Hardy–Weinberg_principle
M z i ( 1 ± c v z i 2 ) = M z i ± S z i c v z i {\displaystyle \mathrm {MPI} _{i}^{\pm }=M_{z_{i}}(1\pm cv_{z_{i}}^{2})=M_{z_{i}}\pm S_{z_{i}}cv_{z_{i}}}
Mazziotta–Pareto_index
Measure of distance between two proportions
probability or proportion p, between 0 and 1, its arcsine transformation is φ = 2 arcsin p . {\displaystyle \varphi =2\arcsin {\sqrt {p}}.} Given two proportions
Cohen's_h
Psychometric factor also known as "general intelligence"
specific situation. Tests that have the same difficulty level, as indexed by the proportion of test items that are failed by test takers, may exhibit
G_factor_(psychometrics)
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)
Family of statistical methods based on sampling of available data
Permutation tests (also re-randomization tests) for generating counterfactual samples Bootstrapping Cross validation Jackknife Permutation tests rely on resampling
Resampling_(statistics)
Statistic used for comparing the similarity of two samples
similarity Proportion of specific agreement or positive agreement Correlation F1 score Hellinger distance Jaccard index Hamming distance Mantel test Morisita's
Dice-Sørensen_coefficient
Econometric effect
Formally, if z i = z i ′ {\displaystyle z_{i}=z_{i}'} , then D i ( z ) = D i ( z ′ ) {\displaystyle D_{i}(\mathbf {z} )=D_{i}(\mathbf {z} ')} , where z {\displaystyle
Local average treatment effect
Local_average_treatment_effect
Ratio estimating the balance between nonsynonymous and synonymous substitutions
nonsynonymous sites in the two sequences, or estimating this number by multiplying the sequence length by the proportion of each class of substitution;
Ka/Ks_ratio
Empirical law on the variance of species in a habitat
alternative significance test for this index has been developed for large samples. z = I m − 1 2 / ( n m 2 ) {\displaystyle z={\frac {I_{m}-1}{2/(nm^{2})}}}
Taylor's_law
Biodiversity ratio in ecology
linearized as: log ( S ) = log ( c A z ) = log ( c ) + z log ( A ) {\displaystyle \log(S)=\log(cA^{z})=\log(c)+z\log(A)} In contrast, Henry Gleason
Species–area_relationship
Cohort born from 2010s to 2020s
often shortened to Gen Alpha, is the demographic cohort succeeding Generation Z and preceding the proposed Generation Beta. While researchers and popular
Generation_Alpha
Conjecture on zeros of the zeta function
Rosser's rule fail in a positive proportion of cases. To be specific, it is expected that in about 66% one zero is enclosed by two successive Gram points, but
Riemann_hypothesis
Observed inability to reproduce scientific studies
negative tests Number of true positives = Probability of obtaining a true positive x Number of positive tests Assuming: Number of tests = 1000 Proportion of
Replication_crisis
1638 book by Galileo Galilei
vacuum that prevents two highly polished plates from separating even though they slide easily gives rise to an experiment to test whether water can be
Two_New_Sciences
High blood sugar levels during pregnancy
Type A1: abnormal oral glucose tolerance test (OGTT), but normal blood glucose levels during fasting and two hours after meals; diet modification is sufficient
Gestational_diabetes
Type of statistical inference
conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics
Frequentist_inference
Measure of wave reflectivity
reference impedance Z 0 = Z S {\displaystyle Z_{0}=Z_{S}} then the source's maximum power is delivered to a load Z L = Z 0 {\displaystyle Z_{L}=Z_{0}} , in which
Reflection_coefficient
Range to estimate an unknown parameter
resampling): "Were this procedure to be repeated on numerous samples, the proportion of calculated 95% confidence intervals that encompassed the true value
Confidence_interval
Probability distribution of the possible sample outcomes
n} is the sample size (number of items in the sample). Mooney, Christopher Z. (1999). Monte Carlo simulation. Thousand Oaks, Calif.: Sage. p. 2. ISBN 9780803959439
Sampling_distribution
Type of machine learning model
on 300 million words, achieved state-of-the-art perplexity on benchmark tests. During the 2000s, with the rise of widespread internet access, researchers
Large_language_model
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TWO PROPORTION-Z-TEST
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