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Card trick and probabilistic concept
The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift
Kruskal_count
American mathematician (1925-2006)
from serious mathematical work, Kruskal was known for mathematical diversions. For example, he invented the Kruskal count, a magical effect that has been
Martin_David_Kruskal
Minimum spanning forest algorithm that greedily adds edges
Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree
Kruskal's_algorithm
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
Instructions directly executable by a computer
limits of the control-flow resynchronizing phenomenon known as the Kruskal count, sometimes possible through opcode-level programming to deliberately
Machine_code
Proof technique in probability theory
converges to the stationary distribution. Copula (probability theory) Kruskal count Dubhashi, Devdatt; Panconesi, Alessandro (June 15, 2009). Concentration
Coupling_(probability)
Algorithm in computational number theory
which have also been called "lambda algorithms". Dynkin's card trick Kruskal count Rainbow table Pollard, John M. (July 1978) [1977-05-01, 1977-11-18]
Pollard's_kangaroo_algorithm
Encoding which maps information to a variable number of bits
possible so that the source can be recovered with zero error. Golomb code Kruskal count Instruction set architecture § Instruction length in computing wchar_t
Variable-length_encoding
Statistic for rank correlation
In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of
Goodman_and_Kruskal's_gamma
Statistical test
the Kruskal-Wallis test in that the null hypothesis is that several independent samples are from the same population. However, with the Kruskal–Wallis
Jonckheere's_trend_test
Statistical test
are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis test to quantiles of the standard normal distribution (details given
Van_der_Waerden_test
Generalized alphabetical order
This is frequently used in combinatorics, for example in the proof of the Kruskal–Katona theorem. In contrast, the ellipses in the above lexicographic ordering
Lexicographic_order
January 2003). "An Algorithm for Computing the Exact Distribution of the Kruskal–Wallis Test". Communications in Statistics - Simulation and Computation
List_of_statistical_tests
Hungarian mathematician (1913–1996)
of people by Erdős number. Erdős's doctoral students included: Joseph Kruskal Béla Bollobás Géza Fodor Erdős won many prizes, including the Wolf Prize
Paul_Erdős
Data transformation of statistics into rank
tests employ calculations based on ranks. Examples include: Friedman test Kruskal–Wallis test Rank products Spearman's rank correlation coefficient Mann–Whitney
Ranking_(statistics)
UK educational YouTube channel (2011-)
mathematical concepts such as Fermat's Last Theorem, the Riemann hypothesis and Kruskal's tree theorem. The videos are produced by Brady Haran, a former BBC video
Numberphile
Nonparametric test of the null hypothesis
CERNO test Cucconi test Kolmogorov–Smirnov test Wilcoxon signed-rank test Kruskal–Wallis one-way analysis of variance Brunner Munzel test Proportional odds
Mann–Whitney_U_test
Statistical model allowing for frequent zero values
basic count model upon which a variety of other count models are based." In a Poisson model, "… the random variable y {\displaystyle y} is the count response
Zero-inflated_model
Fundamental theorem in probability theory and statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Central_limit_theorem
data, it is one of the non-parametric methods. It is an extension of the Kruskal–Wallis test, the non-parametric equivalent for one-way analysis of variance
Scheirer–Ray–Hare_test
Class of statistical models
example of generalized linear models includes Poisson regression which models count data using the Poisson distribution. The link is typically the logarithm
Generalized_linear_model
Type of statistical measure over subsets of a dataset
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Moving_average
Statistical test comparing two probability distributions
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Kolmogorov–Smirnov_test
Concept in machine learning
Benton, Gregory W.; Wilson, Andrew Gordon (2020). "Rethinking Parameter Counting in Deep Models: Effective Dimensionality Revisited". arXiv:2003.02139 [cs
Double_descent
Compilation of concepts primarily for the purposes of lexicostatistics
Indo-European Classification: A Lexicostatistical Experiment by Isidore Dyen, J.B. Kruskal and P.Black. TAPS Monograph 82–5, Philadelphia. in Diachronica Vol. 12
Swadesh_list
Compilation of information about a given population
military operations. The earliest Egyptian census was the cattle count, which counted not people but livestock (especially but not exclusively cows) for
Census
Multivalued function in mathematics
coordinates. For this reason, it also appears in the construction of the Kruskal–Szekeres coordinates. The s-wave resonances of the delta-shell potential
Lambert_W_function
Experiment methodology
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
A/B_testing
Statistical measure of inter-rater agreement
Bennett, E. M., Alpert, R. & Goldstein, A. C. (1954) Goodman, L. A. & Kruskal, W. H. (1954) p. 758 Lin, L. I. (1989) K. Krippendorff, 2013, Content Analysis:
Krippendorff's_alpha
Non-parametric statistical test
analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. The Friedman test is widely
Friedman_test
Distinction between nominal, ordinal, interval and ratio variables
(1997, p. 395) wrote: S. S. Stevens (1946, 1951, 1975) claimed that what counted was having an interval or ratio scale. Subsequent research has given meaning
Level_of_measurement
Measure of linear correlation
ratio Partial correlation Phi coefficient Polychoric correlation Quadrant count ratio RV coefficient Spearman's rank correlation coefficient Kendall rank
Pearson correlation coefficient
Pearson_correlation_coefficient
Model for generating observable data in probability and statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Generative_model
Overview of and topical guide to algorithms
algorithm Johnson's algorithm A* search algorithm Minimum spanning tree Kruskal's algorithm Prim's algorithm Borůvka's algorithm Connected component (graph
Outline_of_algorithms
Approximation method in statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Least_squares
Measure of statistical dispersion
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Interquartile_range
Collection of statistical models
Brown-Forsythe test, Alexander-Govern test, James second order test and Kruskal-Wallis test, available in onewaytests R It is useful to represent each
Analysis_of_variance
Range to estimate an unknown parameter
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Confidence_interval
Numbers significantly larger than those used regularly
However, it can be represented using layers of Knuth's up-arrow notation. Kruskal's tree theorem is a sequence relating to graphs. TREE(3) is larger than
Large_numbers
Statistical property
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Standard_error
Process of using data analysis for predicting population data from sample data
to the Financial Industry. Archived from the original on Jan 16, 2026. Kruskal 1988 Freedman, D.A. (2008) "Survival analysis: An Epidemiological hazard
Statistical_inference
Statistical hypothesis test
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Chi-squared_test
Unit of information
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Data
n+12 = 2(n2) (tetrational growth). The statement is a special case of Kruskal's theorem and has a short proof in second order arithmetic. List of incomplete
List of long mathematical proofs
List_of_long_mathematical_proofs
Selection of data points in statistics
known as the sample counts, whereas according to the Elections Department (ELD), their country's election commission, sample counts help reduce speculation
Sampling_(statistics)
Interpretation of probability
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Bayesian_probability
Sequence of data points over time
years, or even centuries. Common examples include heights of ocean tides, counts of sunspots, daily temperature readings, and the closing values of stock
Time_series
Concept in inferential statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Statistical_significance
Metric for fit of statistical models
_{i=1}^{n}{{\frac {(O_{i}-E_{i})}{E_{i}}}^{2}}} where: Oi = an observed count for bin i Ei = an expected count for bin i, asserted by the null hypothesis. The expected
Goodness_of_fit
Set of statistical processes for estimating the relationships among variables
526–534. doi:10.2139/ssrn.1406472. hdl:2299/965. SSRN 1406472. William H. Kruskal and Judith M. Tanur, ed. (1978), "Linear Hypotheses," International Encyclopedia
Regression_analysis
Value that appears most often in a set of data
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Mode_(statistics)
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Autocorrelation
Apparent lack of pattern or predictability in events
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Randomness
Form of scientific experiment
606. PMC 1112637. PMID 9518917. Jain SL (2010). "The mortality effect: counting the dead in the cancer trial" (PDF). Public Culture. 21 (1): 89–117. doi:10
Randomized_controlled_trial
Method of data analysis
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Principal_component_analysis
Type of bar chart
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Tornado_diagram
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Coefficient_of_variation
Numerical measure of a statistical relationship between variables
of the portion of ranks that match between two data sets. Goodman and Kruskal's gamma is a measure of the strength of association of the cross tabulated
Correlation_coefficient
Fourth standardized moment in statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Kurtosis
Measure of the joint variability
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Covariance
Study of collection and analysis of data
linear regression, Pearson's correlation coefficient, Mann-Whitney U test, Kruskal-Wallis test, Shannon's diversity index, Tukey's range test, cluster analysis
Statistics
Processes that maintain quality at a constant level
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Quality_control
Statistical hypothesis test
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
F-test
Nonparametric measure of rank correlation
added at − ∞ {\displaystyle -\infty } and ∞ {\displaystyle \infty } . A count matrix of size ( m 1 + 1 ) × ( m 2 + 1 ) {\displaystyle (m_{1}+1)\times
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Randomized algorithm for minimum cuts
O(|V|^{2})} . Alternatively, the procedure can be viewed as an execution of Kruskal’s algorithm for constructing the minimum spanning tree in a graph where
Karger's_algorithm
Subset of incomparable elements
distributive lattice, with a Dedekind number of elements. More generally, counting the number of antichains of a finite partially ordered set is #P-complete
Antichain
Middle quantile of a data set or probability distribution
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Median
Measure of the asymmetry of random variables
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Skewness
Probabilistic problem-solving algorithm
square. Count the number of points inside the quadrant, i.e. having a distance from the origin of less than 1. The ratio of the inside-count and the total-sample-count
Monte_Carlo_method
Statistical model for count data
is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable
Poisson_regression
Problem optimization method
116963796250 for n = 8, as we shall see. Dynamic programming makes it possible to count the number of solutions without visiting them all. Imagine backtracking
Dynamic_programming
Function of the observed sample results
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
P-value
Measure of variation in statistics
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Standard_deviation
Sequence of operations for a task
minimal spanning trees of graphs without negative cycles. Huffman Tree, Kruskal, Prim, Sollin are greedy algorithms that can solve this optimization problem
Algorithm
Statistical measure of association
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Cramér's_V
Statistic which divides a data set into 100 parts and analyzes it as a percentage
also a weighted percentile, where the percentage in the total weight is counted instead of the total number. There is no standard function for a weighted
Percentile
Diagnostic plot of binary classifier ability
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Receiver operating characteristic
Receiver_operating_characteristic
Probability distribution
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Student's_t-distribution
Theory and technique of psychological measurement
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Psychometrics
Graphical representation of the distribution of numerical data
values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified
Histogram
Generates a forecast of future values of a time series
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Exponential_smoothing
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Contraharmonic_mean
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Median_polish
Statistical method for handling multiple comparisons
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
False_discovery_rate
Table that displays the frequency of variables
table for the relation between two ordinal variables, see Goodman and Kruskal's gamma. Multiple columns (historically, they were designed to use up all
Contingency_table
Type of statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information
Descriptive_statistics
Statistical measure of variability
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Median_absolute_deviation
Data visualization
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Box_plot
Statistical measure to determine how suited data is for factor analysis
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Kaiser–Meyer–Olkin_test
Statistical considerations on how many observations to make
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Sample_size_determination
Statistical measure of the magnitude of a phenomenon
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Effect_size
Statistic of a given score
{CF-(0.5\times F)}{N}}\times 100,} where CF—the cumulative frequency—is the count of all scores less than or equal to the score of interest, F is the frequency
Percentile_rank
Type of chart
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Bar_chart
Statistic measuring inter-rater agreement for categorical items
Suppose the disagreement count data were as follows, where A and B are readers, data on the main diagonal of the matrix (a and d) count the number of agreements
Cohen's_kappa
Concepts from statistical hypothesis testing
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Type_I_and_type_II_errors
Extremal graph theory bound on clique-free graph edges
all cliques by Reiher (2016). The upper bound is a consequence of the Kruskal–Katona theorem . Erdős–Stone theorem, a generalization of Turán's theorem
Turán's_theorem
Environmental framework
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
System of Integrated Environmental and Economic Accounting
System_of_Integrated_Environmental_and_Economic_Accounting
How many standard deviations apart from the mean an observed datum is
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Standard_score
Type of average of a collection of numbers
the mean or average is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from
Arithmetic_mean
Comparison of two distributions
Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van
Q–Q_plot
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