###### Chi-Square Distribution

A distribution in which a variable is distributed like the sum of the squares of any given independent random variable, each of which has a normal distribution with mean of zero and variance of one. The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution. The oldest of these tests are used to detect whether two or more population distributions differ from one another.

###### Cross-Sectional Studies

###### Questionnaires

###### Retrospective Studies

Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.

###### Prevalence

###### Least-Squares Analysis

###### Logistic Models

Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.

###### Risk Factors

###### Health Knowledge, Attitudes, Practice

###### Age Factors

Age as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or the effect of a circumstance. It is used with human or animal concepts but should be differentiated from AGING, a physiological process, and TIME FACTORS which refers only to the passage of time.

###### Prospective Studies

###### Treatment Outcome

###### Sex Factors

Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.

###### Follow-Up Studies

###### Socioeconomic Factors

###### Case-Control Studies

Studies which start with the identification of persons with a disease of interest and a control (comparison, referent) group without the disease. The relationship of an attribute to the disease is examined by comparing diseased and non-diseased persons with regard to the frequency or levels of the attribute in each group.

###### Prognosis

###### Pregnancy

###### Tai Ji

###### Severity of Illness Index

###### Cohort Studies

Studies in which subsets of a defined population are identified. These groups may or may not be exposed to factors hypothesized to influence the probability of the occurrence of a particular disease or other outcome. Cohorts are defined populations which, as a whole, are followed in an attempt to determine distinguishing subgroup characteristics.

###### Rumen

The first stomach of ruminants. It lies on the left side of the body, occupying the whole of the left side of the abdomen and even stretching across the median plane of the body to the right side. It is capacious, divided into an upper and a lower sac, each of which has a blind sac at its posterior extremity. The rumen is lined by mucous membrane containing no digestive glands, but mucus-secreting glands are present in large numbers. Coarse, partially chewed food is stored and churned in the rumen until the animal finds circumstances convenient for rumination. When this occurs, little balls of food are regurgitated through the esophagus into the mouth, and are subjected to a second more thorough mastication, swallowed, and passed on into other parts of the compound stomach. (From Black's Veterinary Dictionary, 17th ed)

###### Algorithms

###### Reproducibility of Results

The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.

###### Computer Simulation

###### Models, Statistical

###### Cattle

###### Exodeoxyribonuclease V

###### Nitrogen

###### Poaceae

###### Fatty Acids, Volatile

###### Models, Biological

###### Mathematics

###### Models, Theoretical

###### Random Allocation

###### Fermentation

###### Data Interpretation, Statistical

###### Regression Analysis

Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.

###### Sensitivity and Specificity

###### Analysis of Variance

###### Silage

###### Linear Models

###### Models, Molecular

###### Zea mays

###### Genotype

###### Discriminant Analysis

###### Dietary Fiber

###### Models, Genetic

###### Spectroscopy, Near-Infrared

A noninvasive technique that uses the differential absorption properties of hemoglobin and myoglobin to evaluate tissue oxygenation and indirectly can measure regional hemodynamics and blood flow. Near-infrared light (NIR) can propagate through tissues and at particular wavelengths is differentially absorbed by oxygenated vs. deoxygenated forms of hemoglobin and myoglobin. Illumination of intact tissue with NIR allows qualitative assessment of changes in the tissue concentration of these molecules. The analysis is also used to determine body composition.

###### Signal Processing, Computer-Assisted

###### Principal Component Analysis

###### Dietary Proteins

###### Image Processing, Computer-Assisted

###### Statistics as Topic

###### Models, Chemical

###### Multivariate Analysis

###### Calibration

###### Nutritive Value

An indication of the contribution of a food to the nutrient content of the diet. This value depends on the quantity of a food which is digested and absorbed and the amounts of the essential nutrients (protein, fat, carbohydrate, minerals, vitamins) which it contains. This value can be affected by soil and growing conditions, handling and storage, and processing.

###### Protein Conformation

The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).

###### Swine

Any of various animals that constitute the family Suidae and comprise stout-bodied, short-legged omnivorous mammals with thick skin, usually covered with coarse bristles, a rather long mobile snout, and small tail. Included are the genera Babyrousa, Phacochoerus (wart hogs), and Sus, the latter containing the domestic pig (see SUS SCROFA).

###### Ammonia

###### Molasses

###### Quantitative Structure-Activity Relationship

###### Soybeans

###### Breeding

###### Software

###### Image Interpretation, Computer-Assisted

###### Gene Frequency

###### Food Handling

###### Freeze Fracturing

Preparation for electron microscopy of minute replicas of exposed surfaces of the cell which have been ruptured in the frozen state. The specimen is frozen, then cleaved under high vacuum at the same temperature. The exposed surface is shadowed with carbon and platinum and coated with carbon to obtain a carbon replica.

###### Magnetic Resonance Spectroscopy

###### Hydrogen-Ion Concentration

###### Exodeoxyribonucleases

###### Predictive Value of Tests

In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test.

###### Temperature

###### Normal Distribution

###### Photic Stimulation

###### Escherichia coli

A species of gram-negative, facultatively anaerobic, rod-shaped bacteria (GRAM-NEGATIVE FACULTATIVELY ANAEROBIC RODS) commonly found in the lower part of the intestine of warm-blooded animals. It is usually nonpathogenic, but some strains are known to produce DIARRHEA and pyogenic infections. Pathogenic strains (virotypes) are classified by their specific pathogenic mechanisms such as toxins (ENTEROTOXIGENIC ESCHERICHIA COLI), etc.

###### X-Ray Diffraction

The scattering of x-rays by matter, especially crystals, with accompanying variation in intensity due to interference effects. Analysis of the crystal structure of materials is performed by passing x-rays through them and registering the diffraction image of the rays (CRYSTALLOGRAPHY, X-RAY). (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)

###### Congenital Hyperinsulinism

A familial, nontransient HYPOGLYCEMIA with defects in negative feedback of GLUCOSE-regulated INSULIN release. Clinical phenotypes include HYPOGLYCEMIA; HYPERINSULINEMIA; SEIZURES; COMA; and often large BIRTH WEIGHT. Several sub-types exist with the most common, type 1, associated with mutations on an ATP-BINDING CASSETTE TRANSPORTERS (subfamily C, member 8).

###### Amino Acids

###### Pattern Recognition, Visual

###### Likelihood Functions

###### Sheep

###### Factor Analysis, Statistical

A set of statistical methods for analyzing the correlations among several variables in order to estimate the number of fundamental dimensions that underlie the observed data and to describe and measure those dimensions. It is used frequently in the development of scoring systems for rating scales and questionnaires.

###### Electrodes

###### Alleles

###### Duodenum

###### Neural Networks (Computer)

A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.

###### Starch

###### Polymorphism, Genetic

The regular and simultaneous occurrence in a single interbreeding population of two or more discontinuous genotypes. The concept includes differences in genotypes ranging in size from a single nucleotide site (POLYMORPHISM, SINGLE NUCLEOTIDE) to large nucleotide sequences visible at a chromosomal level.

###### Image Enhancement

###### Genetic Predisposition to Disease

###### Contrast Sensitivity

###### Monte Carlo Method

In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)

###### Feces

###### Nonlinear Dynamics

The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.

###### Magnetic Resonance Imaging

###### Mathematical Computing

###### Polymorphism, Single Nucleotide

###### Solutions

###### Molecular Sequence Data

Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.

###### Water

###### Fourier Analysis

Analysis based on the mathematical function first formulated by Jean-Baptiste-Joseph Fourier in 1807. The function, known as the Fourier transform, describes the sinusoidal pattern of any fluctuating pattern in the physical world in terms of its amplitude and its phase. It has broad applications in biomedicine, e.g., analysis of the x-ray crystallography data pivotal in identifying the double helical nature of DNA and in analysis of other molecules, including viruses, and the modified back-projection algorithm universally used in computerized tomography imaging, etc. (From Segen, The Dictionary of Modern Medicine, 1992)

###### Psychophysics

###### Ileum

###### Phantoms, Imaging

Devices or objects in various imaging techniques used to visualize or enhance visualization by simulating conditions encountered in the procedure. Phantoms are used very often in procedures employing or measuring x-irradiation or radioactive material to evaluate performance. Phantoms often have properties similar to human tissue. Water demonstrates absorbing properties similar to normal tissue, hence water-filled phantoms are used to map radiation levels. Phantoms are used also as teaching aids to simulate real conditions with x-ray or ultrasonic machines. (From Iturralde, Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990)

###### Motion

###### Dietary Supplements

Products in capsule, tablet or liquid form that provide dietary ingredients, and that are intended to be taken by mouth to increase the intake of nutrients. Dietary supplements can include macronutrients, such as proteins, carbohydrates, and fats; and/or MICRONUTRIENTS, such as VITAMINS; MINERALS; and PHYTOCHEMICALS.

###### Postural Balance

###### Reference Values

###### Artifacts

Any visible result of a procedure which is caused by the procedure itself and not by the entity being analyzed. Common examples include histological structures introduced by tissue processing, radiographic images of structures that are not naturally present in living tissue, and products of chemical reactions that occur during analysis.

###### Double-Blind Method

###### Thermodynamics

A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed)

###### Lighting

###### Signal-To-Noise Ratio

###### Proteins

Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.

###### Corneal Topography

The measurement of curvature and shape of the anterior surface of the cornea using techniques such as keratometry, keratoscopy, photokeratoscopy, profile photography, computer-assisted image processing and videokeratography. This measurement is often applied in the fitting of contact lenses and in diagnosing corneal diseases or corneal changes including keratoconus, which occur after keratotomy and keratoplasty.

###### Equipment Failure Analysis

###### Body Weight

###### Intramolecular Lyases

###### Animal Husbandry

###### Transducers

Any device or element which converts an input signal into an output signal of a different form. Examples include the microphone, phonographic pickup, loudspeaker, barometer, photoelectric cell, automobile horn, doorbell, and underwater sound transducer. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed)

###### Diffusion

###### Incidence

###### Surface Properties

###### Support Vector Machines

###### Head Injuries, Closed

Traumatic injuries to the cranium where the integrity of the skull is not compromised and no bone fragments or other objects penetrate the skull and dura mater. This frequently results in mechanical injury being transmitted to intracranial structures which may produce traumatic brain injuries, hemorrhage, or cranial nerve injury. (From Rowland, Merritt's Textbook of Neurology, 9th ed, p417)

###### Crystallography, X-Ray

###### Visual Perception

###### Molecular Structure

###### Metabolomics

###### Body Mass Index

An indicator of body density as determined by the relationship of BODY WEIGHT to BODY HEIGHT. BMI=weight (kg)/height squared (m2). BMI correlates with body fat (ADIPOSE TISSUE). Their relationship varies with age and gender. For adults, BMI falls into these categories: below 18.5 (underweight); 18.5-24.9 (normal); 25.0-29.9 (overweight); 30.0 and above (obese). (National Center for Health Statistics, Centers for Disease Control and Prevention)

###### Corneal Wavefront Aberration

###### Computational Biology

A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.

###### Mutation

###### Adipokines

###### Risk Assessment

###### Electromyography

###### Cross-Over Studies

Studies comparing two or more treatments or interventions in which the subjects or patients, upon completion of the course of one treatment, are switched to another. In the case of two treatments, A and B, half the subjects are randomly allocated to receive these in the order A, B and half to receive them in the order B, A. A criticism of this design is that effects of the first treatment may carry over into the period when the second is given. (Last, A Dictionary of Epidemiology, 2d ed)

###### Biomechanical Phenomena

###### Facility Design and Construction

Architecture, exterior and interior design, and construction of facilities other than hospitals, e.g., dental schools, medical schools, ambulatory care clinics, and specified units of health care facilities. The concept also includes architecture, design, and construction of specialized contained, controlled, or closed research environments including those of space labs and stations.

###### Electrochemistry

###### Urea

###### Movement

The act, process, or result of passing from one place or position to another. It differs from LOCOMOTION in that locomotion is restricted to the passing of the whole body from one place to another, while movement encompasses both locomotion but also a change of the position of the whole body or any of its parts. Movement may be used with reference to humans, vertebrate and invertebrate animals, and microorganisms. Differentiate also from MOTOR ACTIVITY, movement associated with behavior.

###### Physical Phenomena

###### Pattern Recognition, Automated

###### Seasons

###### Pilot Projects

###### Quality of Life

###### Brain

The part of CENTRAL NERVOUS SYSTEM that is contained within the skull (CRANIUM). Arising from the NEURAL TUBE, the embryonic brain is comprised of three major parts including PROSENCEPHALON (the forebrain); MESENCEPHALON (the midbrain); and RHOMBENCEPHALON (the hindbrain). The developed brain consists of CEREBRUM; CEREBELLUM; and other structures in the BRAIN STEM.

###### Spectroscopy, Fourier Transform Infrared

###### Scattering, Radiation

###### Phenotype

###### Martial Arts

###### Numerical Analysis, Computer-Assisted

###### Survival Analysis

A class of statistical procedures for estimating the survival function (function of time, starting with a population 100% well at a given time and providing the percentage of the population still well at later times). The survival analysis is then used for making inferences about the effects of treatments, prognostic factors, exposures, and other covariates on the function.

###### Feeding Behavior

###### Gastrointestinal Transit

###### Imaging, Three-Dimensional

The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.

###### Recombination, Genetic

###### Genetic Markers

## Sex differences in the effects of early neocortical injury on neuronal size distribution of the medial geniculate nucleus in the rat are mediated by perinatal gonadal steroids. (1/11846)

Freezing injury to the cortical plate of rats induces cerebrocortical microgyria and, in males but not females, a shift toward greater numbers of small neurons in the medial geniculate nucleus (MGN). The purpose of the current study was to examine a hormonal basis for this sex difference. Cross-sectional neuronal areas of the MGN were measured in male rats, untreated female rats and female rats treated perinatally with testosterone propionate, all of which had received either neonatal cortical freezing or sham injury. Both male and androgenized female rats with microgyria had significantly smaller MGN neurons when compared to their sham-operated counterparts, whereas untreated females with microgyria did not. These differences were also reflected in MGN neuronal size distribution: both male and androgenized female rats with microgyria had more small and fewer large neurons in their MGN in comparison to shams, while there was no difference in MGN neuronal size distribution between lesioned and sham females. These findings suggest that perinatal gonadal steroids mediate the sex difference in thalamic response to induction of microgyria in the rat cortex. (+info)## Natural history of dysplasia of the uterine cervix. (2/11846)

BACKGROUND: A historical cohort of Toronto (Ontario, Canada) women whose Pap smear histories were recorded at a major cytopathology laboratory provided the opportunity to study progression and regression of cervical dysplasia in an era (1962-1980) during which cervical squamous lesions were managed conservatively. METHODS: Actuarial and Cox's survival analyses were used to estimate the rates and relative risks of progression and regression of mild (cervical intraepithelial neoplasia 1 [CIN1]) and moderate (CIN2) dysplasias. In addition, more than 17,000 women with a history of Pap smears between 1970 and 1980 inclusive and who were diagnosed as having mild, moderate, or severe dysplasia were linked to the Ontario Cancer Registry for the outcome of any subsequent cervical cancers occurring through 1989. RESULTS: Both mild and moderate dysplasias were more likely to regress than to progress. The risk of progression from mild to severe dysplasia or worse was only 1% per year, but the risk of progression from moderate dysplasia was 16% within 2 years and 25% within 5 years. Most of the excess risk of cervical cancer for severe and moderate dysplasias occurred within 2 years of the initial dysplastic smear. After 2 years, in comparison with mild dysplasia, the relative risks for progression from severe or moderate dysplasia to cervical cancer in situ or worse was 4.2 (95% confidence interval [CI] = 3.0-5.7) and 2.5 (95% CI = 2.2-3.0), respectively. CONCLUSION: The risk of progression for moderate dysplasia was intermediate between the risks for mild and severe dysplasia; thus, the moderate category may represent a clinically useful distinction. The majority of untreated mild dysplasias were recorded as regressing to yield a normal smear within 2 years. (+info)## Low-dose combination therapy as first-line hypertension treatment for blacks and nonblacks. (3/11846)

To assess the efficacy and safety of bisoprolol/6.25-mg hydrochlorothiazide (HCTZ), amlodipine, and enalapril in black and nonblack patients, data from two comparative studies were pooled and subgroup analyses performed. Both studies had similar designs and included all three active treatments. The second study also included a placebo group. Subjects (n = 541) with a sitting diastolic blood pressure of 95-114 mmHg were titrated to achieve a diastolic blood pressure < or = 90 mmHg. The studies included 114 blacks and 427 nonblacks. Results of an intention-to-treat analysis of mean change from baseline after 12 weeks of treatment showed the following: 1) blood pressure was significantly lowered by all three active drugs compared with baseline or placebo; 2) in blacks, bisoprolol/6.25-mg HCTZ resulted in significantly greater reductions of systolic and diastolic blood pressure than enalapril or placebo, but was not significantly different from amlodipine; 3) in nonblacks, bisoprolol/6.25-mg HCTZ resulted in significantly greater reduction of diastolic blood pressure than amlodipine, enalapril, or placebo. The placebo-corrected change in blood pressure was greater for blacks than whites on the bisoprolol/6.25-mg HCTZ combination, but this was not statistically significant. Bisoprolol/6.25-mg HCTZ controlled diastolic blood pressure to < or = 90 mmHg in significantly more patients than enalapril or placebo in blacks and nonblacks. The difference in control rates was not significant versus amlodipine. The incidence of drug-related adverse events was similar between treatments; however, bisoprolol/6.25-mg HCTZ had a lower discontinuation rate due to lack of blood pressure control or adverse experiences in both blacks and nonblacks. (+info)## Extent and severity of atherosclerotic involvement of the aortic valve and root in familial hypercholesterolaemia. (4/11846)

OBJECTIVE: To compare the frequency of valvar and supravalvar aortic stenosis in homozygous and heterozygous familial hypercholesterolaemia (FH). DESIGN: Analysis of life time cholesterol exposure and prevalence of aortic atherosclerosis in 84 consecutive cases attending a lipid clinic. SETTING: A tertiary referral centre in London. PATIENTS: Outpatients with FH (six homozygous, 78 heterozygous). INTERVENTIONS: Maintenance of lipid lowering treatment. MAIN OUTCOME MEASURES: Calculated cholesterol x years score (CYS) and echocardiographic measurement of aortic root diameter, aortic valve thickness, and transaortic gradient. RESULTS: Four homozygotes with a mean (SD) CYS of 387 (124) mmol/1 x years had severe aortic stenosis (treatment started after seven years of age), whereas the other two had echocardiographic evidence of supravalvar thickening but no aortic valve stenosis (treatment started before three years of age). On multivariate analysis, mean transaortic gradient correlated significantly with CYS (mean = 523 (175) mmol/1 x years) in heterozygotes (p = 0.0001), but only two had severe aortic valve and root involvement. CONCLUSIONS: In patients with familial hypercholesterolaemia, aortic stenosis is common in homozygotes, and aortic root involvement is always present despite the lower CYS than in heterozygotes. It appears to be determined by short term exposure to high cholesterol concentrations in early life. Conversely, aortic root and valve involvement are rare in heterozygotes and occur only with severe, prolonged hypercholesterolaemia, possibly accelerating age related degenerative effects. (+info)## Amino acid composition of protein termini are biased in different manners. (5/11846)

An exhaustive statistical analysis of the amino acid sequences at the carboxyl (C) and amino (N) termini of proteins and of coding nucleic acid sequences at the 5' side of the stop codons was undertaken. At the N ends, Met and Ala residues are over-represented at the first (+1) position whereas at positions 2 and 5 Thr is preferred. These peculiarities at N-termini are most probably related to the mechanism of initiation of translation (for Met) and to the mechanisms governing the life-span of proteins via regulation of their degradation (for Ala and Thr). We assume that the C-terminal bias facilitates fixation of the C ends on the protein globule by a preference for charged and Cys residues. The terminal biases, a novel feature of protein structure, have to be taken into account when molecular evolution, three-dimensional structure, initiation and termination of translation, protein folding and life-span are concerned. In addition, the bias of protein termini composition is an important feature which should be considered in protein engineering experiments. (+info)## Prevalence of true vein graft aneurysms: implications for aneurysm pathogenesis. (6/11846)

BACKGROUND: Circumstantial evidence suggests that arterial aneurysms have a different cause than atherosclerosis and may form part of a generalized dilating diathesis. The aim of this study was to compare the rates of spontaneous aneurysm formation in vein grafts performed either for popliteal aneurysms or for occlusive disease. The hypothesis was that if arterial aneurysms form a part of a systemic process, then the rates of vein graft aneurysms should be higher for patients with popliteal aneurysms than for patients with lower limb ischemia caused by atherosclerosis. METHODS: Infrainguinal vein grafting procedures performed from 1990 to 1995 were entered into a prospective audit and graft surveillance program. Aneurysmal change was defined as a focal increase in the graft diameter of 1.5 cm or greater, excluding false aneurysms and dilatations after graft angioplasty. RESULTS: During the study period, 221 grafting procedures were performed in 200 patients with occlusive disease and 24 grafting procedures were performed in 21 patients with popliteal aneurysms. Graft surveillance revealed spontaneous aneurysm formation in 10 of the 24 bypass grafts (42%) for popliteal aneurysms but in only 4 of the 221 grafting procedures (2%) that were performed for chronic lower limb ischemia. CONCLUSION: This study provides further evidence that aneurysmal disease is a systemic process, and this finding has clinical implications for the treatment of popliteal aneurysms. (+info)## Cryoglobulinaemia and rheumatic manifestations in patients with hepatitis C virus infection. (7/11846)

OBJECTIVES: To investigate the association of cryoglobulinaemia and rheumatic manifestations in Korean patients with hepatitis C virus (HCV) infection. METHODS: Forty nine Korean patients with HCV infection were recruited. The prevalence, concentration, and type of cryoglobulin (by immunofixation), rheumatoid factor (RF), antinuclear antibody (ANA), and various rheumatological symptoms were investigated and HCV genotype was determined by polymerase chain reaction with genotype specific primer. RESULTS: The prevalence of cryoglobulin was 59% in Korean HCV patients and the concentration of cryoglobulin was 9.8 (7.9) g/l (mean (SD)). The type of cryoglobulinaemia was identified in 23 (80%) of 29 HCV patients with cryoglobulinaemia and they were all type III. There were no differences in age, sex, history of operation and transfusion, proportion of liver cirrhosis between the patients with cryoglobulinaemia and those without cryoglobulinaemia. The frequencies of RF and ANA were 14% and 3.4% respectively in HCV patients with cryoglobulinaemia. There was no difference in HCV genotype between the patients with cryoglobulinaemia and those without cryoglobulinaemia. Clinical features of HCV patients were as follows: arthralgia/arthritis (35%), cutaneous manifestation (37%), Raynaud's phenomenon (8%), paresthesia (44%), dry eyes (22%), dry mouth (10%), oral ulcer (33%), and abdominal pain (14%). However, these rheumatological symptoms did not differ between the two groups. CONCLUSION: Although the rheumatological symptoms were not different between HCV patients with and without cryoglobulinaemia, HCV patients showed various rheumatological manifestations. These result suggests that HCV infection could be included as one of the causes in patients with unexplained rheumatological symptoms. (+info)## Fetal tachycardias: management and outcome of 127 consecutive cases. (8/11846)

OBJECTIVE: To review the management and outcome of fetal tachycardia, and to determine the problems encountered with various treatment protocols. STUDY DESIGN: Retrospective analysis. SUBJECTS: 127 consecutive fetuses with a tachycardia presenting between 1980 and 1996 to a single tertiary centre for fetal cardiology. The median gestational age at presentation was 32 weeks (range 18 to 42). RESULTS: 105 fetuses had a supraventricular tachycardia and 22 had atrial flutter. Overall, 52 fetuses were hydropic and 75 non-hydropic. Prenatal control of the tachycardia was achieved in 83% of treated non-hydropic fetuses compared with 66% of the treated hydropic fetuses. Digoxin monotherapy converted most (62%) of the treated non-hydropic fetuses, and 96% survived through the neonatal period. First line drug treatment for hydropic fetuses was more diverse, including digoxin (n = 5), digoxin plus verapamil (n = 14), and flecainide (n = 27). The response rates to these drugs were 20%, 57%, and 59%, respectively, confirming that digoxin monotherapy is a poor choice for the hydropic fetus. Response to flecainide was faster than to the other drugs. Direct fetal treatment was used in four fetuses, of whom two survived. Overall, 73% (n = 38) of the hydropic fetuses survived. Postnatally, 4% of the non-hydropic group had ECG evidence of pre-excitation, compared with 16% of the hydropic group; 57% of non-hydropic fetuses were treated with long term anti-arrhythmics compared with 79% of hydropic fetuses. CONCLUSIONS: Non-hydropic fetuses with tachycardias have a very good prognosis with transplacental treatment. Most arrhythmias associated with fetal hydrops can be controlled with transplacental treatment, but the mortality in this group is 27%. At present, there is no ideal treatment protocol for these fetuses and a large prospective multicentre trial is required to optimise treatment of both hydropic and non-hydropic fetuses. (+info)###### Chi-square distribution legal definition of Chi-square distribution

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###### Doc. Ing. Ji Jaro , Ph.D. - Publications

###### Poster Presentation - ASN Events

###### topic:Chi-Square Distribution found 2865 records • Arctic Health

###### R] Query : Chi Square goodness of fit test

###### Analyzing Quantitative Data: An Introduction for Social Researchers | Quality Productivity & Reliability | General &...

###### 1st International Course on Integrated Biomarkers

###### Chi-square Goodness of Fit Test in R - Easy Guides - Wiki - STHDA

###### multivariate logistic reg | Statistics Help @ Talk Stats Forum

###### Chi Square Goodness of Fit

###### Microsoft Access Crosstab and Chi-Square with Total Access Statistics

###### Fisher Exact Test - Statdisk - Help Site

###### Fishers exact test | Statistics Help @ Talk Stats Forum

###### Institute for Capacity Strengthening

###### István Vincze (mathematician)

"On limiting

**distribution**laws of statistics analogous to Pearson's**chi**-**square**". Statistics: A Journal of Theoretical and ... Z. W. Birnbaum; I. Vincze (1973). "Limiting**Distributions**of Statistics Similar to Student's". Annals of Statistics. 1 (1973): ... Vincze, István (1996). "Cramér-Rao type inequality and a problem of mixture of**distributions**". Mathematical Institute, Slovak ... empirical**distribution**, Cramér-Rao inequality, and information theory. Considered by many, as an expert in theoretical and ...###### Differential item functioning

This test yields a Wald statistic which follows a

**chi**-**square****distribution**. In this case the null hypothesis being tested is H0 ... G2 approximately follows a**chi****square****distribution**, especially with larger samples. Therefore, it is evaluated by the degrees ... Determination of DIF is made by evaluating the obtained**chi**-**square**statistic with 2 degrees of freedom. Additionally, parameter ... In this case, the absence of DIF is determined by the fact that the conditional probability**distribution**of Y is not dependent ...###### Linkage disequilibrium

displaystyle \

**chi**^{2}=wy^{2}\;\left[=193,\**chi**^{2}(p=0.001,\;df=1)=10.8\right]}. follows the**chi**-**square****distribution**with d. f ... displaystyle \**chi**^{2}}. test calculating χ. 2. =. (. a. d. −. b. c. ). 2. N. A. B. C. D. (. =. 336. ,. for data in Table 3; P ... displaystyle \**chi**^{2}={\frac {(ad-bc)^{2}N}{ABCD}}\;(=336,{\text{ for data in Table 3; }}P,0.001).}. where d. f. =. 1. {\ ... is the correlation coefficient between pairs of loci, usually expressed as its**square**, r. 2. {\displaystyle r^{2}}. [6] ...###### Anil Kumar Bhattacharya

"A note on the

**distribution**of the sum of**chi**-**squares**", Sankhya, 7 (1945), 27 - 28. "On some analogues of the amount of ... Distance between statistical**distributions**had been addressed in 1936 by Mahalanobis, who proposed the D2 metric, now known as ... Inst., 33, Part II (1951). "On some uses of the t-**distribution**in multivariate analysis", Sankhya, 12 (1952), 89 - 104. "Notes ... "On a measure of divergence between two statistical populations defined by their probability**distributions**", Bull. Cal. Math. ...###### Welch's t-test

The statistic is approximately from the t-

**distribution**since we have an approximation of the**chi**-**square****distribution**. This ... Welch's t-test remains robust for skewed**distributions**and large sample sizes. Reliability decreases for skewed**distributions**... Student's t-test assumes that the sample means (test statistics) of two population**distributions**being compared are normally ... Welch's t-test is designed for unequal sample**distribution**variance, but the assumption of normally distributed sample is ...###### Patrick J. Curran

Curran, P. J., Bollen, K. A., Paxton, P., Kirby, J., & Chen, F. (2002). The noncentral

**chi**-**square****distribution**in misspecified ...###### Zero degrees of freedom

...

**chi**-**square****distribution**with zero degrees of freedom concentrates all probability at zero. All of this leaves open the question ... The**chi**-squared**distribution**with n degrees of freedom is the probability**distribution**of the sum X 1 2 + ⋯ + X n 2 {\ ... The noncentral**chi**-squared**distribution**with zero degrees of freedom and with noncentrality parameter μ is the**distribution**of ... then the sum of**squares**above has a non-central**chi**-squared**distribution**with n degrees of freedom and "noncentrality parameter ...###### ANOVA on ranks

Sawilowsky, S. (1985). "A comparison of random normal scores test under the F and

**Chi**-**square****distributions**to the 2x2x2 ANOVA ... Treat the mean for each group as a score, and compute the variability (again, the sum of**squares**) of those three scores. When ... Under the truth of the null hypothesis, the sampling**distribution**of the F ratio depends on the degrees of freedom for the ... or sum of**squares**) of scores on some dependent variable will be the same within each group. When divided by the degrees of ...###### Wald test

Typically the

**square**of the difference is compared to a**chi**-squared**distribution**. ... Recalling that a quadratic form of normal**distribution**has a**Chi**-squared**distribution**: n. (. R. θ. ^. n. −. r. ). ′. [. R. V. R ...**chi**_{Q}^{2}}. Rearranging n finally gives: (. R. θ. ^. n. −. r. ). ′. [. R. (. V. /. n. ). R. ′. ]. −. 1. (. R. θ. ^. n. −. r ... multiplying by R has**distribution**: R. n. (. θ. ^. n. −. θ. ). =. n. (. R. θ. ^. n. −. r. ). →. D. N. (. 0. ,. R. V. R. ′. ). {\ ...###### Early Edu-Ware products

**Chi**-

**square**test, and T-Test. The program was offered in both disk and cassette stand-alone versions, as well as in a compendium ... Calculations performed by the program included mean, variance, standard deviation, Pearson correlation, normal

**distribution**, ...

###### Logistic regression

When assessed upon a

**chi**-**square****distribution**, nonsignificant**chi**-**square**values indicate very little unexplained variance and ...**chi**_{s-p}^{2},}**chi**-**square****distribution**with degrees of freedom equal to the difference in the number of parameters estimated ... to the**square**of the standard error of the coefficient and is asymptotically distributed as a**chi**-**square****distribution**. W j = β ... one simply compares the deviance of the predictor model with that of the null model on a**chi**-**square****distribution**with a single ...###### List of English inventions and discoveries

...

**chi**-**square**); William Gosset (1876-1937) (Student's t-**distribution**); Ronald Fisher (1890-1962) (Analysis of variance); Frank ... "Paterson, Rex (1955). Fertilizer**Distribution**- Problems of Corrosion Prevention on the Farm. The International Fertilizer ...###### Thomas Royen

Royen worked mainly on probability

**distributions**, in particular multivariate**chi**-**squares**and gamma**distributions**, to improve ... Thomas Royen: A simple proof of the Gaussian correlation conjecture extended to some multivariate gamma**distributions**, in: Far ... Royen, T. (2014). "A simple proof of the Gaussian correlation conjecture extended to multivariate gamma**distributions**". arXiv: ... Supplemented by Royen, Thomas (2015). "Some probability inequalities for multivariate gamma and normal**distributions**". arXiv: ...###### Unbiased estimation of standard deviation

has a

**chi****square****distribution**with n − 1 degrees of freedom and thus its**square**root, n. −. 1. s. /. σ. {\displaystyle {\sqrt { ... where the correction factor c4(n) is the scale mean of the**chi****distribution**with n − 1 degrees of freedom, μ. 1. (. n. −. 1. ) ... has a**chi****distribution**with n − 1 degrees of freedom. Consequently, calculating the expectation of this last expression and ... Other**distributions**[edit]. In cases where statistically independent data are modelled by a parametric family of**distributions**...###### KIMEP University

Vassily Voinov, statistician, major developer of extensions of

**khi**-**square****distributions**KIMEP has active partnerships with more ... The 325-**square**-meter facility includes a basketball court, two fitness rooms and a yoga studio. All the technology is state-of- ...###### Genomic control

The

**distribution**of the**chi**-**square**statistics for a given allele that is suspected to be associated with a given trait can then ... using a set of anonymous genetic markers to estimate the effect of population structure on the**distribution**of the**chi**-**square**... be compared to the**distribution**of the same statistics for an allele that is expected not to be related to the trait. The ...###### Degrees of freedom (statistics)

... the sums-of-

**squares**no longer have scaled**chi**-squared**distributions**. Comparison of sum-of-**squares**with degrees-of-freedom is no ... The residual sum-of-**squares**‖ y − H y ‖ 2 {\displaystyle \,y-Hy\,^{2}} has a generalized**chi**-squared**distribution**, and the ... the sums of**squares**have scaled**chi**-squared**distributions**, with the corresponding degrees of freedom. The F-test statistic is ... these sums-of-**squares**no longer have (scaled, non-central)**chi**-squared**distributions**, and dimensionally defined degrees-of- ...###### Normally distributed and uncorrelated does not imply independent

... the

**square**root of the median of a**chi**-squared**distribution**with 3 degrees of freedom.. ... The left panel shows the joint**distribution**of X 1 {\displaystyle X_{1}} and Y 2 {\displaystyle Y_{2}} ; the**distribution**has ... The right panel shows the joint**distribution**of Y 1 {\displaystyle Y_{1}} and Y 2 {\displaystyle Y_{2}} ; the**distribution**has ... This furnishes two examples of bivariate**distributions**that are uncorrelated and have normal marginal**distributions**but are not ...###### Heteroscedasticity

This result is used to justify using a normal

**distribution**, or a**chi****square****distribution**(depending on how the test statistic ... In 1980, White proposed a consistent estimator for the variance-covariance matrix of the asymptotic**distribution**of the OLS ... While the ordinary least**squares**estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and ... Gupta, A. K.; Tang, J. (1984). "**Distribution**of likelihood ratio statistic for testing equality of covariance matrices of ...###### Data validation and reconciliation

... the objective function is a random variable which follows a

**chi**-**square****distribution**, since it is the sum of the**square**of ... one only has to compare the value of the objective function with the critical value of the**chi****square****distribution**. The ... of the probability density function of a**chi**-**square****distribution**(e.g. the 95th percentile for a 95% confidence) gives an ... The**chi****square**test gives only a rough indication about the existence of gross errors, and it is easy to conduct: ...###### Gamma **distribution**

The exponential

**distribution**, Erlang**distribution**, and**chi**-**square****distribution**are special cases of the gamma**distribution**. ... If α is a positive integer (i.e., the**distribution**is an Erlang**distribution**), the cumulative**distribution**function has the ... The gamma**distribution**is a special case of the generalized gamma**distribution**, the generalized integer gamma**distribution**, and ... see also Rayleigh**distribution**and Rician**distribution**. In oncology, the age**distribution**of cancer incidence often follows the ...###### Gary Robinson

... an approach based on the

**chi**-**square****distribution**for combining the individual word probabilities into a combined probability ( ... Robinson's method used math-intensive algorithms combined with**Chi**-**square**statistical testing to enable computers to examine an ... Fischer's combination of probabilities into a**chi**-squared**distribution**, has been extensively tested and is used by the most ... Gary Robinson's Linux Journal article discussed using the**chi**squared**distribution**. CS1 maint: discouraged parameter (link) Ben ...###### F-**distribution**

...

**distribution**is an instance of ratio**distributions**Beta prime**distribution****Chi**-**square****distribution**Chow test Gamma**distribution**... has the**chi**-squared**distribution**χ d 1 2 {\displaystyle \**chi**_{d_{1}}^{2}} F ( d 1 , d 2 ) {\displaystyle F(d_{1},d_{2})} is ... The F-**distribution**is a particular parametrization of the beta prime**distribution**, which is also called the beta**distribution**... Fisher's z-**distribution**) The noncentral F-**distribution**simplifies to the F-**distribution**if λ = 0 {\displaystyle \lambda =0} . ...###### Degrees of freedom (statistics)

The residual sum-of-

**squares**‖. y. −. H. y. ‖. 2. {\displaystyle \,y-Hy\,^{2}}. has a generalized**chi**-squared**distribution**, and ... then the residual sum of**squares**has a scaled**chi**-squared**distribution**(scaled by the factor σ. 2. {\displaystyle \sigma ^{2}} ... the sums-of-**squares**no longer have scaled**chi**-squared**distributions**. Comparison of sum-of-**squares**with degrees-of-freedom is no ... In the example above, the residual sum-of-**squares**is ∑. i. =. 1. n. (. X. i. −. X. ¯. ). 2. =. ‖. X. 1. −. X. ¯. ⋮. X. n. −. X ...###### OpenPuff

... size reduction after compression

**chi****square****distribution**test: 40% < deviation < 60% mean value test: 127.4x / 127.5 Monte ...###### Bartlett's test

This test procedure is based on the statistic whose sampling

**distribution**is approximately a**Chi**-**Square****distribution**with (k-1 ...**distribution**. Thus the null hypothesis is rejected if χ 2 > χ k − 1 , α 2 {\displaystyle \**chi**^{2}>\**chi**_{k-1,\alpha }^{2}} ( ...**chi**_{k-1}^{2}}**distribution**better (Bartlett, 1937). The test statistics may be written in some sources with logarithms of ...**chi**_{k-1}^{2}}**distribution**). Bartlett's test is a modification of the corresponding likelihood ratio test designed to make ...###### Pearson's

...

**chi**-squared test, a statistical procedure whose results are evaluated by reference to the**chi**-**square****distribution**...###### List of MeSH codes (G03)

...

**chi**-**square****distribution**MeSH G03.850.520.830.994.500 - normal**distribution**MeSH G03.850.520.830.994.750 - poisson**distribution**... statistical**distributions**MeSH G03.850.520.830.994.250 - binomial**distribution**MeSH G03.850.520.830.994.300 - ... sex**distribution**MeSH G03.850.505.400.850.815 - sex ratio MeSH G03.850.505.400.975 - vital statistics MeSH G03.850.505.400. ... least-**squares**analysis MeSH G03.850.520.830.750.425 - linear models MeSH G03.850.520.830.750.450 - logistic models MeSH G03.850 ...###### List of MeSH codes (N05)

...

**chi**-**square****distribution**MeSH N05.715.360.750.750.565 - normal**distribution**MeSH N05.715.360.750.750.620 - poisson**distribution**... statistical**distributions**MeSH N05.715.360.750.750.150 - binomial**distribution**MeSH N05.715.360.750.750.200 - ... least-**squares**analysis MeSH N05.715.360.750.695.460 - linear models MeSH N05.715.360.750.695.470 - logistic models MeSH N05.715 ...###### Level of measurement

... the

**square**root of) a central moment. ... Probability**distribution**. *Sampling**distribution***Order ...###### Glossary of graph theory terms

**square**. 1. The

**square**of a graph G is the graph power G2; in the other direction, G is the

**square**root of G2. The half-

**square**... χ(G) (using the Greek letter

**chi**) is the chromatic number of G and χ ′(G) is its chromatic index; see chromatic and coloring.. ... 3. Power laws in the degree

**distributions**of scale-free networks are a phenomenon in which the number of vertices of a given ...

**Square**brackets [ ]. G[S] is the induced subgraph of a graph G for vertex subset S.. Prime symbol '. The prime symbol is often ...

###### Mann-Whitney U test

If the two

**distributions**are normal with the same mean but different variances, then Pr[ X,Y]=Pr[Y,X] but the size of the Mann- ... Different**distributions**[edit]. If one is only interested in stochastic ordering of the two populations (i.e., the concordance ... Unlike the t-test it does not require the assumption of normal**distributions**. It is nearly as efficient as the t-test on normal ... If one desires a simple shift interpretation, the Mann-Whitney U test should not be used when the**distributions**of the two ...###### Diamagnetism

is the mean

**square**distance of the electrons from the nucleus. Therefore, ⟨. ρ. 2. ⟩. =. ⟨. x. 2. ⟩. +. ⟨. y. 2. ⟩. =. 2. 3. ⟨ ... If the**distribution**of charge is spherically symmetric, we can suppose that the**distribution**of x,y,z. coordinates are ... displaystyle \**chi**=-\mu _{0}{\frac {e^{2}}{12\pi ^{2}m\hbar }}{\sqrt {2mE_{\rm {F}}}},}. where E. F. {\displaystyle E_{\rm {F ... displaystyle \**chi**={\frac {\mu _{0}n\mu }{B}}=-{\frac {\mu _{0}e^{2}Zn}{6m}}\langle r^{2}\rangle .}. In atoms, Langevin ...###### Pu'er tea

**Square**方茶 方茶 Fāngchá A flat

**square**of tea, usually in 100g or 200g sizes. Characters are often pressed into the

**square**, as in ... Pu'er journals and similar annual guides such as The Profound World of

**Chi**Tse, Pu-erh Yearbook, and Pu-erh Teapot Magazine ... Pu'er tea

**distribution**in Yunnan]. 7yunnan.cn. 2006. Archived from the original on 2006-12-02.. ... For instance, brick or

**square**teas often are not compressed using bags.[14][better source needed] ...

###### Isotonic regression

minimizes the weighted least

**squares**-like condition: min. g. ∈. A. ∑. i. =. 1. n. w. i. (. g. (. x. i. ). −. f. (. x. i. ). ). ... Probability**distribution**. *Sampling**distribution***Order statistic. *Empirical**distribution***Density estimation. *Statistical ... In terms of numerical analysis, isotonic regression involves finding a weighted least-**squares**fit x. ∈. R. n. {\displaystyle x\ ...###### Probability **distribution**

Student's t

**distribution**, the**distribution**of the ratio of a standard normal variable and the**square**root of a scaled**chi**... the Bernoulli**distribution**, the binomial**distribution**, the geometric**distribution**, and the negative binomial**distribution**. ... F-**distribution**, the**distribution**of the ratio of two scaled**chi**squared variables; useful e.g. for inferences that involve ...**Chi**-squared**distribution**, the**distribution**of a sum of squared standard normal variables; useful e.g. for inference regarding ...###### TeX

... is distributed as part of the larger TeX Live

**distribution**. (Prior to TeX Live, the teTeX**distribution**was the de facto ... The algorithm will then find the breakpoints that will minimize the sum of**squares**of the badness (including penalties) of the ... and**chi**, as TeX is an abbreviation of τέχνη (ΤΕΧΝΗ - technē), Greek for both "art" and "craft", which is also the root word of ...**Distributions**and extensions[edit]. TeX is usually provided in the form of an easy-to-install bundle of TeX itself along with ...###### Opinion poll

An estimate of the margin of error in percentage terms can be gained by the formula 100 ÷

**square**root of sample size ... Probability**distribution**. *Sampling**distribution***Order statistic. *Empirical**distribution***Density estimation. *Statistical ...###### Mississippi River

Ye, S.; Li, Z.; Liu, J;, Zhang, T.; and Xie, S. (2011). "

**Distribution**, Endemism and Conservation Status of Fishes in the ... The basin covers more than 1,245,000**square**miles (3,220,000 km2), including all or parts of 32 U.S. states and two Canadian ...**Chi**-squared test

The Wald test can be evaluated against a

**chi**-**square****distribution**.. References[edit]. *^ a b Pearson, Karl (1900). "On the ... Other examples of**chi**-squared tests[edit]. One test statistic that follows a**chi**-squared**distribution**exactly is the test that ... Using the**chi**-squared**distribution**to interpret Pearson's**chi**-squared statistic requires one to assume that the discrete ... Without other qualification, '**chi**-squared test' often is used as short for Pearson's**chi**-squared test. The**chi**-squared test is ...###### Random assignment

... given the probability

**distribution**, the null hypothesis will sometimes be "rejected," that is, deemed not plausible. That is, ... Latin**square**. *Graeco-Latin**square**. *Orthogonal array. *Latin hypercube Repeated measures design ...###### Carswell Air Force Base

The B-52 effort was concentrated primarily against suspected Viet Cong targets in South Vietnam, but the Ho

**Chi**Min Trail and ... for property**distribution**and reuse.[19] ... Sundance**Square***Sid Richardson Museum. *Texas Rodeo Cowboy ...###### Student's t-test

least-

**squares**estimators. ,. S. E. α. ^. ,. S. E. β. ^. =. the standard errors of least-**squares**estimators. .. {\displaystyle ... Another is Hotelling's T2 statistic follows a T2**distribution**. However, in practice the**distribution**is rarely used, since ... sum of**squares**of residuals}}.\end{aligned}}}. Then tscore is given by: t. score. =. (. β. ^. −. β. 0. ). n. −. 2. SSR. /. ∑. i ... For non-normal data, the**distribution**of the sample variance may deviate substantially from a χ2**distribution**. However, if the ...###### Wikipedia:Reference desk/Archives/Mathematics/2008 March 12

**Chi**-

**square**test[edit]. When calculating a

**chi**-

**square**test what are the steps between calculating the differences between the ... Call that value X. Then the p-value is just the probability that a χ2

**distribution**with the appropriate degrees of freedom is ... how is the p-value of the

**chi**-

**square**obtained (other than by looking it up in a table)? Thanks. The

**chi**-

**square**test article ... Least

**Squares**Question[edit]. Let v. 1. =. [. 1. 1. 0. 1. ]. {\displaystyle v_{1}={\begin{bmatrix}1\\1\\0\\1\end{bmatrix}}}. ...

###### Structural equation modeling

... weighted least

**squares**or asymptotically**distribution**-free methods. This is often accomplished by using a specialized SEM ...**Chi**-squared *A fundamental measure of fit used in the calculation of many other fit measures. Conceptually it is a function of ... which indirectly included the two-stage least**squares**estimator and its asymptotic**distribution**(Anderson, 2005) and ... Root Mean**Square**Error of Approximation (RMSEA) *Fit index where a value of zero indicates the best fit.[15] While the ...###### Anglo-Saxons

Page with

**Chi**Rho monogram from the Gospel of Matthew in the Lindisfarne Gospels c. 700, possibly created by Eadfrith of ... Various studies have been carried out investigating the**distribution**and chronological change of bead types.[232][233] The ... One style flourished from the late 5th century, and continued throughout the 6th, and is on many**square**-headed brooches, it is ... Buildings vary widely in size, most were**square**or rectangular, though some round houses have been found. Frequently these ...###### Structural break

"Tests for Causality between Integrated Variables Using Asymptotic and Bootstrap

**Distributions**: Theory and Application". Applied ...###### Design of experiments

... frequentist statistics studies the sampling

**distribution**while Bayesian statistics updates a probability**distribution**on the ... Latin**square**. *Graeco-Latin**square**. *Orthogonal array. *Latin hypercube. Repeated measures design ... The average error is zero; the standard deviations of the probability**distribution**of the errors is the same number σ on ...###### Wald-Wolfowitz runs test

... is complementary to the

**chi****square**test, which takes into account the distances but not the signs. The Kolmogorov-Smirnov test ... Runs tests can be used to test: the randomness of a**distribution**, by taking the data in the given order and marking with + the ... However, the reverse is true if the**distributions**differ in variance and have at the most only a small difference in location.[ ... Under the null hypothesis, the number of runs in a sequence of N elements is a random variable whose conditional**distribution**...###### Go (game)

The board is not

**square**; there is a 15:14 ratio in length to width, because with a perfectly**square**board, from the player's ... Taiwan**Chi**Yuan Culture Foundation), the United States (AGA Professional System) and Europe (European Professional System). ... and decisions or moves create discrete outcome vectors rather than probability**distributions**), the underlying math is ... The ko is at the point marked with a**square**-Black has "taken the ko" first. The ko fight determines the life of the A and B ...###### Blinded experiment

Latin

**square**. *Graeco-Latin**square**. *Orthogonal array. *Latin hypercube Repeated measures design ... Probability**distribution**. *Sampling**distribution***Order statistic. *Empirical**distribution***Density estimation. *Statistical ...###### Shanghai Ghetto

The Shanghai Ghetto, formally known as the Restricted Sector for Stateless Refugees, was an area of approximately one

**square**... "Refuge in Shanghai (1938-1953)" American Jewish Joint**Distribution**Committee Archives. *Jewish Voice of the Far East = ... Wu2 kuo2-chi2 nan4-min2 hsien4-ting4 ti4-ch'ü1. ... The Baghdadis and later the American Jewish Joint**Distribution**... In 1943, the occupying Japanese army required these 18,000 Jews to relocate to a 3/4**square**mile area of Shanghai's Hongkou ...###### C++11

**chi**_squared_

**distribution**. ,. *. cauchy_

**distribution**. ,. *. fisher_f_

**distribution**. ,. *. student_t_

**distribution**. ,. *. discrete_ ... for Microsoft). With the new syntax, added information can be specified in a form of an attribute enclosed in double

**square**... include ,random, #include ,functional, std::uniform_int_

**distribution**,int,

**distribution**(0, 99); std::mt19937 engine; // Mersenne ... and a

**distribution**, which determines the range and mathematical

**distribution**of the outcome. These two are combined to form a ...

###### Electroencephalography

In 2008 the Final Fantasy developer

**Square**Enix announced that it was partnering with NeuroSky to create a game, Judecca.[115][ ... both sides, symmetrical**distribution**, most evident frontally; low-amplitude waves. *range span: active calm → intense → ... Wan, Feng; da Cruz, Janir Nuno; Nan, Wenya; Wong,**Chi**Man; Vai, Mang I; Rosa, Agostinho (2016-05-06). "Alpha neurofeedback ... It can be seen as a focal disturbance in focal subcortical lesions; it can be seen in generalized**distribution**in diffuse ...###### Analysis of variance

... specifies a

**chi**-squared**distribution**which describes the associated sum of**squares**, while the same is true for "treatments" if ... to the F-**distribution**with I. −. 1. {\displaystyle I-1}. , n. T. −. I. {\displaystyle n_{T}-I}. degrees of freedom. Using the F ... because the test statistic is the ratio of two scaled sums of**squares**each of which follows a scaled**chi**-squared**distribution**. ... where MS is mean**square**, I. {\displaystyle I}. = number of treatments and n. T. {\displaystyle n_{T}}. = total number of cases ...###### Statistics

Widely used pivots include the z-score, the

**chi****square**statistic and Student's t-value. ... the method of moments for the fitting of**distributions**to samples and the Pearson**distribution**, among many other things.[22] ... Least**squares**applied to linear regression is called ordinary least**squares**method and least**squares**applied to nonlinear ... Many statistical methods seek to minimize the residual sum of**squares**, and these are called "methods of least**squares**" in ...###### Hong Kong

Kwong,

**Chi**Man (9 September 2015). "Hong Kong during World War II: A Transnational Battlefield". University of Nottingham. ... With over 7.4 million people of various nationalities[d] in a 1,104-**square**-kilometre (426 sq mi) territory, Hong Kong is one of ... Thematic Report: Household Income**Distribution**in Hong Kong (PDF). 2016 Population By-Census (Report). Census and Statistics ... Tam, Maria Wai-chu; Chan, Eugene Kin-keung; Choi Kwan, Janice Wing-kum; Leung, Gloria**Chi**-kin; Lo, Alexandra Dak-wai; Tang, ...###### Spatial analysis

The Euclidean metric (Principal Component Analysis), the

**Chi**-**Square**distance (Correspondence Analysis) or the Generalized ... Spatial**distribution**: the similar spatial object groups positioning information, including**distribution**, trends, contrast etc.. ... Scheldeman, X. & van Zonneveld, M. (2010). Training Manual on Spatial Analysis of Plant Diversity and**Distribution**. Bioversity ... Spread of bubonic plague in medieval Europe.[citation needed] The colors indicate the spatial**distribution**of plague outbreaks ...###### Surnames by country

The forms for visa application many Western countries use, has a

**square**for writing the last name which cannot be left unfilled ... Ho**Chi**Minh) and Japanese names do (Kenzaburō Ōe).[11] However, numerous exceptions exist, particularly for people born in ... the systematic**distribution**of surnames to Filipinos without prior surnames and the universal implementation of the Spanish ...###### A **Chi**-**Square** Approximation for the F **Distribution**

In this paper, a simple

**chi**-**square**approximation for the cumulative**distribution**of the F-**distribution**is obtained via an ... For example, it is used for testing: equality of variances of two independent normal**distributions**, equality of means in the ... This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F**distribution**are small. ... F**distribution**is one of the most frequently used**distributions**in statistics. ...###### Classroom Activities: **Chi**-**Square** **Distributions** - Texas Instruments - content

Students compare the

**chi**-**square****distribution**to the standard normal**distribution**and determine how the**Chi**-**Square****distribution**... Students compare the**chi**-**square****distribution**to the standard normal**distribution**and determine how the**Chi**-**Square****distribution**... Problem 2 gives students the opportunity to explore the critical values for a**Chi**-**Square****Distribution**. They find the critical ... In Problem 1, students will explore the characteristics of the**Chi**-**Square****Distribution**. They will increase the degree of ...**Chi**-**Square** Probability **Distribution** - The Complete Idiot's Guide to Statistics, 2nd Edition [Book]

Table 5

**Chi**-**Square**Probability**Distribution**Selected right-tail areas - Selection from The Complete Idiots Guide to Statistics ...**Chi**-**Square**Probability**Distribution**Table 5 provides the**chi**-**square**for the corresponding value of alpha and the number of ...**Chi**-**Square**Probability**Distribution**. Table 5 provides the**chi**-**square**for the corresponding value of alpha and the number of ...**Chi**-**square** **distribution** - Wikipedia

Generalized

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Test Statistic in

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###### Central limit t2

- For these hypothesis tests, as the sample size, n, increases, the sampling distribution of the test statistic approaches the normal distribution (central limit theorem). (wikipedia.org)
- The normal, or Gaussian, distribution is one of the most familiar in statistics, endeared to statisticians by its simplicity and by virtue of the Central Limit Theorem (which states that a sample mean will follow an approximately normal distribution, if sample size is large enough, even if the data themselves are not normally distributed). (gsu.edu)

###### Binomial4

- The negative binomial distribution is the distribution of the number of failures before k successes in a series of Bernoulli events. (wikibooks.org)
- This applet demonstrates the Binomial distribution by simulating Galton's Board, dropping balls through a triangular array of nails. (causeweb.org)
- function uses the binomial distribution. (delorie.com)
- tables, the Pearson chi-square is also appropriate for testing the equality of two binomial proportions. (sas.com)

###### Variance16

- Another example is the test statistic for testing equality of means of k independent normal distributions with homogeneous variance is also distributed as an F distribution. (scirp.org)
- In this paper, we consider the problem of testing equality of means of k independent normal distributions with homogeneous variance. (scirp.org)
- Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks. (wikipedia.org)
- The chi-square distribution is used primarily in hypothesis testing, and to a lesser extent for confidence intervals for population variance when the underlying distribution is normal. (wikipedia.org)
- a distribution in which a variable is distributed like the sum of the the squares of any given independent random variable , each of which has a normal distribution with mean of zero and variance of one. (biology-online.org)
- Xv*Xv is Chi-square distributed with v degrees of freedom with mean = v and variance = 2*v . The importance of the Chi-square distribution stems from the fact that it describes the distribution of the Variance of a sample taken from a Normal distributed population. (uva.nl)
- The distribution of the underlying sample values X has mean = 0 and variance = 1 , i.e., is Standard Normal . (uva.nl)
- Okay, so I am interested if there is a way to derive the variance for a Chi-Square distribution using the property that it is the sum of independent unit normal distributions squared. (stackexchange.com)
- distribution is obtained from the values of the ratio of the sample variance and population variance multiplied by the degrees of freedom. (richland.edu)
- The mean and variance of the chi square distribution also increase as k increases and the mean = k and variance = 2 k . (symynet.com)
- The normal distribution has two parameters, one representing the mean of the variable and one representing the variance. (gsu.edu)
- The standard normal distribution, which constrains the mean to 0 and the variance to 1, is probably the most widely known statistical distribution. (gsu.edu)
- The mean of a chi-square distribution is equal to its degrees of freedom, and the variance is equal to twice the degrees of freedom. (gsu.edu)
- Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. (causeweb.org)
- Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance. (causeweb.org)
- Understand the role and use of moment generating functions and be able to use them to compute the expectation and variance of standard distributions. (york.ac.uk)

###### Sampling Distributions3

- This is a graduate level introduction to statistics including topics such as probabilty/sampling distributions, confidence intervals, hypothesis testing, ANOVA, and regression. (causeweb.org)
- The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. (causeweb.org)
- Students can see both sampling distributions at the same time making them easy to compare. (causeweb.org)

###### Degrees34

- This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small. (scirp.org)
- distribution, where r is the degrees of freedom, which is the difference in the number of unconstrained parameters being estimated and the number of constrained parameters being estimated. (scirp.org)
- Students compare the chi-square distribution to the standard normal distribution and determine how the Chi-Square distribution changes as they increase the degrees of freedom. (ti.com)
- As the degrees of freedom increase the distribution becomes less skewed and more symmetric. (ti.com)
- In probability theory and statistics, the chi-square distribution (also chi-squared or χ2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. (wikipedia.org)
- Zk are independent, standard normal random variables, then the sum of their squares, Q = ∑ i = 1 k Z i 2 , {\displaystyle Q\ =\sum _{i=1}^{k}Z_{i}^{2},} is distributed according to the chi-square distribution with k degrees of freedom. (wikipedia.org)
- The chi-square distribution has one parameter: a positive integer k that specifies the number of degrees of freedom (the number of random variables being summed, Zi s). (wikipedia.org)
- Table 5 provides the chi-square for the corresponding value of alpha and the number of degrees of freedom. (oreilly.com)
- Each distribution is defined by the degrees of freedom . (jmp.com)
- The figure below shows three different Chi-square distributions with different degrees of freedom. (jmp.com)
- The higher the degrees of freedom for a Chi-square distribution, the more it looks like a normal distribution. (jmp.com)
- The rows in a Chi-square table correspond to different degrees of freedom. (jmp.com)
- The chi-square distribution has one parameter k , the degrees of freedom. (symynet.com)
- If we wish to reject H o at the .05 level, we will determine if our value of chi square is greater than the critical value of chi square that cuts off the upper 5% of the distribution at our particular degrees of freedom value. (symynet.com)
- Degrees of freedom of the non-central chi-square distribution. (scilab.org)
- The degrees of freedom of the resulting chi-square distribution are equal to the number of variables that are summed. (gsu.edu)
- That is, a chi-square-distributed variable with d1 degrees of freedom can be added to one with d2 degrees of freedom to yield a chi-square-distributed variable with d1 + d2 degrees of freedom, as long as the two added variables are independent. (gsu.edu)
- Generate sample data of size 1000 from a noncentral chi-square distribution with degrees of freedom 8 and noncentrality parameter 3. (mathworks.com)
- Compute the probability density function (PDF) for the chi-square distribution, given the degrees of freedom and the point at which to evaluate the function x. (analyticscalculators.com)
- where df = degrees of freedom which depends on how chi-square is being used. (openstax.org)
- The random variable for a chi-square distribution with k degrees of freedom is the sum of k independent, squared standard normal variables. (openstax.org)
- and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom. (wikipedia.org)
- Explain how the degrees of freedom affect a Chi-Square Distribution. (foxessays.com)
- Chi square distribution explains a variable with k degrees of liberty, dispersed like the amount of the squares of n independent random variables each which have a typical distribution with mean of absolutely no and variation of 1. (academicpaperwriter.com)
- You can quickly depend on our Chi-Square Distributions composing Help as we offer the very best services and these services are supplied to the students by our professionals who all hold master and specialized degrees or more. (academicpaperwriter.com)
- Visualize how changes in degrees of freedom affect the shape of the chi square distribution. (rdrr.io)
- We can use a chi square test with 12-1=11 degrees of freedom to compare the observed data against our null hypothesis. (ucla.edu)
- Using the SOCR Chi-Square Distribution Calculator, at 11 degrees of freedom, a chi square value of 8.8 gives us a p-value of 0.36. (ucla.edu)
- f_{Y_{k+2i}}(x),} where Y q {\displaystyle Y_{q}} is distributed as chi-square with q {\displaystyle q} degrees of freedom. (wikipedia.org)
- Suppose that a random variable J has a Poisson distribution with mean λ / 2 {\displaystyle \lambda /2} , and the conditional distribution of Z given J = i is chi-square with k + 2i degrees of freedom. (wikipedia.org)
- Siegel (1979) discusses the case k = 0 specifically (zero degrees of freedom), in which case the distribution has a discrete component at zero. (wikipedia.org)
- Dear Li, if you're interested in the values rather than in doing a programming exercise, you can use the statistics2 package by Shin-ichi Hara: blade.nagaokaut.ac.jp/~sinara/ruby/math/statistics2/statistics2-0.50/README From the README: --- Statistics2.chi2dist(n, x) Returns the integral of Chi-squared distribution with n degrees of freedom over (-Infty, x]. (ruby-forum.com)
- Statistics2.chi2X_(n, x) Returns the integral of Chi-squared distribution with n degrees of freedom over [0, x]. (ruby-forum.com)
- has an asymptotic chi-square distribution with C -1 degrees of freedom. (sas.com)

###### Probabilities5

- The chi-square distribution PDF identifies the relative likelihood that an associated random variable will have a particular value, and is very useful for analytics studies that consider chi-square distribution probabilities. (analyticscalculators.com)
- If you want to practice calculating chi-square probabilities then use df = n - 1. (openstax.org)
- This page provides a table of Chi-square distribution probabilities with degress of freedom 1-45. (causeweb.org)
- This page provides a table of F distribution probabilities for alpha = 0.10, 0.05, 0.025, and 0.01. (causeweb.org)
- these two values and two probabilities make up the probability distribution of the single coin flipping event. (mcgill.ca)

###### Confidence intervals2

- The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. (wikipedia.org)
- The intervals next to the parameter estimates are the 95% confidence intervals for the distribution parameters. (mathworks.com)

###### Noncentral chi-square15

- This distribution is sometimes called the central chi-square distribution, a special case of the more general noncentral chi-square distribution. (wikipedia.org)
- We derive Laguerre expansions for the density and distribution functions of a sum of positive weighted noncentral chi-square variables. (springer.com)
- On the computation of noncentral chi-square distribution function. (springer.com)
- Some alternative expansions for the distribution function of a noncentral chi-square random variable. (springer.com)
- 1] has a noncentral chi-square distribution then the distribution of X = [square root of [X. (thefreedictionary.com)
- In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. (ed.gov)
- Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the noncentral chi-square distribution is justified by statistical theory. (ed.gov)
- Actually, when the null hypothesis is not trivially violated, the noncentral chi-square distribution cannot describe the LR statistic well even when data are normally distributed and the sample size is large. (ed.gov)
- Examples with real data illustrate the difference between the noncentral chi-square distribution and the normal distribution. (ed.gov)
- Monte Carlo results compare the strength of the normal distribution against that of the noncentral chi-square distribution. (ed.gov)
- The aim is to provide the least technical material for quantitative graduate students in social science to understand the condition and limitation of the noncentral chi-square distribution. (ed.gov)
- Estimate the parameters of the noncentral chi-square distribution from the sample data. (mathworks.com)
- In probability theory and statistics, the noncentral chi-square distribution (or noncentral chi-squared distribution, noncentral χ 2 {\displaystyle \chi ^{2}} distribution) is a noncentral generalization of the chi-square distribution. (wikipedia.org)
- Then the random variable ∑ i = 1 k X i 2 {\displaystyle \sum _{i=1}^{k}X_{i}^{2}} is distributed according to the noncentral chi-square distribution. (wikipedia.org)
- From this representation, the noncentral chi-square distribution is seen to be a Poisson-weighted mixture of central chi-square distributions. (wikipedia.org)

###### Compute4

- Formula 26.4.25 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to compute the cumulative distribution function. (scilab.org)
- The functions in this section compute various probability distributions. (delorie.com)
- Compute the 99% confidence interval for the distribution parameters. (mathworks.com)
- The following sections give the formulas that PROC FREQ uses to compute the chi-square tests and statistics. (sas.com)

###### Approximation9

- In this paper, a simple chi-square approximation for the cumulative distribution of the F -distribution is obtained via an adjusted log-likelihood ratio statistic. (scirp.org)
- As a result, a normal approximation for the cdf of the F distribution is obtained. (scirp.org)
- approximation for the cdf of the F distribution is obtained. (scirp.org)
- For this reason, it is preferable to use the t distribution rather than the normal approximation or the chi-square approximation for a small sample size. (wikipedia.org)
- A gaussian approximation to the distribution of a definite quadratic form. (springer.com)
- Note on an approximation to the distribution of non-central χ 2 . (springer.com)
- This applet demonstrates the Normal approximation to the Poisson Distribution. (causeweb.org)
- The basis for his statistical mathematics came from a long tradition of work on the method of least squares approximation , worked out early in the 19th century in order to estimate quantities from repeated astronomical and geodetic measures using probability theory . (britannica.com)
- The proposed low complexity technique is analyzed in an oversampled OFDM system and a simple distribution approximation of the oversampled and linearly filtered OFDM signals is also proposed. (scirp.org)

###### Random variables7

- Distribution for random variables constrained to be equal to or greater than 0 and which (unlike normal distribution) traces an asymmetric curve. (businessdictionary.com)
- Browse other questions tagged probability statistics probability-distributions random-variables covariance or ask your own question . (stackexchange.com)
- Probability Distributions An example will make clear the relationship between random variables and probability distributions. (slideplayer.com)
- This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions. (maplesoft.com)
- The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory , and the science of statistics . (mcgill.ca)
- Probability and Statistical Inference 1 (Autumn) will give students a theoretical and mathematically formal framework for joint and conditional distributions of random variables and for studying the asymptotic behaviour of sequences of random variables. (york.ac.uk)
- Be able to apply various limit theorems to prove convergence in probability or in distribution of a sequence of random variables. (york.ac.uk)

###### Probability Density2

- Below you will find descriptions and links to 10 different statistics calculators that are related to the free probability density function (pdf) calculator for the chi-square distribution. (danielsoper.com)
- Discrete distributions are defined by their probability function rather than by their probability density function in order to avoid singularities. (maplesoft.com)

###### Continuous Distributions1

- absolutely continuous distributions. (mcgill.ca)

###### Multivariate8

- Note that the multivariate normal distribution is not a mere composite of univariate normal distributions. (gsu.edu)
- Even if every variable in a set is normally distributed, it is still possible that the combined distribution is NOT multivariate normal. (gsu.edu)
- This distribution arises in multivariate statistics as a derivative of the multivariate normal distribution . (wikipedia.org)
- Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- θk)T, on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. (eudml.org)
- We have applied the properties of MVUE's and the results from the theory of MVU estimation to construct a goodness-of-fit chi-squared test for multivariate modified power series distributions. (eudml.org)
- BAN estimator}, language = {eng}, number = {3}, pages = {301-326}, title = {Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- 2011. On the distribution of sample measure of multivariate kurtosis. (springer.com)

###### Cumulative8

- Johnson and Kotz [1] give a comprehensive review on the approximations to the cumulative distribution function (cdf) of the F distribution. (scirp.org)
- They find the critical values using a chart and then confirm the area between the critical values and in each tail using the cumulative Chi-Square command. (ti.com)
- From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. (scilab.org)
- Define a custom probability density and cumulative distribution function. (mathworks.com)
- Cumulative Probability Distributions A cumulative probability refers to the probability that the value of a random variable falls within a specified range. (slideplayer.com)
- 1) = P(X = 0) + P(X = 1) = = 0.75 Like a probability distribution, a cumulative probability distribution can be represented by a table or an equation. (slideplayer.com)
- A probability distribution is called discrete if its cumulative distribution function only increases in jumps. (mcgill.ca)
- Returns the cumulative distribution function, its inverse, or one of its parameters, of the beta distribution. (php.net)

###### Different Chi-square distributions1

- There are many different chi-square distributions, one for each degree of freedom. (richland.edu)

###### Maximum likelihood2

- Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares. (wiley.com)
- Be able to estimate parameters of standard distributions following the Maximum Likelihood approach. (york.ac.uk)

###### Univariate distributions2

- Continuous univariate distributions , vol. 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics . (springer.com)
- Distributions in Statistics: Continuous Univariate Distributions-2. (mathworks.com)

###### Variances4

- For example, it is used for testing: equality of variances of two independent normal distributions, equality of means in the one-way ANOVA setting, overall significance of a normal linear regression model, and so on. (scirp.org)
- For example, the test statistic for testing equality of variances of two independently distributed normal distributions is distributed as an F distribution. (scirp.org)
- On the other hand, considering testing equality of variances of two independent normal distributions, Wong [3] derives the modified signed log-likelihood ratio statistic. (scirp.org)
- In classical statistics, there are three distributions often used in hypothesis testing: F and Chi-square distributions used in comparing variances and t distributions in comparing means. (thefreedictionary.com)

###### Parameters4

- On the bad side, normal distributions increase the likelihood that the parameters of statistical models will not be identified , because there will be relatively few pieces of distinct information--fewer "knowns"--available for this purpose ( Bekker, Merckens and Wansbeek, 1994 ). (gsu.edu)
- Be able to derive a confidence interval, exact and/or approximate, for parameters of probability distributions. (york.ac.uk)
- Understand the theoretical framework of linear regression models: standard model assumptions, Least Squares estimators for the model parameters and their properties, inference techniques for the model parameters. (york.ac.uk)
- The arguments to the algebraic functions are the value of the random variable first, then whatever other parameters define the distribution. (delorie.com)

###### Symmetric8

- But, it has a longer tail to the right than a normal distribution and is not symmetric. (jmp.com)
- Chi-square is non-symmetric. (richland.edu)
- Since the chi-square distribution isn't symmetric, the method for looking up left-tail values is different from the method for looking up right tail values. (richland.edu)
- The chi squared distribution becomes more symmetric as k increases. (symynet.com)
- The distribution is unimodal and symmetric about the mean. (gsu.edu)
- Elliptical distributions are symmetric and unimodal, but are not constrained regarding kurtosis. (gsu.edu)
- While the normal distribution is symmetric, the chi-square distribution is skewed to the right, and has a minimum of 0. (gsu.edu)
- A symmetric distribution, such as normal distribution, might not be a good fit. (mathworks.com)

###### Estimators1

- Bentler's EQS package includes estimators specifically designed to be appropriate for elliptical distributions. (gsu.edu)

###### Independence5

- The chi-square distribution is used in the common chi-square tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. (wikipedia.org)
- Two common tests that rely on the Chi-square distribution are the Chi-square goodness of fit test and the Chi-square test of independence . (jmp.com)
- The Chi-Square distribution is used in the chi-square tests for goodness of fit of an observed distribution to a theoretical one and the independence of two criteria of classification of qualitative data. (ucla.edu)
- The CHISQ option provides chi-square tests of homogeneity or independence and measures of association that are based on the chi-square statistic. (sas.com)
- The Pearson chi-square for two-way tables involves the differences between the observed and expected frequencies, where the expected frequencies are computed under the null hypothesis of independence. (sas.com)

###### Null hypothesis7

- Using the one-dimensional case, this article provides the details showing that the LR statistic asymptotically follows a normal distribution, which also leads to an asymptotically correct confidence interval for the discrepancy between the null hypothesis/model and the population. (ed.gov)
- recency effects * halo effects * primacy effects * leniency effects For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. (cram.com)
- A Chi-square test is a statistical hypothesis test where tasting distribution of the test data is specified as a chi square distribution while either the null hypothesis holds true or it is asymptotically real. (academicpaperwriter.com)
- Simply puts chi-square test is a test with test fact that has a chi-square distribution when the null hypothesis holds true, or any where the likelihood distribution of the test figure (presuming the null hypothesis holds true) can be made to approximate a chi-square distribution as carefully as preferred by making the sample size huge enough. (academicpaperwriter.com)
- If there is substantial distinction from the null hypothesis or weather the outcomes support the null hypothesis, Chi square table is made use of in Chi square test to examine. (academicpaperwriter.com)
- For two-way tables, the null hypothesis for the chi-square tests is no association between the row variable and the column variable. (sas.com)
- When the sample size n is large, the test statistics have asymptotic chi-square distributions under the null hypothesis. (sas.com)

###### Likelihood6

- is based on the asymptotic distribution of the log-likelihood ratio statistic. (scirp.org)
- An additional reason that the chi-square distribution is widely used is that it turns up as the large sample distribution of generalized likelihood ratio tests (LRT). (wikipedia.org)
- Chi square distribution is a theoretical likelihood distribution in inferential data. (academicpaperwriter.com)
- When you specify the CHISQ option in the TABLES statement, PROC FREQ computes the following chi-square tests for each two-way table: Pearson chi-square, likelihood ratio chi-square, and Mantel-Haenszel chi-square tests. (sas.com)
- PROC FREQ provides exact p -values for the Pearson chi-square, likelihood ratio chi-square, and Mantel-Haenszel chi-square tests, in addition to Fisher's exact test. (sas.com)
- For one-way tables, PROC FREQ provides exact p -values for the Pearson and likelihood ratio chi-square goodness-of-fit tests. (sas.com)

###### Statistics7

- F distribution is one of the most frequently used distributions in statistics. (scirp.org)
- But many statistics books show Chi-square tables, so understanding how to use a table might be helpful. (jmp.com)
- Information about and tables for the chi-square distribution can be found in any elementary statistics text. (thefreedictionary.com)
- Chi- Square Goodness of Fit Testing Assuming Equal Expected A handful of students loves numbers and selects a major in Finance, Statistics, or Marketing. (cram.com)
- Presenters: Nouruddin Boojhawoonah & Poonam Gopaul Notes reffered from statistics tutorial: Probability distribution. (slideplayer.com)
- Chi Square Test for Goodness of Fit: There are 60 people in a statistics class, and we have data on the month of their birth. (ucla.edu)
- The other chi-square tests and statistics in this section are appropriate for either nominal or ordinal variables. (sas.com)

###### Describes the probability1

- A smooth function that describes the probability of landing anywhere on the dartboard is the probability distribution of the dart throwing event. (mcgill.ca)

###### Significance3

- Conducting a Chi-Square Goodness of the Fit Test revealed that the class of 200 students does not fit the historical pattern when using a .05 significance level. (cram.com)
- Chi-Square Distributions has fantastic significance in stats. (academicpaperwriter.com)
- At the .05 significance level is there a difference in the two distributions? (scribd.com)

###### Statistic7

- Because the test statistic (such as t) is asymptotically normally distributed, provided the sample size is sufficiently large, the distribution used for hypothesis testing may be approximated by a normal distribution. (wikipedia.org)
- Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution. (wikipedia.org)
- It is used for statistical tests where the test statistic follows a Chi-squared distribution. (jmp.com)
- Compare your test statistic to the distribution value and make the appropriate conclusion. (jmp.com)
- The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution . (biology-online.org)
- tables, the CHISQ option also provides Fisher's exact test and the continuity-adjusted chi-square statistic. (sas.com)
- The Mantel-Haenszel chi-square statistic is appropriate only when both variables lie on an ordinal scale. (sas.com)

###### Estimation4

- Thus, elliptical distributions themselves can be thought of as an intermediate point between the normal distribution and the general continuous distribution described in Browne's (1982) work on asymptotically distribution-free (ADF) estimation. (gsu.edu)
- Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. (eudml.org)
- It is also used in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. (ucla.edu)
- In between there are full chapters on parametric probability distributions, sampling, Chi-Square distributions, point estimation, and tests of parametric statistical hypotheses. (maa.org)

###### Poisson Distribution1

- The Poisson distribution is shown in blue, and the Normal distribution is shown in red. (causeweb.org)

###### Exponential1

- Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-square distribution is not as often applied in the direct modeling of natural phenomena. (wikipedia.org)

###### Monte Carlo2

- In our example, the p-values based on the nominal chi-square distribution were often similar to those based on the Monte Carlo simulations. (thefreedictionary.com)
- Monte Carlo and Statistical Distributions. (routledge.com)

###### Noncentrality parameter1

- The resulting noncentral distributions are characterized by one additional parameter--a noncentrality parameter. (gsu.edu)

###### Geometric distribution1

- The geometric distribution . (wikibooks.org)

###### Homogeneous1

- The distribution of homogeneous and non-homogeneous quadratic functions of normal variables. (springer.com)

###### Gamma1

- The Chi-Square distribution is a special case of the Gamma distribution [link to gamma]. (ucla.edu)

###### Coefficient1

- The general sampling distribution of multiple correlation coefficient. (springer.com)

###### Theoretical3

- The Chi-square distribution is a theoretical distribution of values for a population. (jmp.com)
- Does the sample represent the theoretical distribution? (physicsforums.com)
- That would depend on what theoretical distribution was stated in the problem. (physicsforums.com)

###### Frequency4

- The distribution of the frequency of words is known as Zipf's Law . (wikibooks.org)
- Frequency Distributions. (routledge.com)
- The author also presents the Statistical Theory of Rollback, which allows data analysts and regulatory officials to estimate the effect of different emission control strategies on environmental quality frequency distributions. (epa.gov)
- For one-way frequency tables, the CHISQ option in the TABLES statement provides a chi-square goodness-of-fit test. (sas.com)

###### Hypothesis Testing1

- The primary reason for which the chi-square distribution is extensively used in hypothesis testing is its relationship to the normal distribution. (wikipedia.org)

###### LogNormal1

- and the two- and three-parameter lognormal distributions. (epa.gov)

###### Test10

- So wherever a normal distribution could be used for a hypothesis test, a chi-square distribution could be used. (wikipedia.org)
- Click the image or link below for tables of critical test values for different distributions. (oup.com)
- This is not a test, but a distribution. (uva.nl)
- The Chi-Square Goodness of Fit Test are calculations done on categorical data. (cram.com)
- Chi Square Test for Niche lab conducted at Owings Mills North.Behaivors of several species of birds (Tufted titmouse, dark eyed junco, black-capped chickadee, northern cardinal, mourning dove, purple finch, house sparrow, and white breasted nuthatch) were observed at feeding station. (cram.com)
- Chi-square test is based on the chi square distribution. (symynet.com)
- Pearson chi-squared test (χ2): differences? (physicsforums.com)
- If you specify the CHISQ option for one-way tables, PROC FREQ provides a one-way Pearson chi-square goodness-of-fit test. (sas.com)
- In addition to the asymptotic test, you can request an exact one-way chi-square test by specifying the CHISQ option in the EXACT statement. (sas.com)
- In addition to the asymptotic test, you can request an exact Pearson chi-square test by specifying the PCHI or CHISQ option in the EXACT statement. (sas.com)

###### Testing hypotheses1

- Testing hypotheses using a normal distribution is well understood and relatively easy. (wikipedia.org)

###### Displaystyle2

- Note that some references define λ {\displaystyle \lambda } in other ways, such as half of the above sum, or its square root. (wikipedia.org)
- While the central chi-square distribution is the squared norm of a random vector with N ( 0 k , I k ) {\displaystyle N(0_{k},I_{k})} distribution (i.e., the squared distance from the origin to a point taken at random from that distribution), the non-central χ 2 {\displaystyle \chi ^{2}} is the squared norm of a random vector with N ( μ , I k ) {\displaystyle N(\mu ,I_{k})} distribution. (wikipedia.org)

###### Contingency1

- So, we construct a contingency table that shows the distribution of one variable at each level of the other variable. (symynet.com)

###### Density1

- Propability density function ( chi-square distribution). (blogspot.com)