**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**: Studies in which the presence or absence of disease or other health-related variables are determined in each member of the study population or in a representative sample at one particular time. This contrasts with LONGITUDINAL STUDIES which are followed over a period of time.

**Brazil**

**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.

**Questionnaires**: Predetermined sets of questions used to collect data - clinical data, social status, occupational group, etc. The term is often applied to a self-completed survey instrument.

**Risk Factors**: An aspect of personal behavior or lifestyle, environmental exposure, or inborn or inherited characteristic, which, on the basis of epidemiologic evidence, is known to be associated with a health-related condition considered important to prevent.

**Prevalence**: The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.

**India**

**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.

**Dentition, Permanent**: The 32 teeth of adulthood that either replace or are added to the complement of deciduous teeth. (Boucher's Clinical Dental Terminology, 4th ed)

**Prospective Studies**: Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.

**Turkey**

**Socioeconomic Factors**: Social and economic factors that characterize the individual or group within the social structure.

**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.

**Malocclusion**: Such malposition and contact of the maxillary and mandibular teeth as to interfere with the highest efficiency during the excursive movements of the jaw that are essential for mastication. (Jablonski, Illustrated Dictionary of Dentistry, 1982)

**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.

**Fingersucking**: Sucking of the finger. This is one of the most common manipulations of the body found in young children.

**Treatment Outcome**: Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.

**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.

**Health Knowledge, Attitudes, Practice**: Knowledge, attitudes, and associated behaviors which pertain to health-related topics such as PATHOLOGIC PROCESSES or diseases, their prevention, and treatment. This term refers to non-health workers and health workers (HEALTH PERSONNEL).

**Iran**

**Open Bite**: A condition in which certain opposing teeth fail to establish occlusal contact when the jaws are closed.

**Statistics, Nonparametric**: A class of statistical methods applicable to a large set of probability distributions used to test for correlation, location, independence, etc. In most nonparametric statistical tests, the original scores or observations are replaced by another variable containing less information. An important class of nonparametric tests employs the ordinal properties of the data. Another class of tests uses information about whether an observation is above or below some fixed value such as the median, and a third class is based on the frequency of the occurrence of runs in the data. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed, p1284; Corsini, Concise Encyclopedia of Psychology, 1987, p764-5)

**Time Factors**: Elements of limited time intervals, contributing to particular results or situations.

**Prognosis**: A prediction of the probable outcome of a disease based on a individual's condition and the usual course of the disease as seen in similar situations.

**Esthetics, Dental**: Skills, techniques, standards, and principles used to improve the art and symmetry of the teeth and face to improve the appearance as well as the function of the teeth, mouth, and face. (From Boucher's Clinical Dental Terminology, 4th ed, p108)

**Follow-Up Studies**: Studies in which individuals or populations are followed to assess the outcome of exposures, procedures, or effects of a characteristic, e.g., occurrence of disease.

**Analysis of Variance**: A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.

**Students, Dental**: Individuals enrolled a school of dentistry or a formal educational program in leading to a degree in dentistry.

**Orthodontic Brackets**: Small metal or ceramic attachments used to fasten an arch wire. These attachments are soldered or welded to an orthodontic band or cemented directly onto the teeth. Bowles brackets, edgewise brackets, multiphase brackets, ribbon arch brackets, twin-wire brackets, and universal brackets are all types of orthodontic brackets.

**Oral Hygiene**: The practice of personal hygiene of the mouth. It includes the maintenance of oral cleanliness, tissue tone, and general preservation of oral health.

**Toothbrushing**: The act of cleaning teeth with a brush to remove plaque and prevent tooth decay. (From Webster, 3d ed)

**Pregnancy**: The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.

**Dental Caries**: Localized destruction of the tooth surface initiated by decalcification of the enamel followed by enzymatic lysis of organic structures and leading to cavity formation. If left unchecked, the cavity may penetrate the enamel and dentin and reach the pulp.

**China**: A country spanning from central Asia to the Pacific Ocean.

**Dental Prosthesis**: An artificial replacement for one or more natural teeth or part of a tooth, or associated structures, ranging from a portion of a tooth to a complete denture. The dental prosthesis is used for cosmetic or functional reasons, or both. DENTURES and specific types of dentures are also available. (From Boucher's Clinical Dental Terminology, 4th ed, p244 & Jablonski, Dictionary of Dentistry, 1992, p643)

**Epidemiologic Methods**: Research techniques that focus on study designs and data gathering methods in human and animal populations.

**Gene Frequency**: The proportion of one particular in the total of all ALLELES for one genetic locus in a breeding POPULATION.

**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.

**Diastema**: An abnormal opening or fissure between two adjacent teeth.

**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.

**Genotype**: The genetic constitution of the individual, comprising the ALLELES present at each GENETIC LOCUS.

**Rural Population**: The inhabitants of rural areas or of small towns classified as rural.

**Orthodontics**: A dental specialty concerned with the prevention and correction of dental and oral anomalies (malocclusion).

**Tooth Injuries**: Traumatic or other damage to teeth including fractures (TOOTH FRACTURES) or displacements (TOOTH LUXATION).

**Multivariate Analysis**: A set of techniques used when variation in several variables has to be studied simultaneously. In statistics, multivariate analysis is interpreted as any analytic method that allows simultaneous study of two or more dependent variables.

**Pacifiers**: Devices that babies can suck on when they are not feeding. The extra sucking can be comforting to the babies and pacify them. Pacifiers usually are used as a substitute for the thumb in babies who suck on their thumb or fingers almost constantly.

**Gingival Hemorrhage**: The flowing of blood from the marginal gingival area, particularly the sulcus, seen in such conditions as GINGIVITIS, marginal PERIODONTITIS, injury, and ASCORBIC ACID DEFICIENCY.

**Risk Assessment**: The qualitative or quantitative estimation of the likelihood of adverse effects that may result from exposure to specified health hazards or from the absence of beneficial influences. (Last, Dictionary of Epidemiology, 1988)

**Urban Population**: The inhabitants of a city or town, including metropolitan areas and suburban areas.

**Odds Ratio**: The ratio of two odds. The exposure-odds ratio for case control data is the ratio of the odds in favor of exposure among cases to the odds in favor of exposure among noncases. The disease-odds ratio for a cohort or cross section is the ratio of the odds in favor of disease among the exposed to the odds in favor of disease among the unexposed. The prevalence-odds ratio refers to an odds ratio derived cross-sectionally from studies of prevalent cases.

**Age Distribution**: The frequency of different ages or age groups in a given population. The distribution may refer to either how many or what proportion of the group. The population is usually patients with a specific disease but the concept is not restricted to humans and is not restricted to medicine.

**Severity of Illness Index**: Levels within a diagnostic group which are established by various measurement criteria applied to the seriousness of a patient's disorder.

**Oral Health**: The optimal state of the mouth and normal functioning of the organs of the mouth without evidence of disease.

**Incisor**: Any of the eight frontal teeth (four maxillary and four mandibular) having a sharp incisal edge for cutting food and a single root, which occurs in man both as a deciduous and a permanent tooth. (Jablonski, Dictionary of Dentistry, 1992, p820)

**Students**: Individuals enrolled in a school or formal educational program.

**Sex Distribution**: The number of males and females in a given population. The distribution may refer to how many men or women or what proportion of either in the group. The population is usually patients with a specific disease but the concept is not restricted to humans and is not restricted to medicine.

**Infant, Newborn**: An infant during the first month after birth.

**Tooth, Deciduous**: The teeth of the first dentition, which are shed and replaced by the permanent teeth.

**Surgery, Oral**: A dental specialty concerned with the diagnosis and surgical treatment of disease, injuries, and defects of the human oral and maxillofacial region.

**Trinidad and Tobago**: An independent state in the Lesser Antilles in the West Indies, north of Venezuela, comprising the islands of Trinidad and Tobago. Its capital is Port of Spain. Both islands were discovered by Columbus in 1498. The Spanish, English, Dutch, and French figure in their history over four centuries. Trinidad and Tobago united in 1898 and were made part of the British colony of Trinidad and Tobago in 1899. The colony became an independent state in 1962. Trinidad was so named by Columbus either because he arrived on Trinity Sunday or because three mountain peaks suggested the Holy Trinity. Tobago was given the name by Columbus from the Haitian tambaku, pipe, from the natives' habit of smoking tobacco leaves. (Webster's New Geographical Dictionary, 1988, p1228, 1216 & Room, Brewer's Dictionary of Names, 1992, p555, 547)

**United States**

**Tertiary Healthcare**: Care of a highly technical and specialized nature, provided in a medical center, usually one affiliated with a university, for patients with unusually severe, complex, or uncommon health problems.

**Shear Strength**: The internal resistance of a material to moving some parts of it parallel to a fixed plane, in contrast to stretching (TENSILE STRENGTH) or compression (COMPRESSIVE STRENGTH). Ionic crystals are brittle because, when subjected to shear, ions of the same charge are brought next to each other, which causes repulsion.

**Bicuspid**: One of the eight permanent teeth, two on either side in each jaw, between the canines (CUSPID) and the molars (MOLAR), serving for grinding and crushing food. The upper have two cusps (bicuspid) but the lower have one to three. (Jablonski, Dictionary of Dentistry, 1992, p822)

**Educational Status**: Educational attainment or level of education of individuals.

**Anodontia**: Congenital absence of the teeth; it may involve all (total anodontia) or only some of the teeth (partial anodontia, hypodontia), and both the deciduous and the permanent dentition, or only teeth of the permanent dentition. (Dorland, 27th ed)

**Incidence**: The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from PREVALENCE, which refers to all cases, new or old, in the population at a given time.

**Genetic Predisposition to Disease**: A latent susceptibility to disease at the genetic level, which may be activated under certain conditions.

**Sucking Behavior**: Any suction exerted by the mouth; response of the mammalian infant to draw milk from the breast. Includes sucking on inanimate objects. Not to be used for thumb sucking, which is indexed under fingersucking.

**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.

**Croatia**: Created 7 April 1992 as a result of the division of Yugoslavia.

**Pakistan**

**Temporomandibular Joint Disorders**: A variety of conditions affecting the anatomic and functional characteristics of the temporomandibular joint. Factors contributing to the complexity of temporomandibular diseases are its relation to dentition and mastication and the symptomatic effects in other areas which account for referred pain to the joint and the difficulties in applying traditional diagnostic procedures to temporomandibular joint pathology where tissue is rarely obtained and x-rays are often inadequate or nonspecific. Common diseases are developmental abnormalities, trauma, subluxation, luxation, arthritis, and neoplasia. (From Thoma's Oral Pathology, 6th ed, pp577-600)

**Maxilla**: One of a pair of irregularly shaped bones that form the upper jaw. A maxillary bone provides tooth sockets for the superior teeth, forms part of the ORBIT, and contains the MAXILLARY SINUS.

**DMF Index**: "Decayed, missing and filled teeth," a routinely used statistical concept in dentistry.

**Nigeria**: A republic in western Africa, south of NIGER between BENIN and CAMEROON. Its capital is Abuja.

**Radiography, Bitewing**: Technique involving the passage of X-rays through oral structures to create a film record while a central tab or wing of dental X-ray film is being held between upper and lower teeth.

**Mouth Diseases**

**Models, Statistical**: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.

**Molar**: The most posterior teeth on either side of the jaw, totaling eight in the deciduous dentition (2 on each side, upper and lower), and usually 12 in the permanent dentition (three on each side, upper and lower). They are grinding teeth, having large crowns and broad chewing surfaces. (Jablonski, Dictionary of Dentistry, 1992, p821)

**Universities**: Educational institutions providing facilities for teaching and research and authorized to grant academic degrees.

**Dental Prophylaxis**: Treatment for the prevention of periodontal diseases or other dental diseases by the cleaning of the teeth in the dental office using the procedures of DENTAL SCALING and DENTAL POLISHING. The treatment may include plaque detection, removal of supra- and subgingival plaque and calculus, application of caries-preventing agents, checking of restorations and prostheses and correcting overhanging margins and proximal contours of restorations, and checking for signs of food impaction.

**Dental Occlusion**: The relationship of all the components of the masticatory system in normal function. It has special reference to the position and contact of the maxillary and mandibular teeth for the highest efficiency during the excursive movements of the jaw that are essential for mastication. (From Jablonski, Dictionary of Dentistry, 1992, p556, p472)

**Polymorphism, Single Nucleotide**: A single nucleotide variation in a genetic sequence that occurs at appreciable frequency in the population.

**Mandible**: The largest and strongest bone of the FACE constituting the lower jaw. It supports the lower teeth.

**Tooth Apex**: The tip or terminal end of the root of a tooth. (Jablonski, Dictionary of Dentistry, 1992, p62)

**Odontometry**: Measurement of tooth characteristics.

**Resin Cements**: Dental cements composed either of polymethyl methacrylate or dimethacrylate, produced by mixing an acrylic monomer liquid with acrylic polymers and mineral fillers. The cement is insoluble in water and is thus resistant to fluids in the mouth, but is also irritating to the dental pulp. It is used chiefly as a luting agent for fabricated and temporary restorations. (Jablonski's Dictionary of Dentistry, 1992, p159)

**Dental Arch**: The curve formed by the row of TEETH in their normal position in the JAW. The inferior dental arch is formed by the mandibular teeth, and the superior dental arch by the maxillary teeth.

**Dentists**: Individuals licensed to practice DENTISTRY.

**Alleles**: Variant forms of the same gene, occupying the same locus on homologous CHROMOSOMES, and governing the variants in production of the same gene product.

**Asian Continental Ancestry Group**: Individuals whose ancestral origins are in the southeastern and eastern areas of the Asian continent.

**Acid Etching, Dental**: Preparation of TOOTH surfaces and DENTAL MATERIALS with etching agents, usually phosphoric acid, to roughen the surface to increase adhesion or osteointegration.

**Radiography, Panoramic**: Extraoral body-section radiography depicting an entire maxilla, or both maxilla and mandible, on a single film.

**Dental Enamel**: A hard thin translucent layer of calcified substance which envelops and protects the dentin of the crown of the tooth. It is the hardest substance in the body and is almost entirely composed of calcium salts. Under the microscope, it is composed of thin rods (enamel prisms) held together by cementing substance, and surrounded by an enamel sheath. (From Jablonski, Dictionary of Dentistry, 1992, p286)

**Dental Care**: The total of dental diagnostic, preventive, and restorative services provided to meet the needs of a patient (from Illustrated Dictionary of Dentistry, 1982).

**Stainless Steel**: Stainless steel. A steel containing Ni, Cr, or both. It does not tarnish on exposure and is used in corrosive environments. (Grant & Hack's Chemical Dictionary, 5th ed)

**Attitude to Health**: Public attitudes toward health, disease, and the medical care system.

**Smoking**: Inhaling and exhaling the smoke of burning TOBACCO.

**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.

**Dental Plaque Index**: An index which scores the degree of dental plaque accumulation.

**Dental Cements**: Substances used to bond COMPOSITE RESINS to DENTAL ENAMEL and DENTIN. These bonding or luting agents are used in restorative dentistry, ROOT CANAL THERAPY; PROSTHODONTICS; and ORTHODONTICS.

**Tooth Eruption, Ectopic**: An abnormality in the direction of a TOOTH ERUPTION.

**Sensitivity and Specificity**: Binary classification measures to assess test results. Sensitivity or recall rate is the proportion of true positives. Specificity is the probability of correctly determining the absence of a condition. (From Last, Dictionary of Epidemiology, 2d ed)

**Health Education, Dental**: Education which increases the awareness and favorably influences the attitudes and knowledge relating to the improvement of dental health on a personal or community basis.

**Dentist's Practice Patterns**: Patterns of practice in dentistry related to diagnosis and treatment.

**Radiography, Dental**: Radiographic techniques used in dentistry.

**Periodontal Pocket**: An abnormal extension of a gingival sulcus accompanied by the apical migration of the epithelial attachment and bone resorption.

**Toothpastes**: Dentifrices that are formulated into a paste form. They typically contain abrasives, HUMECTANTS; DETERGENTS; FLAVORING AGENTS; and CARIOSTATIC AGENTS.

**Malaysia**: A parliamentary democracy with a constitutional monarch in southeast Asia, consisting of 11 states (West Malaysia) on the Malay Peninsula and two states (East Malaysia) on the island of BORNEO. It is also called the Federation of Malaysia. Its capital is Kuala Lumpur. Before 1963 it was the Union of Malaya. It reorganized in 1948 as the Federation of Malaya, becoming independent from British Malaya in 1957 and becoming Malaysia in 1963 as a federation of Malaya, Sabah, Sarawak, and Singapore (which seceded in 1965). The form Malay- probably derives from the Tamil malay, mountain, with reference to its geography. (From Webster's New Geographical Dictionary, 1988, p715 & Room, Brewer's Dictionary of Names, 1992, p329)

**European Continental Ancestry Group**: Individuals whose ancestral origins are in the continent of Europe.

**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.

**Attitude of Health Personnel**: Attitudes of personnel toward their patients, other professionals, toward the medical care system, etc.

**Burning Mouth Syndrome**: A group of painful oral symptoms associated with a burning or similar sensation. There is usually a significant organic component with a degree of functional overlay; it is not limited to the psychophysiologic group of disorders.

**Poland**

**Preventive Dentistry**: The branch of dentistry concerned with the prevention of disease and the maintenance and promotion of oral health.

**Taiwan**

**Periapical Periodontitis**: Inflammation of the PERIAPICAL TISSUE. It includes general, unspecified, or acute nonsuppurative inflammation. Chronic nonsuppurative inflammation is PERIAPICAL GRANULOMA. Suppurative inflammation is PERIAPICAL ABSCESS.

**Root Resorption**: Resorption in which cementum or dentin is lost from the root of a tooth owing to cementoclastic or osteoclastic activity in conditions such as trauma of occlusion or neoplasms. (Dorland, 27th ed)

**Physician's Practice Patterns**: Patterns of practice related to diagnosis and treatment as especially influenced by cost of the service requested and provided.

**Chronic Periodontitis**: Chronic inflammation and loss of PERIODONTIUM that is associated with the amount of DENTAL PLAQUE or DENTAL CALCULUS present. Chronic periodontitis occurs mostly in adults and was called adult periodontitis, but this disease can appear in young people.

**Quality of Life**: A generic concept reflecting concern with the modification and enhancement of life attributes, e.g., physical, political, moral and social environment; the overall condition of a human life.

**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.

**Survival Rate**: The proportion of survivors in a group, e.g., of patients, studied and followed over a period, or the proportion of persons in a specified group alive at the beginning of a time interval who survive to the end of the interval. It is often studied using life table methods.

**Dental Bonding**: An adhesion procedure for orthodontic attachments, such as plastic DENTAL CROWNS. This process usually includes the application of an adhesive material (DENTAL CEMENTS) and letting it harden in-place by light or chemical curing.

**Kuwait**

**Proportional Hazards Models**: Statistical models used in survival analysis that assert that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time.

**Kentucky**

**Breast Neoplasms**: Tumors or cancer of the human BREAST.

**Postoperative Complications**: Pathologic processes that affect patients after a surgical procedure. They may or may not be related to the disease for which the surgery was done, and they may or may not be direct results of the surgery.

**Orthodontic Retainers**: Orthodontic appliances, fixed or removable, used to maintain teeth in corrected positions during the period of functional adaptation following corrective treatment. These appliances are also used to maintain the positions of the teeth and jaws gained by orthodontic procedures. (From Zwemer, Boucher's Clinical Dental Terminology, 4th ed, p263)

**African Americans**: Persons living in the United States having origins in any of the black groups of Africa.

###### **Chi**-**square** **distribution** - Biology-Online Dictionary

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https://rdrr.io/github/rsquaredacademy/descriptr/man/dist_chi_plot.html**chi****square****distribution**. Compute & visualize quantiles out ... visualize**chi****square****distribution**dist_**chi**_plot() dist_**chi**_plot(df = 5) dist_**chi**_plot(df = 5, normal = TRUE) # visualize ...**chi**_plot(). ,**chi**_prob(). and**chi**_per(). have been deprecated. Instead use dist_**chi**_plot(). , dist_**chi**_prob(). and dist_**chi**_ ... dist_**chi**_plot(df = 3, normal = FALSE) dist_**chi**_perc(probs = 0.95, df = 3, type = c('lower', 'upper')) dist_**chi**_prob(perc, df, ...###### A **Chi**-**Square** Approximation for the F **Distribution**

In this paper, a simple

https://www.scirp.org/journal/PaperInformation.aspx?PaperID=82593**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. ...###### **Chi**-**square**+Test-Gender+**distribution** - **Chi** **square** test 2-The student population at the state college consists of 55 female and...

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TABLE 2:

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For qualitative variables, Pearson`s

http://ro-journal.biomedcentral.com.preview-live.oscarjournals.springer.com/articles/10.1186/1748-717X-7-169**chi**-**square**or Fisher`s exact test were used. The analysis of overall and disease-free ... However, by studying the**distribution**of these patients in different N-category N-ratio categories, individuals with N1 and N2 ... N-ratio**distribution**was uniform, with slightly higher number of NR0 and NR1 patients. ...**distribution**, and reproduction in any medium, provided the original work is properly cited. ...**University of Campinas**

**Closed-ended question**: A closed-ended question is a question format that limits respondents with a list of answer choices from which they must choose to answer the question.Dillman D.

**QRISK**: QRISK2 (the most recent version of QRISK) is a prediction algorithm for cardiovascular disease (CVD) that uses traditional risk factors (age, systolic blood pressure, smoking status and ratio of total serum cholesterol to high-density lipoprotein cholesterol) together with body mass index, ethnicity, measures of deprivation, family history, chronic kidney disease, rheumatoid arthritis, atrial fibrillation, diabetes mellitus, and antihypertensive treatment.

**Tamil Nadu Dr. M.G.R. Medical University**

**Kocaeli University**: The University of Kocaeli (KOU) is a state university in Kocaeli, Turkey. It was founded as the Academy of Engineering and Architecture of Kocaeli in 1976.

**Nested case-control study**: A nested case control (NCC) study is a variation of a case-control study in which only a subset of controls from the cohort are compared to the incident cases. In a case-cohort study, all incident cases in the cohort are compared to a random subset of participants who do not develop the disease of interest.

**Equine malocclusion**: An equine malocclusion is a misalignment between the upper and lower jaws of a horse or other equine. It results in a faulty bite with the upper and lower teeth failing to meet correctly.

**Age adjustment**: In epidemiology and demography, age adjustment, also called age standardization, is a technique used to allow populations to be compared when the age profiles of the populations are quite different.

**Behavior change (public health)**: Behavior change is a central objective in public health interventions,WHO 2002: World Health Report 2002 - Reducing Risks, Promoting Healthy Life Accessed Feb 2015 http://www.who.

**List of universities in Iran**: This is a list of universities in Iran.

**Temporal analysis of products**: Temporal Analysis of Products (TAP), (TAP-2), (TAP-3) is an experimental technique for studying

**Bracket (mathematics)**: In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses ( ), square brackets [ ], braces { }, and angle brackets \langle\,\,\rangle. In the typical use, a mathematical expression is enclosed between an "opening bracket" and a matching "closing bracket".

**Toothbrush**: The toothbrush is an oral hygiene instrument used to clean the teeth and gums that consists of a head of tightly clustered bristles mounted on a handle, which facilitates the cleansing of hard-to-reach areas of the mouth.

**Prenatal nutrition**: Nutrition and weight management before and during :pregnancy has a profound effect on the development of infants. This is a rather critical time for healthy fetal development as infants rely heavily on maternal stores and nutrient for optimal growth and health outcome later in life.

**Dental caries**

**Layout of the Port of Tianjin**: The Port of Tianjin is divided into nine areas: the three core (“Tianjin Xingang”) areas of Beijiang, Nanjiang, and Dongjiang around the Xingang fairway; the Haihe area along the river; the Beitang port area around the Beitangkou estuary; the Dagukou port area in the estuary of the Haihe River; and three areas under construction (Hanggu, Gaoshaling, Nangang).

**Epidemiological method**: The science of epidemiology has matured significantly from the times of Hippocrates and John Snow. The techniques for gathering and analyzing epidemiological data vary depending on the type of disease being monitored but each study will have overarching similarities.

**Micrurus diastema**

**British Orthodontic Society**: The British Orthodontic Society (BOS) is a membership organisation with over 1800 members in the United Kingdom. It is the largest of the dental specialist groups and dates back nearly a century to the formation of the British Society for the Study of Orthodontics.

**Dental subluxation**: Dental subluxation is a traumatic injury in which the tooth has increased mobility (i.e.

**Pacifier**: A pacifier (American English), dummy (United Kingdom, other Commonwealth countries and Ireland), binky, or soother (Canadian English) is a rubber, plastic, or silicone nipple given to an infant or other young child to suck upon. In its standard appearance it has a teat, mouth shield, and handle.

**Global Risks Report**: The Global Risks Report is an annual study published by the World Economic Forum ahead of the Forum’s Annual Meeting in Davos, Switzerland. Based on the work of the Global Risk Network, the report describes changes occurring in the global risks landscape from year to year and identifies the global risks that could play a critical role in the upcoming year.

**Overjet**

**Cigarette smoking among college students**: The rates of college students smoking in the United States have fluctuated for the past twenty years. Majority of lifelong smokers begin smoking habits before the age of 24, which makes the college years a crucial time in the study of cigarette consumption.

**Neonatal line**: The neonatal line is a particular band of incremental growth lines seen in histologic sections of a deciduous tooth. It belongs to a series of a growth lines in tooth enamel known as the Striae of Retzius.

**British Association of Oral and Maxillofacial Surgeons**: The British Association of Oral and Maxillofacial Surgeons is the British medical association for oral and maxillofacial (mouth, jaws and face) surgeons - dentists who are also trained in oral surgery.

**Environment of Trinidad and Tobago**: The environment of Trinidad and Tobago reflects the interaction between its biotic diversity, high population density, and industrialised economy.

**List of Parliamentary constituencies in Kent**: The ceremonial county of Kent,

**Customer communications management**

**Bagnold's fluid**: Bagnold's fluid refers to a suspension of neutrally buoyant particles in a Newtonian fluid such as water or air. The term is named after Ralph Alger Bagnold, who placed such a suspension in an annular coaxial cylindrical rheometer in order to investigate the effects of grain interaction in the suspension.

**Hypodontia**

**Incidence (epidemiology)**: Incidence is a measure of the probability of occurrence of a given medical condition in a population within a specified period of time. Although sometimes loosely expressed simply as the number of new cases during some time period, it is better expressed as a proportion or a rate with a denominator.

**Gene polymorphism**

**University Hospital Centre Zagreb**: The University Hospital Centre (sometimes also Clinical Hospital Centre, ) in Zagreb, Croatia, is the largest hospital in Croatia and the teaching hospital of the University of Zagreb. It serves most of Central and Northern Croatia for specialist and acute medical procedures.

**Aga Khan University Hospital, Karachi**: The Aga Khan University Hospital (AKUH) in Karachi, established in 1985, is the primary teaching site of the Aga Khan University’s (AKU) Faculty of Health Sciences. Founded by His Highness the Aga Khan, the hospital provides a broad range of secondary and tertiary care, including diagnosis of disease and team management of patient care.

**Nigerian Ports Authority**: The Nigerian Ports Authority (NPA) is a federal government agency that governs and operates the ports of Nigeria. The major ports controlled by the NPA include: the Lagos Port Complex and Tin Can Island Port in Lagos; Calabar Port, Delta Port, Rivers Port at Port Harcourt, and Onne Port.

**Inverse probability weighting**: Inverse probability weighting is a statistical technique for calculating statistics standardized to a population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application.

**Antenor Orrego Private University**

**Overeruption**: In dentistry, overeruption is the physiological movement of a tooth lacking an opposing partner in the dental occlusion. Because of the lack of opposing force and the natural eruptive potential of the tooth there is a tendency for the tooth to erupt out of the line of the occlusion.

**WGAViewer**: WGAViewer is a bioinformatics software tool which is designed to visualize, annotate, and help interpret the results generated from a genome wide association study (GWAS). Alongside the P values of association, WGAViewer allows a researcher to visualize and consider other supporting evidence, such as the genomic context of the SNP, linkage disequilibrium (LD) with ungenotyped SNPs, gene expression database, and the evidence from other GWAS projects, when determining the potential importance of an individual SNP.

**Electronic apex locator**: 200px|right|thumb

**Malocclusion**

**Infinite alleles model**: The infinite alleles model is a mathematical model for calculating genetic mutations. The Japanese geneticist Motoo Kimura and American geneticist James F.

**Reactive-ion etching**: Reactive-ion etching (RIE) is an etching technology used in microfabrication. RIE is a type of dry etching which has different characteristics than wet etching.

**Panoramic radiograph**

**Enamel spindles**: Enamel spindles are "short, linear defects, found at the dentinoenamel junction (DEJ) and extend into the enamel, often being more prevalent at the cusp tips."Histology Course Notes: "Mature Enamel", New Jersey Dental School, 2003-2004, page 2.

**Dental Procedure Education System**: The Dental Procedure Education System (DPES), is a web-based resource containing a collection of procedures from the dental disciplines. The procedures presented in DPES were developed by individual faculty members at the Faculty of Dentistry, University of Toronto, in collaboration with a group of educational media and technology experts.

**Surgical stainless steel**: Surgical stainless steel is an informal term which refers to certain grades of stainless steel that are used in biomedical applications. The most common "surgical steels" are austenitic 316 stainless and martensitic 440 and 420 stainless steels.

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**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.**

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)

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**Natural history of dysplasia of the uterine cervix.**

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)

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**Low-dose combination therapy as first-line hypertension treatment for blacks and nonblacks.**

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)

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**Extent and severity of atherosclerotic involvement of the aortic valve and root in familial hypercholesterolaemia.**

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)

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**Amino acid composition of protein termini are biased in different manners.**

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)

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**Prevalence of true vein graft aneurysms: implications for aneurysm pathogenesis.**

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)

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**Cryoglobulinaemia and rheumatic manifestations in patients with hepatitis C virus infection.**

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)

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**Fetal tachycardias: management and outcome of 127 consecutive cases.**

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)

###### noncentral chi-square

- 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)
- The noncentral chi-square distribution in misspecified structural equation models: Finite sample results from a Monte Carlo simulation. (wikipedia.org)

###### variance

- 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)
- 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)
- 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)
- A variant of rank-transformation is 'quantile normalization' in which a further transformation is applied to the ranks such that the resulting values have some defined distribution (often a normal distribution with a specified mean and variance). (wikipedia.org)
- It is closely related to the chi-squared distribution and its specific importance is that it arises in the application of Bayesian inference to the normal distribution, where it can be used as the prior and posterior distribution for an unknown variance. (wikipedia.org)
- For instance, while the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient because the true variance and covariance are underestimated. (wikipedia.org)
- Heteroscedasticity does not cause ordinary least squares coefficient estimates to be biased, although it can cause ordinary least squares estimates of the variance (and, thus, standard errors) of the coefficients to be biased, possibly above or below the true or population variance. (wikipedia.org)
- Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks. (wikipedia.org)
- This transformation may result in better estimates particularly when the distribution of the variance itself may be non normal. (wikipedia.org)
- In the case of a unimodal variate the ratio of the jackknife variance to the sample variance tends to be distributed as one half the square of a chi square distribution with two degrees of freedom. (wikipedia.org)

###### variances

- 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)
- 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 derives the modified signed log-likelihood ratio statistic. (scirp.org)
- The difference from the standard chi-squared distribution is that Z i {\displaystyle Z_{i}} are complex and can have different variances, and the difference from the more general generalized chi-squared distribution is that the relevant scaling matrix A is diagonal. (wikipedia.org)
- The jackknife is consistent for the sample means, sample variances, central and non-central t-statistics (with possibly non-normal populations), sample coefficient of variation, maximum likelihood estimators, least squares estimators, correlation coefficients and regression coefficients. (wikipedia.org)

###### least squares

- When using some statistical techniques, such as ordinary least squares (OLS), a number of assumptions are typically made. (wikipedia.org)
- For example, if a predictive model is fitted by least squares but the model errors have either autocorrelation or heteroscedasticity, then a statistical analysis of alternative model structures can be undertaken by relating changes in the sum of squares to an asymptotically valid generalized chi-squared distribution. (wikipedia.org)

###### displaystyle

- An alternative representation can be stated in the form: X = ∑ i = 1 r λ i Y i + f Z 0 , {\displaystyle X=\sum _{i=1}^{r}\lambda _{i}Y_{i}+fZ_{0},} where the Yi represent random variables having (different) noncentral chi-squared distributions, where Z0 has a standard normal distribution, and where all these random variables are independent. (wikipedia.org)
- If μ = σ i 2 {\displaystyle \mu =\sigma _{i}^{2}} for all i, then Q ~ {\displaystyle {\tilde {Q}}} , scaled down by μ / 2 {\displaystyle \mu /2} (i.e. multiplied by 2 / μ {\displaystyle 2/\mu } ), has a chi-squared distribution, χ 2 ( 2 k ) {\displaystyle \chi ^{2}(2k)} , also known as an Erlang distribution. (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-squared distribution with k degrees of freedom. (wikipedia.org)

###### Pearson's

- One could apply Pearson's chi-square test of whether the population distribution is a Poisson distribution with expected value 3.3. (wikipedia.org)
- A Pearson's chi-square test could be used instead of log-linear analysis, but that technique only allows for two of the variables to be compared at a time. (wikipedia.org)

###### Maximum Likelihood

- Minimum Chi-Square, Not Maximum Likelihood! (wikipedia.org)

###### Inferential Statistics

- 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, e. g., in hypothesis testing or in construction of confidence intervals. (wikipedia.org)

###### statistic

- The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution . (biology-online.org)
- 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)
- is based on the asymptotic distribution of the log-likelihood ratio statistic. (scirp.org)
- 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)
- In certain chi-square tests, one rejects a null hypothesis about a population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null hypothesis is true. (wikipedia.org)
- In minimum chi-square estimation, one finds the values of parameters that make that test statistic as small as possible. (wikipedia.org)
- Among the consequences of its use is that the test statistic actually does have approximately a chi-square distribution when the sample size is large. (wikipedia.org)
- One might hope that the resulting test statistic would have approximately a chi-square distribution when the null hypothesis is true. (wikipedia.org)
- Numerical computation shows that the value of λ that minimizes the chi-square statistic is about 3.5242. (wikipedia.org)
- For that value of λ, the chi-square statistic is about 3.062764. (wikipedia.org)
- If the null hypothesis had specified a single distribution, rather than requiring λ to be estimated, then the null distribution of the test statistic would be a chi-square distribution with 10 − 1 = 9 degrees of freedom. (wikipedia.org)
- This result is used to justify using a normal distribution, or a chi square distribution (depending on how the test statistic is calculated), when conducting a hypothesis test. (wikipedia.org)
- 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)
- 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, and the distribution of the square of the test statistic approaches a chi-squared distribution. (wikipedia.org)
- This results in the likelihood ratio chi-square statistic being equal to 0, which is the best model fit. (wikipedia.org)

###### identical

- This might not be true even if the error term is assumed to be drawn from identical distributions. (wikipedia.org)
- Let z have a multivariate normal distribution with zero mean and covariance matrix B, then the value of the quadratic form X = zTAz, where A is a matrix, has a generalised chi-squared distribution with parameters A and B. Note that there is some redundancy in this formulation, as for any matrix C, the distribution with parameters CTAC and B is identical to the distribution with parameters A and CBCT. (wikipedia.org)

###### coefficient

- Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. (wikipedia.org)

###### hypothesis

- In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). (wikipedia.org)
- Consider randomly selected subjects that are subsequently randomly assigned to groups A, B, and C. Under the truth of the null hypothesis, the variability (or sum of squares) of scores on some dependent variable will be the same within each group. (wikipedia.org)
- Under the truth of the null hypothesis, the sampling distribution of the F ratio depends on the degrees of freedom for the numerator and the denominator. (wikipedia.org)
- It is desired to test the null hypothesis that the population from which this sample was taken follows a Poisson distribution. (wikipedia.org)
- However, the null hypothesis did not specify that it was that particular Poisson distribution, but only that it is some Poisson distribution, and the number 3.3 came from the data, not from the null hypothesis. (wikipedia.org)
- The chi-squared distribution is used primarily in hypothesis testing. (wikipedia.org)
- The primary reason that the chi-squared distribution is used extensively in hypothesis testing is its relationship to the normal distribution. (wikipedia.org)
- So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used. (wikipedia.org)

###### asymptotically

- It is however true asymptotically when minimum chi-square estimation is used. (wikipedia.org)
- However, the normal and chi-squared approximations are only valid asymptotically. (wikipedia.org)

###### probability distribution

- In this case, the absence of DIF is determined by the fact that the conditional probability distribution of Y is not dependent on group membership. (wikipedia.org)
- In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. (wikipedia.org)
- The inverse-chi-squared distribution (or inverted-chi-square distribution ) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chi-squared distribution. (wikipedia.org)

###### symmetric

- As the degrees of freedom increase the distribution becomes less skewed and more symmetric. (ti.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)

###### asymptotic distribution

- Under certain assumptions, the OLS estimator has a normal asymptotic distribution when properly normalized and centered (even when the data does not come from a normal distribution). (wikipedia.org)

###### Probabilities

- an approach based on the chi-square distribution for combining the individual word probabilities into a combined probability (actually a pair of probabilities-see below) representing an e-mail. (wikipedia.org)

###### degrees of freedom aff

- Explain how the degrees of freedom affect a Chi-Square Distribution. (foxessays.com)
- Visualize how changes in degrees of freedom affect the shape of the chi square distribution. (rdrr.io)

###### estimates

- The type of generalisation of the chi-squared distribution that is discussed here is of importance because it arises in the context of the distribution of statistical estimates in cases where the usual statistical theory does not hold. (wikipedia.org)

###### Compute

- Treat the mean for each group as a score, and compute the variability (again, the sum of squares) of those three scores. (wikipedia.org)
- Further analyses of quantile-normalized data may then assume that distribution to compute significance values. (wikipedia.org)

###### independent

- In probability theory and statistics, the chi-squared distribution (also chi-square 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)

###### test

- This is not a test, but a distribution. (uva.nl)
- Click the image or link below for tables of critical test values for different distributions. (oup.com)
- Chi-square test is based on the chi square distribution. (symynet.com)
- Chi-squared test of independence in contingency tables Chi-squared test of goodness of fit of observed data to hypothetical distributions Likelihood-ratio test for nested models Log-rank test in survival analysis Cochran-Mantel-Haenszel test for stratified contingency tables It is also a component of the definition of the t-distribution and the F-distribution used in t-tests, analysis of variance, and regression analysis. (wikipedia.org)
- 256MB samples: bit entropy test: >7.9999xx / 8.000000 compression test: 0% size reduction after compression chi square distribution test: 40% (wikipedia.org)

###### drawn

- as the chi square distribution is drawn. (rdrr.io)
- A sample drawn at random from Z is a sample from the distribution shown in the graph of the standard normal distribution. (wikipedia.org)

###### cumulative

- 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)
- Johnson and Kotz give a comprehensive review on the approximations to the cumulative distribution function (cdf) of the F distribution. (scirp.org)
- Computer code for evaluating the cumulative distribution function of the generalized chi-squared distribution has been published, but some preliminary manipulation of the parameters of the distribution is usually necessary. (wikipedia.org)

###### widely

- Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-squared distribution is not as often applied in the direct modeling of natural phenomena. (wikipedia.org)
- An additional reason that the chi-squared distribution is widely used is that it is a member of the class of likelihood ratio tests (LRT). (wikipedia.org)

###### Approximation

- This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small. (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-squared approximation for small sample size. (wikipedia.org)

###### parameter

- The chi-square distribution has one parameter k , the degrees of freedom. (symynet.com)
- The chi-squared distribution has one parameter: k - a positive integer that specifies the number of degrees of freedom (i. e. the number of Zi's). (wikipedia.org)

###### goodness

- The chi-squared distribution is used in the common chi-squared 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)

###### Statistics

- Information about and tables for the chi-square distribution can be found in any elementary statistics text. (thefreedictionary.com)
- F distribution is one of the most frequently used distributions in statistics. (scirp.org)
- In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. (wikipedia.org)
- In probability theory and statistics, the specific name generalized chi-squared distribution (also generalized chi-square distribution) arises in relation to one particular family of variants of the chi-squared distribution. (wikipedia.org)

###### normal distribution

- 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)
- More specifically, the distribution can be defined in terms of a quadratic form derived from a multivariate normal distribution. (wikipedia.org)
- Testing hypotheses using a normal distribution is well understood and relatively easy. (wikipedia.org)
- The simplest chi-squared distribution is the square of a standard normal distribution. (wikipedia.org)
- The subscript 1 indicates that this particular chi-squared distribution is constructed from only 1 standard normal distribution. (wikipedia.org)
- A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. (wikipedia.org)
- Just as extreme values of the normal distribution have low probability (and give small p-values), extreme values of the chi-squared distribution have low probability. (wikipedia.org)

###### gamma

- There are several other such variants for which the same term is sometimes used, or which clearly are generalizations of the chi-squared distribution, and which are treated elsewhere: some are special cases of the family discussed here, for example the noncentral chi-squared distribution and the gamma distribution, while the generalized gamma distribution is outside this family. (wikipedia.org)

###### characteristics

- In Problem 1, students will explore the characteristics of the Chi-Square Distribution. (ti.com)
- The following are proofs of several characteristics related to the chi-squared distribution. (wikipedia.org)

###### differences

- Whereas group differences indicate differing score distributions on Y, DIF explicitly involves conditioning on θ. (wikipedia.org)

###### contingency

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

###### example

- 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)

###### value

- The Chi-Square distribution is based on a sum of squares, therefore the value of X^2 will always be larger than (or equal to) zero. (uva.nl)
- 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)
- If our value of chi square from the formula is greater than the critical value of chi square, we reject H o and conclude that the obtained frequencies differ from the expected frequencies more than would be predicted by chance. (symynet.com)
- The expected value of a chi-square random variable with 8 degrees of freedom is 8. (wikipedia.org)
- Define a new random variable Q. To generate a random sample from Q, take a sample from Z and square the value. (wikipedia.org)

###### different

- There are many different chi-square distributions, one for each degree of freedom. (richland.edu)
- Is the gender distribution for theater goers significantly different from the distribution for the general college? (coursehero.com)
- In other words, members of different groups with the same trait or ability level have unequal probability distributions on Y. Once controlling for θ, there is a clear dependency between group membership and performance on an item. (wikipedia.org)

###### degree of free

- Here is one based on the distribution with 1 degree of freedom. (wikipedia.org)

###### population

- The oldest of these tests are used to detect whether two or more population distributions differ from one another. (biology-online.org)

###### random variable

- It is also often defined as the distribution of a random variable whose reciprocal divided by its degrees of freedom is a chi-squared distribution. (wikipedia.org)
- The distribution of the squared values is given by the random variable Q = Z2. (wikipedia.org)

###### standard

- Some important special cases relating to this particular form either omit the additional standard normal term and/or have central rather than non-central chi-squared distributions for the components of the summation. (wikipedia.org)

###### sample

- If the number of deaths at each hospital is large (say, five or more), then the usual chi-square distribution or other large-sample approach may be used, avoiding the need for simulations that would require a large amount of computer time. (thefreedictionary.com)

###### mean

- In practice it is rare - if not impossible - for an increase of X in a group mean to occur via an increase of each member's score by X.) This will shift the distribution X units in the positive direction, but will not have any impact on the variability within the group. (wikipedia.org)
- The most general form of generalized chi-squared distribution is obtained by extending the above consideration in two ways: firstly, to allow z to have a non-zero mean and, secondly, to include an additional linear combination of z in the definition of X. Note that, in the above formulation, A and B need not be positive definite. (wikipedia.org)

###### particular

- 2}} has a generalized chi-squared distribution of a particular form. (wikipedia.org)

###### parameters

- 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)

###### another

- Should I use some sort of Chi Square Distribution or another method. (talkstats.com)