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Multilevel Model
Multilevel models are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available. Multilevel models are particularly appropriate for research designs where data for participants are organized at more than one level (i.e., nested data). The units of analysis are usually individuals (at a lower level) who are nested within contextual/aggregate units (at a higher level). While the lowest level of data in multilevel models is usually an individual, repeated measurements of individuals may also be examined. As such, multilevel models provide an alternative type ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the Data generating process, data-generating process. When referring specifically to probability, probabilities, the corresponding term is probabilistic model. All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). Introduction Informally, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ANOVA
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation ''between'' the group means to the amount of variation ''within'' each group. If the between-group variation is substantially larger than the within-group variation, it suggests that the group means are likely different. This comparison is done using an F-test. The underlying principle of ANOVA is based on the law of total variance, which states that the total variance in a dataset can be broken down into components attributable to different sources. In the case of ANOVA, these sources are the variation between groups and the variation within groups. ANOVA was developed by the statistician Ronald Fisher. In its simplest form, it provides a statistical test of whether two or more population means are equal, and therefore generalizes the ''t''-test beyond two means. History While the analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mobile, Alabama
Mobile ( , ) is a city and the county seat of Mobile County, Alabama, United States. The population was 187,041 at the 2020 United States census, 2020 census. After a successful vote to annex areas west of the city limits in July 2023, Mobile's population increased to 204,689 residents, making it the List of municipalities in Alabama, second-most populous city in Alabama. Mobile is the principal municipality of the Mobile metropolitan area. Alabama's only saltwater port, Mobile is located on the Mobile River at the head of Mobile Bay on the north-central Gulf Coast of the United States, Gulf Coast. The Port of Mobile has always played a key role in the economic health of the city, beginning with the settlement as an important trading center between the French colonization of the Americas, French colonists and Native Americans in the United States, Native Americans, down to its current role as the 12th-largest port in the United States.Drechsel, Emanuel. ''Mobilian Jargon: Lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seattle
Seattle ( ) is the most populous city in the U.S. state of Washington and in the Pacific Northwest region of North America. With a population of 780,995 in 2024, it is the 18th-most populous city in the United States. The city is the county seat of King County, the most populous county in Washington. The Seattle metropolitan area's population is 4.02 million, making it the 15th-most populous in the United States. Its growth rate of 21.1% between 2010 and 2020 made it one of the country's fastest-growing large cities. Seattle is situated on an isthmus between Puget Sound, an inlet of the Pacific Ocean, and Lake Washington. It is the northernmost major city in the United States, located about south of the Canadian border. A gateway for trade with East Asia, the Port of Seattle is the fourth-largest port in North America in terms of container handling . The Seattle area has been inhabited by Native Americans (such as the Duwamish, who had at least 17 villages a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Variable
In statistics, a categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical distribution. Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Variable
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. In pure mathematics In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers)Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183 and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is , and the most common symbol for the output is ; the function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin language, Latin ) is a Mathematical symbol, symbol, typically a letter, that refers to an unspecified mathematical object. One says colloquially that the variable ''represents'' or ''denotes'' the object, and that any valid candidate for the object is the value (mathematics), value of the variable. The values a variable can take are usually of the same kind, often numbers. More specifically, the values involved may form a Set (mathematics), set, such as the set of real numbers. The object may not always exist, or it might be uncertain whether any valid candidate exists or not. For example, one could represent two integers by the variables and and require that the value of the square of is twice the square of , which in algebraic notation can be written . A definitive proof that this relationship is impossible to satisfy when and are restricted to integer numbers isn't obvious, but it has been known since ancient times and has had a big ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Educational Research
Educational research refers to the systematic collection and analysis of evidence and data related to the field of education. Research may involve a variety of methods and various aspects of education including student learning, interaction, teaching methods, teacher training, and classroom dynamics. Educational researchers generally agree that research should be rigorous and systematic. However, there is less agreement about specific standards, criteria and research procedures. As a result, the value and quality of educational research has been questioned. Educational researchers may draw upon a variety of disciplines including psychology, economics, sociology, anthropology, and philosophy. Methods may be drawn from a range of disciplines. Conclusions drawn from an individual research study may be limited by the characteristics of the participants who were studied and the conditions under which the study was conducted. General characteristics Gary Anderson outlined ten aspect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Power Model
Statistics (from German: ', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is Statistical significance, statistically significant or not. It is any statistical hypothesis testing, statistical hypothesis test in which the test statistic follows a Student's t-distribution, Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a Scale parameter, scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a Z-test, ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z-test
A ''Z''-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. ''Z''-test tests the mean of a distribution. For each statistical significance, significance level in the Confidence intervals, confidence interval, the ''Z''-test has a single critical value (for example, 1.96 for 5% two-tailed), which makes it more convenient than the Student's t-test, Student's ''t''-test whose critical values are defined by the sample size (through the corresponding degrees of freedom (statistics), degrees of freedom). Both the ''Z''-test and Student's ''t''-test have similarities in that they both help determine the significance of a set of data. However, the ''Z''-test is rarely used in practice because the population deviation is difficult to determine. Applicability Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homoscedasticity
In statistics, a sequence of random variables is homoscedastic () if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings ''homoskedasticity'' and ''heteroskedasticity'' are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic () results in Biased estimator, unbiased but Efficiency (statistics), inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson product-moment correlation coefficient, Pearson coefficient. The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical hypothesis testing, statistical tests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
