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Anchor test

In psychometrics, an anchor test is a common set of test items administered in combination with two or more alternative forms of the test with the aim of establishing the equivalence of the test scores on the alternative forms. The purpose of the anchor test is to provide a baseline for an equating analysis between different forms of a test.


Test score

A test score is a piece of information, usually a number, that conveys the performance of an examinee on a test. One formal definition is that it is "a summary of the evidence contained in an examinee's responses to the items of a test that are related to the construct or constructs being measured."

Test scores are interpreted with a norm-referenced or criterion-referenced interpretation, or occasionally both. A norm-referenced interpretation means that the score conveys meaning about the examinee with regards to their standing among other examinees. A criterion-referenced interpretation means that the score conveys information about the examinee with regards a specific subject matter, regardless of other examinees' scores.

Types of test scores

There are two types of test scores: raw scores and scaled scores. A raw score is a score without any sort of adjustment or transformation, such as the simple number of questions answered correctly. A scaled score is the results of some transformation applied to the raw score.

The purpose of scaled scores is to report scores for all examinees on a consistent scale. Suppose that a test has two forms, and one is more difficult than the other. It has been determined by equating that a score of 65% on form 1 is equivalent to a score of 68% on form 2. Scores on both forms can be converted to a scale so that these two equivalent scores have the same reported scores. For example, they could both be a score of 350 on a scale of 100 to 500.

Two well-known tests in the United States that have scaled scores are the ACT and the SAT. The ACT's scale ranges from 0 to 36 and the SAT's from 200 to 800 (per section). Ostensibly, these two scales were selected to represent a mean and standard deviation of 18 and 6 (ACT), and 500 and 100. The upper and lower bounds were selected because an interval of plus or minus three standard deviations contains more than 99% of a population. Scores outside that range are difficult to measure, and return little practical value.

Note that scaling does not affect the psychometric properties of a test, it is something that occurs after the assessment process (and equating, if present) is completed. Therefore, it is not a psychometric issue, but a public relations issue.


Arrhenius equation

The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish chemist Svante Arrhenius provided a physical justification and interpretation for it. Currently, it is best seen as an empirical relationship. It can be used to model the temperature-variance of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions.

A historically useful generalization supported by the Arrhenius equation is that, for many common chemical reactions at room temperature, the reaction rate doubles for every 10 degree Celsius increase in temperature.

Overview

In short, the Arrhenius equation gives "the dependence of the rate constantk of chemical reactions on the temperatureT (in absolute temperature, such as kelvins or degrees Rankine) and activation energyEa", as shown below:

k = A e^/{RT}}

where A is the pre-exponential factor or simply the prefactor and R is the gas constant. The units of the pre-exponential factor are identical to those of the rate constant and will vary depending on the order of the reaction. If the reaction is first order it has the units s−1, and for that reason it is often called the frequency factor or attempt frequency of the reaction. Most simply, k is the number of collisions that result in a reaction per second, A is the total number of collisions (leading to a reaction or not) per second and e^/{RT}} is the probability that any given collision will result in a reaction. When the activation energy is given in molecular units instead of molar units, e.g., joules per molecule instead of joules per mole, the Boltzmann constant is used instead of the gas constant. It can be seen that either increasing the temperature or decreasing the activation energy (for example through the use of catalysts) will result in an increase in rate of reaction.

Given the small temperature range kinetic studies occur in, it is reasonable to approximate the activation energy as being independent of the temperature. Similarly, under a wide range of practical conditions, the weak temperature dependence of the pre-exponential factor is negligible compared to the temperature dependence of the \scriptstyle \exp(-E_a/RT) factor; except in the case of "barrierless" diffusion-limited reactions, in which case the pre-exponential factor is dominant and is directly observable.

Some authors define a modified Arrhenius equation, that makes explicit the temperature dependence of the pre-exponential factor. If one allows arbitrary temperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverse problem (i.e., determining the prefactor and activation energy from experimental data) becomes singular. The modified equation is usually of the form

k = A (T/T_0)^n e^/{RT}}

where T0 is a reference temperature and allows n to be a unitless power. Clearly the original Arrhenius expression above corresponds to n&nbsp;= 0. Fitted rate constants typically lie in the range -1<n<1. Theoretical analyses yield various predictions for n. It has been pointed out that "it is not feasible to establish, on the basis of temperature studies of the rate constant, whether the predicted T½ dependence of the pre-exponential factor is observed experimentally." However, if additional evidence is available, from theory and/or from experiment (such as density dependence), there is no obstacle to incisive tests of the Arrhenius law.

Another common modification is the stretched exponentialform

k = A exp \left[-\left(\frac{E_a}{RT}\right)^{\beta}\right]

where β is a unitless number of order 1. This is typically regarded as a fudge factor to make the model fit the data, but can have theoretical meaning, for example showing the presence of a range of activation energies or in special cases like the Mott variable range hopping.

Taking the natural logarithm of the Arrhenius equation yields:

\ln(k)= \frac{-E_a}{R}\frac{1}{T} + \ln(A)

So, when a reaction has a rate constant that obeys the Arrhenius equation, a plot of ln(k) versus T−1 gives a straight line, whose slope and intercept can be used to determine Ea and A. This procedure has become so common in experimental chemical kinetics that practitioners have taken to using it to define the activation energy for a reaction. That is the activation energy is defined to be (-R) times the slope of a plot of ln(k) vs. (1/T&thinsp;):

\ E_a \equiv -R \left[ \frac{\partial \ln k}{\partial ~(1/T)} \right]_P

Kinetic theory's interpretation of Arrhenius equation

Arrhenius argued that for reactants to transform into products, they must first acquire a minimum amount of energy, called the activation energy Ea. At an absolute temperature T, the fraction of molecules that have a kinetic energy greater than Ea can be calculated from the Maxwell-Boltzmann distribution of statistical mechanics, and turns out to be proportional to \ e^{\frac{-E_a}{RT}}. The concept of activation energy explains the exponential nature of the relationship, and in one way or another, it is present in all kinetic theories.

Collision theory

One example comes from the "collision theory" of chemical reactions, developed by Max Trautz and William Lewis in the years 1916-18. In this theory, molecules are supposed to react if they collide with a relative kinetic energy along their lines-of-center that exceeds Ea

Structural equation modeling

Structural Equation Modeling (SEM) is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions. This definition of SEM was articulated by the geneticist Sewall Wright (1921), the economist Trygve Haavelmo (1943) and the cognitive scientist Herbert Simon (1953), and formally defined by Judea Pearl (2000) using a calculus of counterfactuals.

Structural Equation Models (SEM) allow both confirmatory and exploratory modeling, meaning they are suited to both theory testing and theory development. Confirmatory modeling usually starts out with a hypothesis that gets represented in a causal model. The concepts used in the model must then be operationalized to allow testing of the relationships between the concepts in the model. The model is tested against the obtained measurement data to determine how well the model fits the data. The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data.

With an initial theory SEM can be used inductively by specifying a corresponding model and using data to estimate the values of free parameters. Often the initial hypothesis requires adjustment in light of model evidence. When SEM is used purely for exploration, this is usually in the context of exploratory factor analysis as in psychometric design.

Among the strengths of SEM is the ability to construct latent variables: variables which are not measured directly, but are estimated in the model from several measured variables each of which is predicted to 'tap into' the latent variables. This allows the modeler to explicitly capture the unreliability of measurement in the model, which in theory allows the structural relations between latent variables to be accurately estimated. Factor analysis, path analysis and regression all represent special cases of SEM.

In SEM, the qualitative causal assumptions are represented by the missing variables in each equation, as well as vanishing covariances among some error terms. These assumptions are testable in experimental studies and must be confirmed judgmentally in observational studies.

Steps in performing SEM analysis

Model specification

When SEM is used as a confirmatory technique, the model must be specified correctly based on the type of analysis that the researcher is attempting to confirm. When building the correct model, the researcher uses two different kinds of variables, namely exogenous and endogenous variables. The distinction between these two types of variables is whether the variable regresses on another variable or not. As in regression the dependent variable (DV) regresses on the independent variable (IV), meaning that the DV is being predicted by the IV. In SEM terminology, other variables regress on exogenous variables. Exogenous variables can be recognized in a graphical version of the model, as the variables sending out arrowheads, denoting which variable it is predicting. A variable that regresses on a variable is always an endogenous variable, even if this same variable is also used as a variable to be regressed on. Endogenous variables are recognized as the receivers of an arrowhead in the model.

It is important to note that SEM is more general than regression. In particular a variable can act as both independent and dependent variable.

Two main components of models are distinguished in SEM: the structural model showing potential causal dependencies between endogenous and exogenous variables, and the measurement model showing the relations between latent variables and their indicators. Exploratory and Confirmatory factor analysis models, for example, contain only the measurement part, while path diagrams can be viewed as an SEM that only has the structural part.

In specifying pathways in a model, the modeler can posit two types of relationships: (1) free pathways, in which hypothesised causal (in fact counterfactual) relationships between variables are tested, and therefore are left 'free' to vary, and (2) relationships between variables that already have an estimated relationship, usually based on previous studies, which are 'fixed' in the model.

A modeller will often specify a set of theoretically plausible models in order to assess whether the model proposed is the best of the set of possible models. Not only must the modeller account for the theoretical reasons for building the model as it is, but the modeller must also take into account the number of data points and the number of parameters that the model must estimate to identify the model. An identified model is a model where a specific parameter value uniquely identifies the model, and no other equivalent formulation can be given by a different parameter value. A data point is a variable with observed scores, like a variable containing the scores on a question or the number of times respondents buy a car. The parameter is the value of interest, which might be a regression coefficient between the exogenous and the endogenous variable or the factor loading (regression coefficient between a indicator and its factor). If there are fewer data points than the number of estimated parameters, the resulting model is "unidentified" , since there are too few reference points to account for all the variance in the model. The solution is to constrain one of the paths to zero, which means that it is no longer part of the model.

Estimation of free parameters

Parameter estimation is done by comparing the actual covariance matrices representing the relationships between variables and the estimated covariance matrices of the best fitting model. This is obtained through numerical maximization of a fit criterion as provided by maximum likelihood estimation, weighted least squares or asymptotically distribution-free methods. This is often accomplished by using a specialized SEM analysis program of which several exist.

Assessment of fit

Assessment of fit is a basic task in SEM modeling: forming the basis for accepting or rejecting models and, more usually, accepting one competing model over an


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Answers:no u cant!! all c2 carbons containing a carbonyl group give this test

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Answers:This is Sarah Palin.

Question:using the iodoform test

Answers:the formula of ethanol is CH3 CH2 OH the CH3 is linked to a carbon bonded to an oxygen. this CH3 group is what will become iodoform. the 3 H will be replaced by 3 I and another H will add up to form CHI3 or iodoform. the rest of the fragment, that is CH2 OH has one carbon and will first turn into an acid with one carbon (that is HCOOH) and then form its sodium salt. so the second fragment is converted to HCOO Na. lets do it again for acetone. the formula of acetone is CH3 CO CH3 the CH3 (either of them as there are two of them) will become CHI3 the remaining fragment is CO CH3 . this fragment has 2 carbons. so it will first form an acid with two carbons (CH3 COOH) and then form its sodium salt, that is CH3 COO Na if you have been given the products of iodoform test you can make the original molecule. supposing the products are CHI3 and CH3 CH2 CH2 COO Na you know that CHI3 was originally a CH3 group linked to a carbon with oxygen. the second fragment has 4 carbons. so the original molecule may be CH3 CO CH2 CH2 CH3 or CH3 CH (OH) CH2 CH2 CH3

Question:Ok so I haven't studied in a week and I totally forgot everything and of course theirs a test tomorrow so I just need someone to explain in detail how to solve this problem- 5 + 4x - 7=4x + 3 - x Please Explain step by step and why you did each step thank you.

Answers:Get your variable, x, on one side of the equation since you have just one variable (not x and y, for example). 4x-4x+x=3+7-5 x=5 (You realize that when you move a variable to the other side of the equals sign, you change the sign of the variable and its coefficient, right? What you are really doing is subtracting -4x from both sides, for example, here, and it erases the 4x on the right side of the equation and up pops -4x on the left side of the equation...)

From Youtube

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