Factor loadings are numerical values that indicate the strength and direction of a factor on a measured variable. Factor loadings indicate how strongly the factor influences the measured variable. In order to label the factors in the model, researchers should examine the factor pattern to see which items load highly on which factors and then determine what those items have in common. Whatever the items have in common will indicate the meaning of the factor.
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In statistics, an empirical distribution function is the distribution function associated with the empirical measure of a sample. This cumulative distribution function is a step function that jumps up by at each of the data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value. The empirical distribution function is an estimate of the cumulative distribution function that generated the points in the sample.
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Any difference between the measured variable and the set point generates a signal which is used to modulate the position of a control valve (the final element) to maintain the measured variable at the set point. Valves can be actuated by an electric motor, hydraulic fluid or air. For air-operated control valves, electrical signals from the control system are converted to an air pressure for the valve actuator in a current/pneumatic I/P converter. Upon loss of pneumatic or hydraulic pressure valves can be configured to fail to an open (FO) or fail to a closed (FC) position.
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A bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents a measured value. Some bar graphs present bars clustered in groups of more than one, showing the values of more than one measured variable.
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A variable measured in discrete time can be plotted as a step function, in which each time period is given a region on the horizontal axis of the same length as every other time period, and the measured variable is plotted as a height that stays constant throughout the region of the time period. In this graphical technique, the graph appears as a sequence of horizontal steps. Alternatively, each time period can be viewed as a detached point in time, usually at an integer value on the horizontal axis, and the measured variable is plotted as a height above that time-axis point. In this technique, the graph appears as a set of dots.
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If this is the case, a biserial correlation would be the more appropriate calculation. The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation, that is, if we have one continuously measured variable X and a dichotomous variable Y, rXY = rpb. This can be shown by assigning two distinct numerical values to the dichotomous variable.
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The advanced type of automation that revolutionized manufacturing, aircraft, communications and other industries, is feedback control, which is usually continuous and involves taking measurements using a sensor and making calculated adjustments to keep the measured variable within a set range.Bennett, Stuart (1992). A history of control engineering, 1930–1955. IET. p. 48. . The theoretical basis of closed-loop automation is control theory.
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The parametric alternative to the Scheirer–Ray–Hare test is multi-factorial ANOVA, which requires a normal distribution of data within the samples. The Kruskal–Wallis test, from which the Scheirer–Ray–Hare test is derived, serves in contrast to this to investigate the influence of exactly one factor on the measured variable. A non-parametric test comparing exactly two unpaired samples is the Wilcoxon–Mann–Whitney test.
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Common factors influence more than one manifest variable and "factor loadings" are measures of the influence of a common factor on a manifest variable. For the EFA procedure, we are more interested in identifying the common factors and the related manifest variables. EFA assumes that any indicator/measured variable may be associated with any factor. When developing a scale, researchers should use EFA first before moving on to confirmatory factor analysis (CFA).
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In oblique rotation, one may examine both a pattern matrix and a structure matrix. The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing the variance in a measured variable explained by a factor on both a unique and common contributions basis. The pattern matrix, in contrast, contains coefficients which just represent unique contributions. The more factors, the lower the pattern coefficients as a rule since there will be more common contributions to variance explained.
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From the Economics community, the independent variables are also called exogenous. Depending on the context, a dependent variable is sometimes called a "response variable", "regressand", "criterion", "predicted variable", "measured variable", "explained variable", "experimental variable", "responding variable", "outcome variable", "output variable", "target" or "label".. In economics endogenous variables are usually referencing the target. "Explanatory variable" is preferred by some authors over "independent variable" when the quantities treated as independent variables may not be statistically independent or independently manipulable by the researcher.Everitt, B.S. (2002) Cambridge Dictionary of Statistics, CUP.
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When a manipulation creates significant differences between experimental conditions in both (1) the dependent variable and (2) the measured manipulation check variable, the interpretation is that (1) the manipulation "causes" variation in the dependent variable (the "effect") and (2) the manipulation also explains variation in some other, more theoretically obvious measured variable that it is expected to concurrently influence, which assists in interpreting the "cause" (i.e., it only help interpret the "cause"; it is not necessary to affirm that the "cause" causes an effect).
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Instrumentation includes sensing devices to measure process parameters such as pressure, temperature, liquid level, flow, velocity, composition, density, weight; and mechanical and electrical parameters such as vibration, position, power, current and voltage. The measured value of a parameter can be displayed and recorded either locally and/or in a control room. If the measured variable exceeds pre-defined limits an alarm may be provided to warn the operating personnel of a potential problem. Automatic executive action can also be taken by the instrumentation to close or open shutdown valves and dampers, or to trip (stop) pumps and compressors.
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The difference between actual and desired value of the process variable, called the error signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. This is the basis for the advanced type of automation that revolutionized manufacturing, aircraft, communications and other industries. This is feedback control, which involves taking measurements using a sensor and making calculated adjustments to keep the measured variable within a set range by means of a "final control element", such as a control valve.
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Fitting procedures are used to estimate the factor loadings and unique variances of the model (Factor loadings are the regression coefficients between items and factors and measure the influence of a common factor on a measured variable). There are several factor analysis fitting methods to choose from, however there is little information on all of their strengths and weaknesses and many don't even have an exact name that is used consistently. Principal axis factoring (PAF) and maximum likelihood (ML) are two extraction methods that are generally recommended. In general, ML or PAF give the best results, depending on whether data are normally-distributed or if the assumption of normality has been violated.
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These laboratories were located in Calgary until 1955 when they moved to Edmonton and are still operating alongside the Alberta Research Council at the Coal Research Centre in Devon, Alberta. Visman wrote Towards a Common Basis for the Sampling of Materials, Mines Branch Research Report R 93, which was published in July 1962. He participated in ASTM Committees D-5 on Coal and Coke and E-11 on Statistics. ASTM D 2234 Standard Practice for Collection of a Gross Sample of Coal was the first internationally recognized standard to specify a precision estimate for a measured variable. Visman’s sampling experiment with small and large increments is described in ASTM D 2234, Annex A1.
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Fabrigar et al. argue that in cases where the data correspond to assumptions of the common factor model, the results of PCA are inaccurate results. # There are certain cases where factor analysis leads to 'Heywood cases'. These encompass situations whereby 100% or more of the variance in a measured variable is estimated to be accounted for by the model. Fabrigar et al. suggest that these cases are actually informative to the researcher, indicating an incorrectly specified model or a violation of the common factor model. The lack of Heywood cases in the PCA approach may mean that such issues pass unnoticed. # Researchers gain extra information from a PCA approach, such as an individual's score on a certain component; such information is not yielded from factor analysis.
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This measured temperature is fed into the temperature controller (TIC) where it is compared to the desired set point temperature. The output of the controller, which is related to the difference between the measured variable and the set point, is fed to a control valve (TCV) in the second fluid to adjust the flow of the heating or cooling medium. In the case of a fluid being cooled, if the temperature of the fluid rises the temperature controller acts to open the TCV increasing the flow of the cooling medium which increases the heat transfer and reduces the temperature of the first fluid. Conversely if the temperature falls the controller acts to close the TCV which reduces the heat transfer increasing the temperature of the first fluid.
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