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Hypothesis Testing
Published in Harry G. Perros, An Introduction to IoT Analytics, 2021
For each group i, we calculate the sample meanx¯iand then we calculate the grand mean x¯¯ as the average of all the sample means, i.e., x¯¯=1/c∑i=1cx¯i. We define the following sum of squares SST, SSTR, and SSE. Figure 4.6 gives a pictorial view of these terms.
Determining Whether a Process Is in Control
Published in D. B. Owen, Beating Your Competition Through Quality, 2020
For these variables charts we start with 20 to 30 samples, and for each sample we compute the mean, X¯, and the range, R, or the sample standard deviation, s. The mean of all of the means is represented by X with two bars over it, X¯¯, and is called the grand mean. Similarly, the mean of the ranges is indicated by an R with a bar over it, i.e., R¯, and the mean of the sample standard deviations is indicated by s¯. The three lines on the control chart are then:
One Factor Designs
Published in Thomas J. Lorenzen, Virgil L. Anderson, Design of Experiments, 2018
Thomas J. Lorenzen, Virgil L. Anderson
The total sum of squares is the sum over all the observations of the square of each individual deviation from the overall mean. That is, take each individual observation, subtract the grand mean, square the result, and then sum over all observations.
Modelling Uncertainties of Italian Code-Conforming Structures for the Purpose of Seismic Response Analysis
Published in Journal of Earthquake Engineering, 2018
Paolo Franchin, Laura Ragni, Maria Rota, Alessandro Zona
The grand mean may be calculated by the following relation when only the class means and numerosity (number of test values belonging to the th class or production batch) are known, rather than the individual test values: