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Principles of Symbolization
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
When a geographic phenomenon is measured to create a data set, we commonly speak of the level of measurement associated with the resulting data. Conventionally, four levels of measurement are recognized—nominal, ordinal, interval, and ratio—with each subsequent level including all characteristics of the preceding levels. The nominal level of measurement involves grouping (or categorization) but no ordering. The classic example is religion, in which individuals might be identified as Catholic, Protestant, Jewish, or Other; here, each religious group is different, but one is not more or less religious in value than another. Another example would be classes on a land use/land cover map; for example, grassland, forest, urban, water, and cropland differ from one another, but one class is not more or less in value than another.
Measurements and probability
Published in Shamil G. Naoum, Dissertation Research and Writing for Built Environment Students, 2019
Measurement is a procedure in which a researcher assigns numerals (numbers or other symbols) to empirical properties (variables) according to rules. It is closely linked to the research approach and questionnaire construction, which were discussed in Chapters 4 and 6, respectively. There are four levels of measurement: nominal, ordinal, interval and ratio. In some cases, your research involves a search for a measure that is already developed and in other cases, you need to design a measure. This chapter focuses on these levels of measurements in order to prepare the ground for the next exciting chapter: analysis of the results. This chapter also provides a statement of probability, which is an important term to understand in testing your research hypothesis. The contents of Chapter 7 are illustrated in Figure 7.1.
Data Description and Treatment
Published in Bilal M. Ayyub, Richard H. Mccuen, Numerical Analysis for Engineers, 2015
Bilal M. Ayyub, Richard H. Mccuen
The ratio scale represents the highest level of measurement. In addition to the characteristics of the interval scale, the ratio scale has a true zero point as its origin—unlike the interval scale, for which the zero point is set by some standard. For example, in the interval scale the zero point for temperature (°C) is set at the point where water freezes. However, it could have been set at the point where water boils or based on some other substance.
Study of a fixed-lag Kalman smoother for input and state estimation in vibrating structures
Published in Inverse Problems in Science and Engineering, 2021
Ulrika Lagerblad, Henrik Wentzel, Artem Kulachenko
The level of measurement noise corresponds to a measurement noise covariance as . Both algorithms were tuned according to Section 3.2 with all four strain response measurements. The tuning is presented in Figures 10 and 11 and resulted in covariance matrices and for the AKF-FLS and and for the AKF.
An analytical model to quantify the impact of the propagation of uncertainty in knee joint angle computation
Published in International Biomechanics, 2022
Mickael Fonseca, Stéphane Armand, Raphaël Dumas
The measurement of gait data, as any other measure, is prone to measurement error. Thus, any complete acquired measurement is accompanied by a quantitative level of measurement uncertainty. Uncertainty is a parameter associated with any measurement that characterizes a dispersion of values around the true value measured (Farrance and Frenkel 2012). In terms of the propagation of uncertainty, the variability in kinematic curves can be understood to depend on the intrinsic variability of joint motion and on the extrinsic variability of the definition of the three joint axes. The intrinsic variability is associated with the ability of a subject to perform repeated movements, and it is considered as an irreductible variability. On the other hand, extrinsic variability is related to the error of measurement and it is characterized by a combination of factors (e.g. placement of the reflective markers, soft tissue artifacts, calibration of motion capture system). To the best of our knowledge, no previous attempts have been made to separate the intrinsic and extrinsic variabilities in the measurement of knee joint kinematics. Intrinsic variability is linked to the movement of the joint itself, independently of any coordinate system, and it can be assessed by looking at the dispersion of the knee’s rotation angle θ and of the orientation of the rotation axis k. In other words, intrinsic variability is dependent on the ability of the subject to perform a repetitive movement during gait. Intrinsic variability may be affected by the presence of motor disorders, so it is considered an indicator of gait deviations (Chau et al. 2005). Extrinsic variability arises from the inaccurate measure of the real movement of the subject (whether due to instrumentation, mathematical or human factors), which results in dispersion in the orientation of the joint axes e1, e2 and e3. In other words, it is characterised by the error in the definition of the three axes used to interpret the movement of the joint. The theoretical propagation of uncertainty in joint angle computation can be analysed based on the equations used to project the attitude vector onto the three joint axes. These equations only include dot and cross products, which enable the use of the additive rules for calculating uncertainty components through functional relationships (Farrance and Frenkel 2012).