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Dimension Reduction Breaking the Curse of Dimensionality
Published in Chong Ho Alex Yu, Data Mining and Exploration, 2022
One may argue that when a high Cronbach Alpha indicates a high degree of internal consistency (e.g., 0.8), the test or the survey must be uni-dimensional rather than multi-dimensional. Thus, there is no need to further investigate its subscales. This is another misconception. Actually, consistency and dimensionality must be assessed separately. Uni-dimensionality is a subset of consistency If a test is uni-dimensional, then it will show internal consistency. But if a test is internally consistent, it does not necessarily entail one concept or one dimension (Gardner 1995; 1996). Reliability is a necessary, but not a sufficient condition for validity. This logic works like this: If I am a man, I must be a human. But if I am a human, I may not be a man (I could be a woman). The logical fallacy that “if A then B; if B then A” is termed as “affirming the consequent” (Kelley and Hutchins 2020). This fallacy often happens in the misinterpretation of Cronbach Alpha. Many statistical software packages can run Cronbach Alpha. JMP Pro is used for the following illustration.
Unsustainable agriculture
Published in Peter N. Nemetz, Unsustainable World, 2022
There is a logical fallacy with the argument advanced in this particular case study because of an incorrect definition of system boundaries. In essence, the argument is that the current system of livestock production achieves significant economic efficiencies but has some inherent risks that require offsetting actions such as the use of antibiotics. Cessation of this preventative measure will expose consumers to the inherent system risk. The implicit assumption—and logical pitfall—is that the current system of meat production is a given, and that no other alternatives are possible or economically desirable. If one expands the range of alternatives to include grass-fed, integrated crop-livestock systems (ICLSs) or smaller scale production systems rather than CAFOs, then a comprehensive life-cycle systems analysis that recognizes and incorporates all externalities might suggest that the feedlot system is less economically efficient from a societal perspective than the alternatives. The major study of the hidden costs of feedlots by the Union of Concerned Scientists (2008, p. 1) focuses on market distortions which tilt the simple economics trade-offs in favor of CAFOs. To quote:alternatives are at a competitive disadvantage because CAFOs have reduced their costs through subsidies that come at the public’s expense, including (until very recently) low cost feed. CAFOs have also benefited from taxpayer supported pollution cleanup programs and technological “fixes” that may be counterproductive, such as the overuse of antibiotics. … Subsidies have included payments to grain farmers that historically supported unrealistically low animal feed prices, and payments to CAFOs to prevent water pollution.
Wrap-Up
Published in Steve Warren, Radio, 2004
“Where there’s smoke there’s fire!” This is usually used as tacit confirmation of rumors or suspicions. Actually, a lot of times there’s smoke when there’s no sign of fire. And often the tiniest fire can create a huge volume of smoke. So, presume nothing. Better to suggest, “Where there’s smoke there’s smoke!” There’s a logical fallacy here. Just because the pavements are wet, we can’t conclude that it’s been raining. Maybe there was a water leak in a nearby building.
Maths in the time of social media: conceptualizing the Internet phenomenon of mathematical memes
Published in International Journal of Mathematical Education in Science and Technology, 2022
Giulia Bini, Ornella Robutti, Angelika Bikner-Ahsbahs
Contextual description: The meme in this example (Figure 17) is used to label as Mega Wrong the proof of the indicated limit using differentiation (i.e. L’Hôpital’s rule). The proof is considered Mega Wrong because it is circular, involving a logical fallacy that occurs if we assume that the derivative of the sine function is obtained using the result of the , which is the usual development of the topic in high school. This same procedure would be logically sound if, for example, we accept power-series definitions for trigonometric functions, and obtain the derivative of the sine function from these premises. This knowledge is mastered and disseminated by the author of the meme and by several commenters, as will be shown in the analysis. We chose key parts of the exchange taking a large section from the beginning where the engagement is established. We are taking further parts following the same mathematical topic. The selection is also made according to indicators related to the analysis perspective. The development of the comments goes in various directions, several proofs are offered, only one is included in the analysed excerpt (Table 2).
Graph-theoretic approaches and tools for quantitatively assessing curricula coherence
Published in European Journal of Engineering Education, 2021
Damiano Varagnolo, Steffi Knorn, Kjell Staffas, Eva Fjällström, Tobias Wrigstad
Another pedagogically interesting analysis of a DCCG is related to detecting cycles in the graph. For example, consider the situation in Figure 4: here, course i has concept x as a required knowledge and prepares students to course j by teaching concept y. The situation is though symmetric, since j has concept y as a required knowledge and prepares students to course i by teaching concept x. Thus, as soon as i and j are not taught in the same learning period, students will not be prepared to take the first of the courses being taught (something that theoretically will also affect their understanding, eventually inficiating also the attendance to the second one). And even if i and j are instead taught in the same learning period, then this logical fallacy can be resolved only through a great care by the teachers of i and j in designing their own courses so that the understanding and usage of concepts x and y happens in parallel and simultaneously.