Baye’s Theorem explained

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8 Bayes’ Theorem

…in no other branch of mathematics is it so easy for experts to blunder as in probability theory.
—Martin Gardner

In a famous psychology experiment, subjects were asked to solve the following problem. The experiment was first published in 1971. It was performed by Daniel Kahneman and Amos Tversky. Their work on human reasoning reshaped the field of psychology, and eventually won a Nobel prize in 2002.

A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data:

85% of the cabs in the city are Green and 15% are Blue.
A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80%
of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was blue rather green?

Source: https://jonathanweisberg.org/vip/chbayes.html

The Lure of Statistics for Educational Researchers

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During the course of the 20th century, educational research yielded to the lure of Galileo’s vision of a universe that could be measured in numbers. This was especially true in the United States, where quantification had long enjoyed a prominent place in public policy and professional discourse. But the process of reframing reality in countable terms began eight centuries earlier in Western Europe, where it transformed everything from navigation to painting, then arrived fully formed on the shores of the New World, where it shaped the late-blooming field of scholarship in education. Like converts everywhere, the new American quantifiers in education became more Catholic than the pope, quickly developing a zeal for measurement that outdid the astronomers and mathematicians that preceded them. The consequences for both education and educational research have been deep and devastating..

Source: Labaree, David. (2010). The Lure of Statistics for Educational Researchers. 10.1007/978-90-481-9873-3_2.

source: https://www.researchgate.net/publication/226205657_The_Lure_of_Statistics_for_Educational_Researchers

THE INTELLECTUAL DEVELOPMENT OF SCIENCE AND ENGINEERING STUDENTS

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“Kroll [1] describes intellectual growth as the progression from ignorant certainty to intelligent confusion. Many entering college students are firmly rooted in ignorant certainty. Their beliefs about the world are clear, absolute, and based entirely on what they have been told by others—parents, teachers, and influential peers. They have never subjected these beliefs to critical questioning or looked for evidence to test their validity. They view all knowledge as either certain or unknowable, with scientific knowledge residing squarely in the domain of certainty. In their minds, the role of teachers is to know The Truth and to tell it to them and their role as students is to absorb it and repeat it back on assignments and tests.

source: Richard M. Felder, North Carolina State University Rebecca Brent, Education Designs, Inc. ; The Intellectual Development of Science and Engineering Students. Part 1: Models and Challenges. Available from: https://www.researchgate.net/publication/247916554_The_Intellectual_Development_of_Science_and_Engineering_Students_Part_1_Models_and_Challenges [accessed Apr 10 2020].