Overview. All of the material in this supplemental online text is purely optional and is meant to enhance the textbook. Use whatever aspects of it help to deepen your understanding of the material and ignore the rest. It assumes you have already read the relevant chapter. I will be adding more material as the semester progresses.
In teaching about statistics--the primary tool scientists use to make sense of their data,--it is important to me that I elucidate the differences between the scientific approach to knowledge and the religious approach to knowledge. It is also important to me that I point out that both approaches have value, depending upon the context in which they are used. I would like to take advantage of this opportunity of creating supplemental information for the text, to expand this topic to the point where it encompasses a topic that is important to me and that I would like to share. This involves talking at a conceptual level that is far beyond where the rest of this supplemental material will reside. After this chapter I will settle down to simply giving additional examples of the story problems covered in later chapters of the text.
In the first chapter of the text I describe the fundamental attributes of the scientific approach to knowledge. These attributes make the scientific approach distinctly different from other approaches, including religion. What I would like to add to that description is that while the scientific approach and the religious approach have important, fundamental, differences, they both arose from the same culture and at a deep level they share some basic assumptions about the nature of reality. These assumptions are rarely brought to light to be examined because, obviously, they are assumed to be true.
The dictionary defines a worldview as a culture's set of concepts and beliefs about the nature of reality. Both science and Western religion reside within the modern Western worldview. There are other worldviews on the planet, and there have been other worldviews in the Western world in earlier times. If we know only one worldview we tend to think it is the only one that exists and that all other worldviews are simply variations of our own. In the case of indigenous worldviews we tend to think of them as primitive versions of our Western worldview, like our own worldview but with more superstitions and less knowledge.
For the past 24 years I have been immersing myself in the worldview of the indigenous people who live in the high Andes of Peru. Their worldview, the Andean Cosmovision, supports a way of perceiving and interacting with reality that is fundamentally different than that of the Western worldview. It is a way of understanding reality that has not been influenced by the Bible, or by the classic Greek philosophers, or by Descartes' division of reality into separate mind and matter, or by the scientific revolution. This worldview simply cannot be understood through the spectacles of science or Western religion, which we in the West assume can handle anything. I speak of the Andean Cosmovision simply because it is the only worldview which which I am intimately familiar other than my own modern, Western, worldview, but I believe the same holds true for other worldviews as well.
So my point is this. In the textbook I have described the important differences between science and Western religion. They are two distinct approaches to knowledge. They both arose, however, from the same worldview and share some basic assumptions about the nature of reality. When we step out of the Western worldview, and into other worldviews we can find other ways of perceiving and interacting with reality that cannot be encompassed, described, or understood from within the Western worldview. If we don't recognize this, then when we consider other worldviews, rather than looking through a window at a new way of perceiving reality we are instead simply looking into a mirror.
If you would like to know more about the Andean Cosmovision you can visit my blog at Salka Wind Blog where I have published a great deal of information stemming from my research in Peru.
Identify each of the following measurement scales. Click "See Answer" to see answer (did I need to say that?).
This is a cardinal measure as it directly measures a quantity (number of students).
This is a nominal scale as the numbers reflect qualitative (categorical) differences rather than quantities.
This is an ordinal scale. The scores reflect a change in quantity in a specific direction (the greater the score the more likely to purchase a phone). The sizes of the steps are not necessarily equal (i.e. the difference between 'unlikely' and 'somewhat likely' may not be the same size as the difference between 'somewhat likely' and 'very likely').
This is a rank scale. While the size of a university is a cardinal scale (see above) what is being measured here is how the university ranks in comparison to other universities. The score for the largest university would be "1" which tells us how it compares to others but does not actually tell us how many students there are. While rank scales are a subset of ordinal scales, what makes a rank scale different is that the score is dependent upon how the subject compares to others in some group. While the largest university in Utah would receive a rank score of "1" if we compared it to others in the Utah, it would get a different rank score if we compared it to other universities in the whole country.
This is an ordinal scale. The scores reflect a change in quantity in a specific direction (the greater the score the lower the level of satisfaction) and the sizes of the steps are not necessarily equal.
This is a rank scale. Your score reflects your ranking in birth order in your family.
This is a nominal scale.
This is a cardinal scale.
You sample from a population and obtain the following scores. Y = 8, 7, 5, 7, 6, 4
Descriptive Statistics. Compute the following, be sure to use the correct symbols.
Inferential Statistics. Compute the following, be sure to use the correct symbols.