|
||||||||||||||||||||||||||||||||||||||||||
![]() |
|
Numbers are not that simple. There are several scales we use, or ways of using numbers. Briefly we will discuss four scales. . . nominal, ordinal, interval and rational. The first letters spell out N*O*I*R - noir - the word for black in French . . .And this whole discussion may seem rather dark to you | ![]() |
Nominal is a naming scale - male or female, age, weight, racial or ethnic background. It is like an on or off switch. It really does not have much use as a number -- instead it is more or a namer - nominal = naming. If you need to put data in a computer, you may arbitrarily decide that male =1 and female = 2. You may decide that Caucasian = 1, Hispanic =2, Native American = 3, Asian decent = 4. Another example might be going to the drive through hamburger place. Ordering a number 2 does not mean you get second best, it means getting the burger with bacon and cheese. When we are using a nominal scare these numbers look like numbers but they have no real numeric value. Because values on a nominal scale represent names or labels rather than values, they are not useful for doing numeric operations.
Ordinal is a ranking scale - first second, third, last. It is a way of ordering people or ideas. It has a lot of usefulness when we are doing research with people because we can make comparisons or compete between two things. He is oldest. She got the highest score. Jan is the tallest. It is useful, allows us to make comparisons but it isn't real good information.
He is oldest - of the triplets; of the octogenarians. She got the highest score by one point - and no one passed the test. Oh, by the way, half the class got one point less than she, and no one seems to have the concepts of working problems suing binomials. Jan is the tallest - and he is ten feet tall; tallest in the fifth grade; taller than the teacher, and the only male.
We can make a comparison, rank things, put them in order, but we have no way of reporting how close the next two in the rank are. So, ordinal data is useful and it is often used when comparing things like achievement and IQ. After all, we do not really know that an IQ of 100 is the same distance from 99 as it is from 101. We don't really know if an IQ of 69 is the same distance away from 70 as 144 is from 145.
We can have people stand in order of height and there can be just centimeters separating the tallest from the next to the next - or there may be three feet difference between numbers four and five and half an inch between numbers one, two, and three. The heights may have been done very accurately, or just estimated, yet there is no way to tell this once a ranking is done.
Some IQ tests are accurate within a few points, and more accurate for some ages and some areas of measuring IQ than others. Some are not very good tests at all - perhaps accurate within 10 points. Some children are not willing to work on a test one time and a lot more willing to give their best one on one with an examiner that gains their trust and cooperation.
So --- ordinal data can be useful, especially for putting people in some sequence, on a continuum with higher and lower values, but it is important to remember that the magnitude of difference has not been established.
Interval may also be referred to as equal interval. In this numbering scale, the numbers are equal distances apart. A rule is a good example. Each number on the scale is exactly the same distance apart. Now, when we measure those students we talked about earlier, we can use a number that gives us definition. The three boys are 48 inches, 56 and 108 inches tall, respectively. Those triplets are the same age. They were born on the same day, and four minutes separated them, so in all they are less than fifteen minutes younger or older.
An interesting thing about interval data - and most of us used this scale all the way through school, is that it does not have an absolute zero - a relative zero or arbitrary zero, yes, but not an absolute zero. That means that we are free to add and subtract these numbers, but we are not really supposed to use them to multiply or divide - that is, to make ratio comparisons. Here is an example: My daughter wears a size three in young ladies, and I wear a size six. Are my feet twice as long as hers? What this supports is the importance of recognizing what kinds of numbers we are using, and what the data are. We can give numbers to occurrences and we can measure things but doing so does not promise us "truth" and it actually may make us more responsible to understand what numbers mean rather than assuming that a number is enough.
Ratio scales are interval scales too, but with the difference of having an absolute zero. We seldom find absolute zero outside of a laboratory setting. One of the easy examples of this is measuring temperatures. To have absolute zero, all atoms must stop moving. That is zero on a Kelvin scale. Of course absolute zero doesn't happen in the real world. Even rocks, which we see as relatively stable, still have atoms moving. Even in the Arctic, where water is frozen solid for miles, the molecules are still moving. So, potentially, this scale is very powerful and we use numbers as though they were ratio numbers all the time, but of course they are not - and so we do not get the absolute ratio data we act like we have.
All in all we love the idea that we can know the truth and the truth will make us free.
And we love to make believe
that we can use numbers in an infallible way
and know who belongs in special education,
in the gifted program,
who deserves an A, who doesn't understand the material and gets a C ,
who studied and who didn't
crack the book
![]() |
We love to use experimental results and act as though we now have irrefutable data, results, conclusions to end all conclusions. |
Assignment One: What do you think? Write a sixty second essay discussing new things you just realized, or countering the previous argument. You may want to talk about the idea of numbers having different importance and value, depending on what scale is being used. If that is new information, discuss what you believe about the reading or feelings you have as a result of learning this new concept.
Possibly this information about the scientific method and number scales is something you have understood well and have a good idea or example of how to present the material more effectively. You may want that to be the substance of a quickie essay. When you are finished, email it to the instructor. Be certain to keep track of the points. [25 points for each essay].
If you are intrigued with these concepts, you may want to read a book about them or see what other professors have to say about the subject. You may want to surf the net and find sites that discuss these concepts [10 points for each site visited; 20 points for sites you find on your own, critique and share in WebCT with classmates, send to a partner in the course or email to the instructor. Remember to keep track of points.] |
Four discussions of Kuhn's ideas about the paradigm shift |
Power point presentation on data and numeration |
Means tests - a way to use nominal and ordinal data |
Definitions of number scales by another author |
Scientific method - a brief discussion from the 1950's |
Scientific method - a quick example |
Lesson on the scientific method for middle grade students |
Thorough review of scientific method |
Assignment Two: Qualitative Methods What about qualitative research? Is it any more or less reliable than the experimental model? How is qualitative data different from quantitative data and how can we use it most effectively?
To begin to answer those questions, surf the web and come up with a definition or set of practices that describe each of the following types of qualitative research. Then give an example of when it might be most appropriate to use each of these methods to determine something about the quality of an educational program or reform, or to better understand human nature and the human condition. [This activity is worth 150 points]
Qualitative Method |
Links
|
Definition
|
Best Fit
|
---|---|---|---|
A. Phenomenology | |||
B. Grounded Theory | |||
C. Ethnography | |||
D. Historiography | |||
E. Aesthetic Inquiry | |||
F. Hermeneutics |
Visit a course module about Qualitative Research