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Statistics Exercise
Week 2, No. 1

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California State University, Dominguez Hills
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Created: September 12, 1999
Latest Update: August 20, 2003

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takata@uwp.edu

Index of Topics on Site Week 2. Exercise 1.
Theory and Dummy Tables

Site Copyright: Jeanne Curran and Susan R. Takata and Individual Authors, August 2003.
"Fair use" encouraged.

Theory is an interconnected set of ideas by which we try to explain the world and how it works and how we can and should live in it. When numbers are involved, we use them to represent objects or transactions in the real world. We can then manipulate them mathematically without altering the validity of what we see, and test those results against the real world. In other words, with numbers we set up a kind of model, and then test it to see if it seems to fit.

For example, long, long ago someone figured out that her tribe was made up of men and women. She pondered that, and noticed that half her tribe was men, and about half women. Then, as she and her family went from tribe to tribe selling their pots, she counted the men and women in each tribe. She found there were about half and half in each tribe. She set up the first mathematical model for sociology: the world, as we know it, is made up of an approximately equal number of men and women. We've been using her model ever since. That's why so many of the forms you fill out ask whether you are male or female.

Gender in Early Tribes
Gender Tribe A
Tribe B Tribe C Tribe D Totals
(Marginals)
Men 47
32 61 26  
Women 51
28 60 27  
Totals (Marginals)  
       

No, I don't know if our early sociologist called them "men" and "women," or if she spoke at all. But I'll bet that early on she found a way to count them. Look at each of the tribes. In most the numbers of men and women are about equal. Look at the marginals - the totals of each row and column. I left them blank. Add them up for yourself. The total for the Men is: 47 + 32 + 61 + 26 = 166. The total for the Women is: 51 + 28 + 60 + 27 = 166 Now add up the Total Men and the Total Women: 166+ 166 = 332. Now add up each of the rows: Tribe A = 98, Tribe B = 60, Tribe C = 121, Tribe D = 53. Now add up the numbers of Men and Women from all the tribes: 98 + 60 + 121 + 53 = 332.

Put the totals in the cells where they belong and look at the table. Isn't it neat? They add up across the rows and columns. You don't need any answers at the back of the book. You can check your own arithmetic. Want a claculator? At the desk top start button, click on all programs>. Click on accessories, and from the resultant list click on calculator. If you don't close the calculator window, it will simply minimize itself to the task bar while you work on other files. When you want it, click on it, and it pops back up.

Have you got any idea how proud our first sociologist was of this model and her table? I'm really surprised she didn't carve it on one of the caves right along with the deer and bison. After all, it was a monumental idea we still use today. Or was it???? We do still use it today, but unfortunately we still count you as either male or female. We assume, as do our religions which grew with our cultures that a binary choice, either/or, is appropriate for gender. We like to count. It's so stable. I mean 46 males are 46 males are 46 males. You can believe in that. Unless one of them was mistakenly called a male at birth, but his brain patterns don't match his genital organs. Well, then 46 males are 45 males and one, hmmm. See the problem?

The problem with numbers isn't numbers themselves. It's our reification of numbers. Mathematics is just a language, a very complicated language, that most of us never learn to speak at levels that would let us do astrophysics problems. But it is just a language. And as we play with these dummy tables, I hope you'll see why math is so useful. It's a kind of shorthand way of saying what you're trying to say, so that you can take it all in at a glance.

Statement of the Theory:

For example, we may decide theoretically that school appeals more to girls than boys because it emphasizes passivity more, where girls have been socialized to be more passive. We can count the girls and the boys. We can introduce two programs: one fairly passive, one fairly active. We can indicate a control group in regular school programs and an experimental group in our new test programs. Then we can compare how girls and boys in the control group feel about school to the way girls and boys feel about the experimental program.

Did you get that? Or would it help if I put it in a table?

Dummy Table:

Satisfaction with Passivity in School
Group Control Group
Experimental Group Totals (Marginals)
 
  Passive
Active
 
Boys 16 10 24 50
Girls 24 22 04 50
Totals
(Marginals)
40 32 28 100

Table 1. Satisfaction with Passivity in School

This is called a dummy table. Dummy because the numbers aren't real. I made them up, just to get a feel for the theory and data we were talking about. I made the marginals come out to 100, to give us easy percentages.

But, before we try anything fancy like putting percentages in the table, let's just see what the table tells us (with phony data; don't forget that) as it stands. Interpretation A:

Table 1 compares the satisfaction of boys and girls with the passivity in school. In the control group of 40 students, 16 boys and 24 girls were satisfied. In the passive experimental group of 32 students, 10 boys and 32 girls were satisfied with that level of passivity. In the active experimental group of 28 students, 24 boys and 4 girls were satisfied with that level of passivity. These numbers tend to show that the hypothesis that girls are more satisfied with school because they are more accepting of the passivity required.

Discussion Questions

  1. Explain the relationship of theory to policy and to practice.

    Theory refers to an interconnected set of ideas that explain and predict behavior according to generalized patterns of behavior believed to apply across actual situations. When numbers are involved, we use them to represent objects or transactions in the real world. We can then manipulate them mathematically without altering the validity of what we see, and test those results agains the real world.

    For example, we may decide theoretically that school appeals more to girls than boys because it emphasizes passivity more, where girls have been socialized to be more passive. We can count the girls and the boys. We can introduce two programs: one fairly passive, one fairly active. We can indicate a control group in regular school programs and an experimental group in our new test programs. Then we can compare how girls and boys in the control group feel about school to the way girls and boys feel about the experimental program.

    Did you get that? Or would it help if I put it in a table?

    Policy is the next lower level of generality at which one seeks to incorporate the general tenets of theory into guides to putting the theory's predictions into practice.

    Practice is at the level of actual data gathering and analysis of your results, and/or putting the theory's tenet into practice.

  2. Why do we insist that you consider the relationship also in the reverse direction: practice to policy to theory?

    We ask that you practice moving in both directions so that you will become comfortable with the respective levels of generalization and their effect on the emotional quality that evokes.

  3. Want to explore further? What does moving a discussion from the practice level to a policy or theoretical level accomplish for discourse? What does it accomplish for the study of society?

    Moving back from the actual situation provides some distance and lessens the affective component, so that we can look for patterns and see from the specific to the more general. Lessening the affect is essential to discourse because if we are caught up emotionally in the situation, it's hard to consider it calmly when there are disagreements.

    Moving from specific instances to the more formal policy level means that we can look for broad patterns and perhaps discover some general solutions that might not be apparent when we are focussed on the specific situations.

  4. At which level do the numbers in the printouts from SPSS fit?

    The numbers on your printout are the data. They are collected, in surveys, in individual situations. To the extent that they report the subjects' perceptions, they are generalized responses to the subjects' analysis of his/her experience. In that sense, we are moving from a single experience to the more general "total of the subjects' experience." Unfortunately, individuals rarely have a broad experience with any given topic. Thus, they tend to generalize from limited instances, and may not take factors into account that could produce different results.

    For example, Hockenberry speaks of the help afforded him in the subway as he struggled to climb subway stairs and drag his wheelchair behind him. Blacks, he reports, were the ones who stopped to help him. He concludes that minorities are more generous of their caring and effort than the average subway passenger. In his experience, that may be true. But his experience was limited. Before we could validly reach his conclusion about whether one group or another is more sensitive to the needs of the disabled, we would need to investigate what happened in a variety of different settings and instances. We would need to check for spurious relationships.

    That same sort of personal experience conclusion is often drawn with respect to women, suggesting that women are more sensitive to the needs of others than are men. Again, we will need much more investigation to establish that as valid theory.

    Here we see that most of us engage in the process of data collection and analysis in our personal experience almost continuously. The danger is that the conditions under which the data were collected were not well controlled, and we did not have a broad enough sampling of instances for our generalizations to be valid.

    Personal experience produces data. We analyze that data. It does not provide solid samples from which we may generalize, and there may be related factors we do not experience. Thus, as scientists we randomize our samples, or do the best we can in that regard, and look self-reflexively for any variables that might show the relationship to be spurious. But that doesn't mean that personal experience isn't valid. It is. Just be careful of generalizing it beyond the reliability of your data. It is often from our personal experiences that we garner the insights that lead to the discovery of new knowledge.