Exercise
on Critical Thinking and Testing Hypotheses Involving Two Variables (CT1)
Ed
Nelson, Department of Sociology 
© SSRIC; Last Modified 21 September 2001
Note to the instructor: The data set used in this exercise is RELG9800 which is a combination of the 1998 and 2000 General Social Surveys. (Some of the variables in the GSS have been recoded to make them easier to use and some new variables have been created.) This exercise uses CROSSTABS to test hypotheses involving the relationship between two variables. There is another exercise that focuses on relationships among three variables. In CROSSTABS, students are asked to use percentages to interpret the tables. You could modify this exercise by adding Chi Square and measures of association. A good reference on using SPSS is SPSS for Windows Version 9.0 A Basic Tutorial by Richard Shaffer, Edward Nelson, Nan Chico, John Korey, Elizabeth Nelson and Jim Ross. To order this book, call McGrawHill at 18003383987. The ISBN is 0072414456 . You have permission to use this exercise and to revise it to fit your needs. Please send a copy of any revision to the author.
Author
Ed Nelson
Department of Sociology, M/S SS107
California State University, Fresno
Fresno, CA 93740
Phone: 5592782275
Email: ednelson@csufresno.edu
Please contact the author for additional information.
Goal:
The goal of this exercise is to learn how to state hypotheses involving two
variables, develop arguments to support these hypotheses, use SPSS to get the
tables to test these hypotheses, and to interpret these tables and decide if
the data support the hypotheses.
There is a PowerPoint presentation to accompany this exercise which can be downloaded from the Teaching Resources Depository by clicking here.
Part I. Hypotheses involving two variables.
A hypothesis states the relationship we expect to find between two variables. For example, we might be interested in opinion on pornography laws and our hypothesis might be that "those who attend church frequently are more likely to think there should be laws against the distribution of pornography for everyone regardless of age."
In this example, we’ll use church attendance as the independent variable and opinion on pornography laws as the dependent variable. In our example, the variable names are ATTEND and PORNLAW.
Look at the codebook for the data set RELG9800. Your instructor will show you how to open this data set. Look through the variables and read the questions that were asked respondents. You’ll choose an independent and a dependent variable for your project. Remember that the independent variable is the potential cause and the dependent variable is the possible effect.
There are lots
of possibilities for you to choose from. To help you, look through this list
of possible independent and dependent variables. If you want to choose something
not on the list, check with your instructor first.
Hypothesis  Dependent Variable  Independent Variable 

ABANY  RELITEN OR BIBLE 

GRASS  DEGREE 

FEAR  SEX 

PRES96  RACE OR SEX 

TRUST  DEGREE 

DEGREE  MADEG OR PADEG 

CAPPUN  POLVIEWS 

FAIR  DEGREE 

COLRAC  CLASS 
Choose one of these as your dependent variable or choose something of your own (be sure to check with your instructor first) and write a clear hypothesis specifying the relationship you expect to find between these two variables. Use the example of church attendance and pornography laws as a model to help you develop your hypothesis. Include in parentheses after your hypothesis the variable names of your independent and dependent variables (e.g., IV=ATTEND, DV=PORNLAW).
Part II. Rationale for hypothesis.
Imagine that someone asks us why we think our hypothesis is true. What would we say? Why do we think that frequent church attenders are more likely to think there should be laws against the distribution of pornography? Our argument might look like this.
This is a pretty simple argument. It includes one link between church attendance and opinions on pornography laws and that link is a person’s moral position on pornography. It argues that frequent church attenders will have stronger positions against pornography compared to less frequent church attenders and that those with stronger moral positions will be more in favor of laws against the distribution of pornography.
You might start with two basic types of arguments.
So far you have stated a hypothesis focusing on the relationship between two variables and have provided a rationale that explains why that relationship might occur (either a "chain" argument or a "becausebecause" argument).
Part III. Dummy table.
What do you think
your table should look like if your hypothesis is true? We’re going to use a
dummy table. It’s a model to which you can compare your actual table. Here’s
what the dummy table will look like for our example.


Feelings About Pornography Laws 






Illegal to all 





Illegal under 18 




Legal 



Rather than filling in numbers in the table, we have used letters to represent each cell. The first row says that the percent of people who attend church often that believe pornography should be illegal to all (cell a) will be greater than the percent who attend church sometimes (cell b) that think pornography should be illegal to all. In other words, cell a should be greater than (>) cell b. And similarly, cell b should be greater than cell c. Why didn’t we fill in the rest of the dummy table? Our hypothesis only says that those who attend church frequently are more likely to feel that there should be laws against the distribution of pornography to everyone regardless of their age. So we don’t need to say anything about the other two rows in the table.
Remember, the dummy table is only a model to be compared to your actual table. If your actual table looks like your dummy table, then your hypothesis is supported by your data. If it does not, then the data do not support your hypothesis. Actually hypotheses are never proven true. They are just supported or not supported by the data used in our analysis.
Use the tables function in Word to create your dummy table. If you don’t know how to use the tables function, then you could look up "tables" in the help menu or, if you don’t want to take the time to do that, use tabs to create your table.
Part IV. Twovariable analysis.
Now it’s time to get the actual table from SPSS. Your instructor will show you how to open the data set in SPSS. Your data set is named RELG9800.
Your instructor will show you how to create tables in SPSS. You can also go to an introduction to SPSS by clicking this link. This will take you to the chapter on crosstabulations. The table we get from SPSS should look like this.
When you ask for a table from SPSS, you will need to specify which percents you want to use. You have a choice among column, row, and total percents. Use the following rule to decide.
In this table, we have recoded the variable ATTEND to reduce the number of categories to three (often, sometimes, infrequently) and we have created another variable called ATTEND1, a recoded version of ATTEND. You may not know how to recode in SPSS. In order to avoid having to recode, all the examples of possible hypotheses that were listed earlier use variables that have only a few categories where recoding will not be necessary. That’s why we wanted you to check with your instructor first before choosing another set of variables for your hypothesis. If you do know how to recode or your instructor wants to show you how to recode, you could use other variables with more categories.
Part V. Interpreting crosstabs.
Now it’s time to interpret your table. To interpret means to describe your results in terms of your hypothesis. First, use the percents to help you understand the relationship between these two variables. Since the percents sum down to 100, you must compare across. This is a very important rule in using percents to interpret the relationship in your table.
Now look across the second row. This time the percents go up from 37% to 59% to 70%. Those who attend church less are more likely to think that pornography ought to be illegal only to those under 18.
Finally, look across the third row. These percents are very small. Hardly anyone thinks that pornography ought to be legal for everyone regardless of age and there is no pattern to the percents.
What about our dummy table? Compare the actual table we got from SPSS with our dummy table? The first row of our dummy table looks exactly like our actual table. So the data support our hypothesis.
Let’s put this all together. How could we write a few sentences using the percents to describe the relationship? What about this?
There’s one word of warning about interpreting percentages. Don’t make too much out of small differences between the percents. If the percents would have increased from 35% to 37% to 39%, we wouldn’t have gotten too excited. These could just be random or chance differences. As a rule of thumb, your percents should differ by at least five points before you even begin to think it might mean something. By the way, it’s very hard to write a general rule like this because the amount by which they should differ before we take the differences seriously really depends on the number of cases in the table. The more cases there are in the table, the smaller that number should be and the fewer cases there are, the larger it should be. But we’ll arbitrarily use five points or more as our rule. It is always safe to say that the more the percents differ, the stronger the relationship.
Now it’s your turn.
Write a short paragraph interpreting your table. Use the percents to help you.
Make sure you include at least one sentence expressing the pattern of the percents
and another sentence using the percents as examples. Be sure to use your dummy
table to help you decide if the data support your hypothesis and explain how
you reached your decision.




