Exercise on Critical Thinking and Testing Hypotheses Involving Two Variables (CT1)

Ed Nelson, Department of Sociology
California State University, Fresno

 © SSRIC; Last Modified 21 September 2001

CT 1 Downloads

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 McGraw-Hill at 1-800-338-3987. The ISBN is 0-07-241445-6 . 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.

Ed Nelson
Department of Sociology, M/S SS107
California State University, Fresno
Fresno, CA 93740
Phone: 559-278-2275
Email: ednelson@csufresno.edu

Please contact the author for additional information.

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, weíll 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. Youíll 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


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.

"People who attend church frequently are more likely to have strong moral positions opposed to pornography and are, therefore, more likely to feel that society ought to make sure that pornography is not available to people regardless of their age." Notice that the argument is stated more formally that we would express it in a conversation with our friends. Written arguments should be expressed formally and, above all, they must be clear.

This is a pretty simple argument. It includes one link between church attendance and opinions on pornography laws and that link is a personís 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.

  1. One is a chain argument that basically takes the form of A à B à C. Youíre providing the "link" between A and C that is B. To make this argument more complex, you could add more links.
  2. Another is the "because-because" argument. Imagine that you are talking with your friends. Someone asks what we should do tonight and you suggest going to the movies. Someone else asks why you want to go to the movies and you respond by saying that there are a number of reasonsóthere are several good movies out and itís not very expensive and the theatre is air-conditioned. Youíre listing three reasons why you think it is a good idea to go to the movies. In other words, you have listed three "becauses."
Write a clear paragraph indicating the reasons that you think your hypothesis might be true. Use formal language. In other words, donít make it sound like a conversation with your friends. Rather, state it clearly and formally. Try to go beyond suggesting one "link" or one "because." Donít settle for a simple argument. Develop your argument into a more complex explanation of why you think your hypothesis is true.

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 "because-because" argument).

Part III. Dummy table.

What do you think your table should look like if your hypothesis is true? Weíre going to use a dummy table. Itís a model to which you can compare your actual table. Hereís what the dummy table will look like for our example.

Dummy Table Ė Opinions on Pornography by Church Attendance
Feelings About Pornography Laws
Church Attendance
Illegal to all
Illegal under 18


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 didnít 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 donít 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 donít know how to use the tables function, then you could look up "tables" in the help menu or, if you donít want to take the time to do that, use tabs to create your table.

Part IV. Two-variable analysis.

Now itís 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.

Rule Ė If your independent variable is the column variable, use the column percents. However, if your independent variable is the row variable, then use the row percents. It is customary to put the independent variable in the columns. If we do this, then we will use the column percents. Put your independent variable in the column box in SPSS and put your dependent variable in the row box.

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. Thatís 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 itís 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.

Rule Ė If your percents sum down to 100, then compare across. However, if your percents sum across to 100, then compare down. Look across the first row. Notice that the percents decrease from 59% to 38% to 25%. Those who attend church often are more likely to feel that pornography should be illegal to everyone.

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.

Letís put this all together. How could we write a few sentences using the percents to describe the relationship? What about this?

Those who attend church frequently are more likely to feel that pornography ought to be illegal for everyone. For example, 58% of those who attend often compared to 25% of those who infrequently attend think that pornography ought to be illegal for everyone regardless of age. But those who attend church infrequently are more likely to feel that pornography ought to be illegal only for those under 18. For example, 70% of those who attend infrequently compared to 37% of those who attend often think pornography ought to be illegal only for those under age 18. Hardly anyone (5% or less) think pornography ought to be legal for everyone. The data support our hypothesis. There are other ways this could be expressed. Your goal is to write a short paragraph that describes your results as clearly as possible.

Thereís one word of warning about interpreting percentages. Donít make too much out of small differences between the percents. If the percents would have increased from 35% to 37% to 39%, we wouldnít 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, itís 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 weíll 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 itís 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.