Statistics-SPSS IBM 21 Needed

Problem 4. Which of these studies might be analyzed with a correlation?

a. The which group has a higher reading comprehension level—dyslexic children versus ADHD (attention deficit hyperactivity disorder) children

b. The amount of religious commitment and frequency of attendance at religious services

c. The number of doctor visits and income level

d. The soft drink preferences of college students

***CAPTION FROM TEXTBOOK : This portion is just for your information.

Experimental Versus Correlational Studies

In Modules 12 to 33, we measured the effect of an independent variable on a dependent variable. Then, we tested the result for statistical significance, effect size, and power. In each of the studies. There were at least two groups that differed on the independent variable. We then examined whether the independent variable (the defining difference between the groups) caused the effect in the dependent variable.

In this module, we begin to look at data from a new perspective. We will look at correlational studies. In a correlational study, we have only a single group of subjects rather than two or more groups. In addition, each of the subjects has a score on two different variables. Also, in a correlational study, we do not seek cause-and-effect relationships between independent and dependent variables. Rather, we simply want to know whether or not the scores on two variables are related.

Sometimes correlational studies are used to establish the properties of the tests themselves. The SAT, for example, is given on multiple test dates throughout the year. Students taking the test on one date do not answer the same questions as students taking the test on another date. Rather, there are parallel forms of the test—a different form for each date. Scores have the same meaning regardless of which form students take because the test forms are comparable. But how do the test developers know that the scores are comparable? During the test development process. They gave the same students (note the single group of subjects) two different forms of the test (note the two variables). Then. They compared the students' scores on both tests (note the correlation). They found that the scores were similar for the same students on both forms of the test. This type of correlation is called test reliability.

Most of the time, correlational studies are used for prediction rather than for establishing the reliability of the tests themselves. That is, we seek to establish relationships so that the score of a person on one variable can be used to predict that person's probable score on a second variable. For example, once a relationship is established between the number of hours children watch television and children's academic performance in school, we can predict any given child's probable academic performance in school just by knowing the number of hours of television he or she watches. Similarly, a researcher interested in prediction may want to know the relationship between

• the amount of time students study and their grade on a test,

• the amount of antidepressant medication clients take and their reported mood level,

• air temperature and crime rate,

• income and years of education,

• height and weight, and

• IQ and shoe size (do you think there is any relationship?).

What are two common uses of correlations?

Complete the following table to compare and contrast studies analyzed by three different statistics.

2. Complete problem 12 on page 425.

Problem 12. For each of the following, indicate whether the expected relationship between the two variables will be positive (+), negative (−), or zero (0):

____a. size of house and size of electric bill

____b. height of parents and height of children

____c. air humidity level and people's energy level

____d. number of books read per year and age at which got first eyeglasses

____e. hours spent at the beach and depth of tan

***CAPTION on next page FROM TEXTBOOK : This portion is just for your information.

If two variables are negatively correlated. Then as the values of one variable go up. The values of the other variable go down. For example. The relationship between the number of absences in a course and score on the final exam in that course is negative. In other words. The more often students are absent from class. The lower their grades tend to be on the final exam. You can see this pattern in the lower scatterplot in Figure 34.4. Note the direction of the data points. With a negative relationship. The data points go from the upper left to the lower right.

He seemed to have very strong intuitions but unfortunately of negative sign.

—the biologist Francis Crick, referring to René Thom, in What Mad Pursuit

Let's return to the set of quiz scores from the beginning of this module. Judging from the scatterplot shown in Figure 34.5, what is the approximate strength of the relationship? What is the direction of the relationship?

Figure 34.5 Scores on Quiz 1 and Quiz 2

The relationship is moderate because the points form an ellipse about halfway between a straight line and a circle. And it is positive because the general trend is from lower left to upper right. That is, as the scores on Quiz 1 go up. The scores on Quiz 2 also go up. What two terms are used to describe a correlational relationship? What does each term indicate?

3. Repeat the SPSS Connection from pages 430–431 on your computer. Copy and paste the SPSS output for the scatterplot to a Word document.

SPSS Connection

Download the file data_quiz 1 quiz 2.sav from www.sagepub.com/steinberg2e. These data are used in the textbook example.

Alternatively, manually enter the scores on Quiz 1 and Quiz 2 into the SPSS Data View spreadsheet: Set it up like this.

Click on the Variable View tab to define the variable. Name the first variable name, set the Type as String, and label the variable as Name. Name the second variable quiz1, set the decimal at 0, and label the variable as Quiz 1 (X). Name the third variable quiz2, set the decimal at 0, and label the variable as Quiz 2(Y).

If the file is not already in Data View, click that tab in the lower left of the screen.

In the toolbar at the top of the screen, click on Graphs, then Legacy Dialogs, then Scatter/Dot. Select the Simple Scatter example, and click Define. Highlight the variable Quiz 1(X) in the left window and click on the arrow before the X axis window (that's the second window, not the top window) on the right. To send the variable into that window. Highlight the variable Quiz 2(Y) in the left window and click on the arrow before the Y axis window (that's the top window, not the second window) on the right. To send the variable into the that window. Click OK. This is what you will see. *** CONTINUED ON NEXT PAGE

This is the scatterplot shown in the textbook. The strength and direction is not as clear as the one in the textbook because the graph violates the guidelines for graph construction that you learned in Module 4 regarding appropriate axis scaling for best graph interpretation. The complete version of SPSS allows for axis demarcation decisions, but the Student version of SPSS does not.

4. Repeat the SPSS Connection from pages 444–445 on your computer. Copy and paste the SPSS output for the correlation to your Word document.

SPSS Connection

Download the file data_quiz 1 quiz 2.sav from www.sagepub.com/steinberg2e. These data are used in the textbook example.

Alternatively, manually enter the scores and name the variables as described in Module 34. If the file is not already in Data View, click that tab in the lower left of the screen. In the toolbar at the top of the screen, click on Analyze, then Correlation, then Bivariate. Highlight the variable Quiz 1(X) in the left window and click on the arrow before the Variables window on the right. To send the variable into that window. Do the same for the Quiz 2(Y) variable. Click OK. This is what you will see.

Correlations

SPSS correlates each selected variable with each other selected variable twice-once in AB order, and again in BA order. Results are identical and therefore redundant. If you draw a diagonal line through the 1.000 correlations (each variable with itself), you need pay attention only to the coefficients triangle either above or below the diagonal line.

5. Complete problem 4 on page 441 using SPSS. Copy and paste the SPSS output to the Word document. Use pages 430–431 and 444–445 as guides (See problems 3 and 4 in this project). Please type the answers to problems 4b, 4c, 4e, and 4f.

Problem 4. Here are hypothetical data for a study of the relationship between intelligence and prejudice in adults. For both variables, higher scores indicate more of the measured trait:

a. Create a scatterplot of the data.

b. From the scatterplot, what direction and approximate strength do you expect the correlation coefficient to take?

c. State the null hypothesis.

d. Calculate Pearson r.

e. Interpret the correlation coefficient for a two-tailed test: Can you reject the null hypothesis? If so, with what confidence?

f. Write the result in APA journal format.

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