Chapter 15: Correlational Research

Activity 15.1: Correlational Research Questions

Activity 15.2: What Kind of Correlation?

Activity 15.3: Think Up an Example

Activity 15.4: Match the Correlation Coefficient to its Scatterplot

Activity 15.5: Calculate a Correlation Coefficient

Activity 15.6: Construct a Scatterplot

Activity 15.7: Correlation in Everyday Life

Activity 15.8: Regression
Activity 15.1:

Correlational Research Questions

Which of the following questions would lend themselves well to correlational research?

  1. What are student attitudes toward environmental organizations?
  1. Do students like history more if taught by the inquiry method?
  1. What does a high school football coach do when he isn’t coaching?
  1. What sorts of themes appear in the editorials in the New York Times?
  1. Does early success in school lead to financial success in adulthood?
  1. Is teacher praise related to student achievement?

Activity 15.2:

What Kind of Correlation?

Would each of the following be positively, negatively, or not correlated?

  1. ______height and weight of people ages 1-18
  1. ______weight and speed of people ages 20-50
  1. ______health and length of life
  1. ______running speed and taste for mystery novels
  1. ______size and strength of people ages 10-30
  1. ______achievement in school and absenteeism
  1. ______television viewing (in hours) and reading achievement
  1. ______food intake at a meal and stomach comfort
  1. ______height and life expectancy

Activity 15.3:

Think Up an Example

In the space provided, write an example of two things that would have:

  1. A strong positive correlation: ______and ______
  1. A strong negative correlation: ______and ______
  1. A weak positive correlation: ______and ______
  1. A weak negative correlation: ______and ______
  1. Little or no correlation: ______and ______

Activity 15.4:

Match the Correlation Coefficient to its Scatterplot

Shown below are eight scatterplots. In the space alongside each, write in the appropriate correlation coefficient from the following list:

r = .90; r = .65; r = .35; r = .00; r = -.90; r = -.75; r = -.50; r = -.10

Activity 15.5:

Calculate a Correlation Coefficient

Actually, there are many different correlation coefficients, each applying to a particular circumstance and each calculated by means of a different computational formula. The one we will use in this exercise is the one most frequently used: the Pearson product-moment coefficient of correlation. It is symbolized by the lowercase letter r. When the data for both variables are expressed in terms of quantitative scores, the Pearson r is the appropriate correlation coefficient to calculate. It is designed for use with interval or ratio data. The formula for calculating the Pearson r coefficient is:

The Pearson formula looks a lot more complicated than it really is. It does have a lot of steps to follow before you actually get to the end, but each step is easy to calculate. For this exercise, let’s imagine we have the following sets of scores for two variables -- reading and writing -- for five students:

Student
Name / Variable X―
Reading Score / Variable Y―
Writing Score
Al / 20 / 20
Beth / 18 / 16
Cathy / 18 / 20
Dave / 15 / 12
Ed / 10 / 10
Total / ΣX = 81 / ΣY = 78
ΣXY = 1328 / ΣX2 = 1373 / ΣY2 = 1300

What we would like to know is whether these two variables are related, and if so, how ― positively or negatively. To answer these questions, apply the Pearson formula and calculate the correlation coefficient for the two sets of scores. In other words, plug the appropriate numbers into the formula to calculate the r. Most of the computation has already been done for you and is provided in the bottom two rows of boxes. (See Appendix D at the end of the textbook for a step-by-step example of how to calculate a correlation coefficient using this formula.) Once you have calculated the correlation coefficient, describe below in one sentence the type of relationship that exists between reading and writing scores among this sample of five students:

______

______

Activity 15.6:

Construct a Scatterplot

In this activity, you are to construct a scatterplot and calculate a correlation coefficient to determine if there is a relationship between the number of hours a student works and his or her grade point average (GPA).

  1. Is there a relationship between hours worked and GPA?
  1. If so, is it positive or negative? Is it strong or weak? Explain in words what the scatterplot reveals.
  1. Calculate the correlation coefficient (Follow the steps shown in Appendix A)
  1. Are there any outliers? What do they suggest?

STUDENT HOURS WORKED GRADE POINT AVERAGE

ALPHONSO301.42

ROBERTO212.75

ELOISE123.64

FELIX182.40

JACK 93.75

OSCAR 04.00

WILLIE203.10

DAVID243.25

SUSAN142.87

FELICIA192.20

BETTYE281.75

JUAN 33.88

ANGELINA 91.52

JESUS162.81

ELLIE182.66

SAM300.87

CHIN212.99

TOGUIAS222.58

JEREMIAH232.85

JOSHUA 94.00

Activity 15.7:

Correlation in Everyday Life

Below we present a number of everyday sayings that suggest relationships. What correlations do they suggest? Are they positive or negative?

  1. A fool and his money are soon parted.
  1. As the twig is bent, so grows the tree.
  1. You can’t grow grass on a busy street.
  1. Virtue is its own reward.
  1. What fails to destroy me makes me stronger.
  1. To get along, go along.
  1. You can’t make an omelet without breaking some eggs.
  1. You can’t make a silk purse out of a sow’s ear.
  1. All that glitters is not gold.
  1. If at first you don’t succeed, try, try again.

Activity 15.8:

Regression

In this activity, you are to use the table below to complete the tasks listed below the table.

Percentages of public school students in 4th grade in 1996 and in 8th grade in 2002 who were at or above the proficient level in mathematics for eight western states are shown in the table below:

STATE4TH GRADE (1996)8TH GRADE (2002)

ARIZONA1521

CALIFORNIA1118

HAWAII1616

MONTANA2237

NEW MEXICO1313

OREGON2132

UTAH2326

WYOMING1925

  1. Construct a scatterplot and discuss the interesting features of the plot.
  1. Find the equation of the least-squares line that summarizes the relationship between x = 1966 4th grade math proficiency and y = 2000 8th grade math proficiency math percentage.
  1. Nevada, a western state not included in the data, had a 1996 4th grade math proficiency of 14%. What would you predict for Nevada’s 2000 8th grade math proficiency percentage? How does your prediction compare to the actual 8th grade math value of 20 for Nevada?