fraenkel6 im ch15

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A. Purposes of Correlational Research

A. Correlational studies are carried out either to help explain important human

behaviors or to predict likely outcomes.

B. If a relationship of sufficient magnitude exists between two variables, it

becomes possible to predict a score on either variable if a score on the other

variable is known.

C. The variable that is used to make the prediction is called the predictor

variable.

D. The variable about which the prediction is made is called the criterion

variable.

E. Both scatterplots and regression lines are used in correlational studies topredict a score on a criterion variable.

F. A predicted score is never exact. As a result, researchers calculate an index of

prediction error which is known as the standard error or estimate.

I. Complex Correlational Techniques

A. Multiple regressions is a technique that enables a researcher to determine a

correlation between a criterion variable and the best combination of two or

more predictor variables.

B. The coefficient of multiple correlations (R) indicates the strength of the

correlation between the combination of the predictor variables and the

criterion variable.

C. The value of a prediction equation depends on whether it predicts successfully

with a new group of individuals.

D. When the criterion variable is categorical rather than quantitative, discriminate

function analysis (rather than multiple regression) must be used.

E. Factor analysis is a technique that allows a researcher to determine whether

many variables can be described by a few factors.

F. Path analysis is a technique used to test a theory about the causal connections

among three or more variables.

II. Basic Steps in Correlational Research

Fraenkel 6e, Instructor's Manual, Ch. 151 of 10


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A. Problem Selection

1. Is variable X related to variable Y?

2. How well does variable P predict variable C?

3. What are the relationships among a large number of variables, and

what predictions can be made that are based on them?

B. Sample

1. Identify an appropriate population, one that is meaningful and from

which data on each of the variables of interest can be collected.

2. The minimum acceptable sample size for a correlational study is

considered by most researchers to be no less than 30.

C. Instruments

1. The instruments must yield quantitative data in a correlational study.

2. Most correlational studies involve the administration of some type of

instrument such as tests, questionnaires, and sometimes observation.

3. Instruments must show evidence of validity and reliability.

D. Design and Procedures

1. The basic design used in a correlational study is quite straightforward.

2. Two or more scores are obtained from each individual in the sample,

one score for each variable of interest.

3. The pairs of scores are then correlated, and the resulting correlation

coefficient indicates the degree of relationship between the variables.

E. Data Collection

1. In an explanatory study, all the data on both variables will usually be

collected within a fairly short time.

2. In a prediction study, the measurement of the criterion variables often

takes place sometime after the measurement of the predictor variables.

F. Data Analysis and Interpretation

1. When variables are correlated, a correlation coefficient is produced.

2. The closer the coefficient is to +1.00 or -1.00, the stronger the

relationship.



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3. Coefficients that are at or near .00 indicate that no relationship exists

between the variables involved.

III.What Do Correlation Coefficients Tell Us?

A. The meaning of a given correlation coefficient depends on how it is applied.

B. Correlation coefficients below .35 show only a slight relationship between

variables.

C. Correlations between .40 and .60 may have theoretical and/or practical value

depending on the context.

D. Only when a correlation of .65 or higher is obtained can reasonably accurate

predictions be made.

E. Correlations over .85 indicate a very strong relationship between the variables

correlated.

IV.Threats to Internal Validity in Correlational Research

A. Subject Characteristics

1. When two or more characteristics of individuals (or groups) are

correlated, there exists the possibility that other characteristics can explain

any relationships that are found.

2. In such cases, the other characteristics can be controlled through a

statistical technique known as partial correlation.

B. Location

1. A location threat is possible whenever all instruments are administered

to each subject at a specified location, but the location is different for

different subjects.

2. If both measures are not administered to all subjects under the same

conditions, the conditions rather than the variables being studied may

account for the relationship.

C. Instrumentation

1. In any study using a particular instrument many times, thought must be

given to the possibility of instrument decay.



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2. When an observational device measures both variables at the same

time, care must be taken to ensure that observers dont become tired,

bored, or inattentive (this may require using additional observers.)

D. Data-collector Characteristics

1. Characteristics of data collectors can create a threat if different persons

administer both instruments.

2. Gender, age, or ethnicity, for example, may affect specific responses,

particularly with opinion or attitudinal instruments.

E. Data-collector Bias

1. Unconscious bias on the part of the data collectors can occur when

both instruments are given or scored by the same person.

2. It is likely that the observed or scored performance on the first test will

affect the way in which the second test is administered and/or scored.

F. Testing

1. The experience of responding to the first instrument that is

administered in a correlational study may influence subject responses to

the second instrument.

2. The solution is to administer instruments at different times and in

different contexts.

G. Mortality

1. Mortality is generally not a problem of internal validity in correlational

studies since anyone lost must be excluded from the study.

2. There are times, however, when loss of subjects may make a

relationship more (or less) likely in the remaining data, thus creating a

threat to external validity. This is because the sample actually studied is

often not the sample initially selected.

V. Evaluating Threats to Internal Validity in Correlational Studies

A. Ask: What are the specific factors that are known to affect one of the variables

being correlated or which logically would affect it?



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B. Ask: What is the likelihood of each of these factors also affecting the other

variable being correlated with the first? A factor must be related to both

variables in order to be a threat.

C. Evaluate the various threats in terms of their likelihood and plan to control

them. If a given threat cannot be controlled, this should be acknowledged and

discussed.

VI.An Example of Correlational Research

Chapter Objectives

Reading this chapter should enable students to:

Describe briefly what is meant by associational research;

State the two major purposes of correlational studies;

Distinguish between predictor and criterion variables;

Explain the role of correlational studies in exploring causation;

Explain how a scatterplot can be used to predict an outcome;

Describe what is meant by a prediction equation;

Explain briefly the main ideas underlying multiple correlation, factor analysis, and

path analysis;

Identify and describebriefly the steps involved in conducting a correlational study;

Interpretcorrelation coefficients of different magnitude;

Explain the rationale underlying partial correlation;

Describe some of the threats to internal validity that exist in correlation studies, andexplain how to identify them;

Discuss how to control for these threats;

Recognize a correlational study when they come across one in the educationalresearch literature.

Points to Stress

The difference between correlation and causation.

How a scatterplot can be used to predict an outcome.

What a correlation coefficient represents.

How to evaluate (and control) threats to internal validity.

Teaching Suggestions and Class Activities

Confer with the class. Hold individual conferences with those students who aredesigning a correlational study and who want to discuss their progress on Problem

Sheet #13.



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Refer to illustrations in the text to review the concept of correlation. Askstudents to review Figure 15.1, "Scatterplot Illustrating a Correlation of +1.00" on

page 336. Point out that all of the dots fall on a diagonal line, and hence the

correlation is a perfect positive correlation. Ask a student to draw on the chalkboard

what a perfect negative correlation (1.00) would look like. Look at Table 15.1,"Three Sets of Data Showing Different Directions and Degrees of Correlation" also

on page 336. Ask students to cover up the headings of Table 15.1 and identify which

of the three distributions the scatterplot in Figure 15.1 represents (it representsdistribution A). Alternatively, make slides of the figures for a digital presentation.

Refer to illustrations in the text to review scatterplots. Ask students to turn toFigure 15.2, "Prediction Using a Scatterplot" on page 337. Have students turn to

page 338 in the text to look at Table 15.2, and point out that the scatterplot in Figure

15.2 represents the data in Table 15.2. To further help students see the relationship

between frequency distributions and scatterplots, have your students make

scatterplots of a number of distributions. Also, use Figure 15.2 to illustrate how ascore can be predicted from a scatterplot. Give some hypothetical "Teacher

Expectation of Failure" scores, and ask students to say what the predicted "DisruptiveBehavior" score would be accordingly.

Refer to illustrations in the text to review relationships among variables. Toillustrate how two variables can be related to each other, but not to a third variable,

ask students to turn to Figure 15.9, "Circle Diagrams Illustrating Relationships among

Variables" on page 350. Discuss.

For discussion. Discuss any of the questions on page 368 of the text with the class.

Prepare an in-class exercise on correlation. Ask your students to bring calculators

to class that can perform basic operations, including square root. Refer to Handout

Master 15A, "How to Calculate a Correlation Coefficient" (see the section titled

"Handout Masters" later in this manual) for instructions on how your students can usethe Pearson product-moment formula to compute and interpret an actual correlation

coefficient.

Assign panelists and fomenters. Discuss the article titled "When Teachers and

Parents Values Differ: Teachers Ratings of Academic Competence in Children from

Low-Income Families" on pages 351-363 in the text. Assign two students to be

"panelists" responsible for presenting the main points of the study, and assign twoother students to be "fomenters" responsible for preparing questions that provoke or

"foment" discussion on the study presented. Ask students to suggest any additional

strengths or weaknesses in the article besides those we identify in our analysis onpages 364-366.

Review important material in the text. Go over the three steps for evaluating the

likelihood of a threat to internal validity occurring in a correlational study that we



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suggest on page 348 of the text. Ask the class to try using the steps themselves with a

correlational study they find in the literature. Have a few students report their results

to the class.

At-home exercise. Direct students to the Regression Toward the Mean simulation

at: http://www.ruf.rice.edu/~lane/stat_sim/reg_to_mean/index.html. Instruct studentsto print out the Instructions and the Exercises for their convenience. Tell them to

experiment with the mean and standard deviation of the true scores and sample size.

Discuss how their actions affect the scatterplots. Talk about your students answersto the provided exercises, and answer any questions they may have.

Use the Internet to review new concepts. If you have an in-class Internetconnection, go to the Guessing Correlations simulation at:

http://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.html. Test your

students knowledge of correlations with this interactive demo. Press the New Plots

button to begin. Ask students to match the plots with the correlations and then press

"Answers" to see if they are correct. Discuss the reasoning behind the correctanswers with the class. Press New Plots to play again. Alternatively, assign this

activity as an at-home exercise.

Refer to illustrations in the text. We have found that most students are able to

follow the rationale for partial correlation (see page 347). If necessary, however, youmay want to have the class look at Figure 15.6 on page 346 of the text as you go over

the steps in class.

Answers to For Discussion Questions on page 368

(Note to Instructor: Many of these "For Discussion" questions are open ended in nature

and have no right answer. Students should be encouraged to offer as many alternativeanswers as they think plausible and to explain the reasons for the answers they give.)

1. Which type of relationship would a researcher be more pleased to have the results

of a study revealpositive or negativeor would it matter? Explain.

Answers: It would depend on the particular research study. The researcher would

want to see a positive relationship in some studies, while in other studies the

researcher would be looking for a negative relationship.

2. What is the difference between an effect and a relationship? Which is more

important or can this be determined?

Answer:An effect implies some degree of causation, a time sequence (effects are

produced by causes). A relationship means only that two variables are connected in

some way, but neither necessarily has to have been caused by the other (a third

variable may be the culprit!).

http://www.ruf.rice.edu/~lane/stat_sim/reg_to_mean/index.htmlhttp://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.htmlhttp://www.ruf.rice.edu/~lane/stat_sim/reg_to_mean/index.htmlhttp://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.html


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3. Are there any types of instruments that could notbe used in a correlational study?

If so, why?

Answer: Those that yield categorical data only, for example, questionnaire data on

ethnicity, political preferences, and so forth.

4. Would it be possible for a correlation to be statistically significant, yet

educationally insignificant? If so, give an example.

Answer: Yes. A correlation of .05 might be statistically significant if the n was

large enough yet would be educationally meaningless.

5. Why do you suppose people often interpret correlational results as provingcausation?

Answer: They think that "A" causes "B" based on prior experience with one (or a

few) instances, or because it is consistent with their own "theories."

6. What is the difference, if any, between thesign of a correlation and thestrengthof a correlation?

Answer: The sign of a correlation indicates the nature of the relationship between

the two variables. A positive sign (positive correlation) means that as one variable

increases, the other also increases. A negative sign (negative correlation) means

that as one variable increases, the other decreases. The strength of a correlation

refers to the degree of intensity of the relationship; the higher the correlation, the

stronger it is, regardless of sign.

7. Correlational studies, in and of themselves, do not establish cause and effect. Isthis true? Why or why not?

Answer: Yes, this is true. The effect may be the result of some third factor.

However, correlational studies may be a step in the search for causes.

8. The possibility of causation (in a correlational study) is strengthened if a time

lapse occurs between measurement of the variables being studied? Why?

Answer: A time lapse between measurement of variables being studied may show

possible causation if the results show consistency over time.

9. To interpret correlation coefficients sensibly, it is a good idea to show the

scatterplots on which they are based. Why is this? Explain.

Answer: Once a scatterplot has been constructed, a straight line, known as a

regression line, can be calculated mathematically. The researcher can then use the

line as a basis for prediction. Being able to predict a score for an individual or



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group on one variable from knowing the individuals or groups score on another

variable can be extremely useful.

10. A researcher wants to predict marital stability by using a measurement of

common interest. What other variables (measurements) would add to predictability

(by means of multiple regression).

Answer: Possibilities include similarity in family background, number of siblings,

educational level, current income, history of emotional stability and family

conflict/divorce, and a measure of compensating strengths.

Resources and References

Chapter-Specific Web sites:

Correlational Research Methods

http://www.naropa.edu/faculty/johndavis/prm2/correl1.html

Research Aids: Correlation

http://www.surveysystem.com/correlation.htm

Vassar Stats: Correlation and Regression

http://faculty.vassar.edu/lowry/VassarStats.html

Correlation

http://www.socialresearchmethods.net/kb/statcorr.htm

Guessing Correlations Simulation

http://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.html

General Web sites:

Measurement, Statistics, and Methodological Studies

http://research.ed.asu.edu/msms/multimedia/multimedia.cfm

American Educational Research

http://www.aera.net/

Journal Articles and Related Texts:

Erdle, S. H., G. Murray, and J. P. Rushton. 1985. Personality, classroom behavior, and

student ratings of college teaching effectiveness: A path analysis.Journal of

Educational Psychology, 77, 394-407.

http://www.naropa.edu/faculty/johndavis/prm2/correl1.htmlhttp://www.naropa.edu/faculty/johndavis/prm2/correl1.htmlhttp://www.surveysystem.com/correlation.htmhttp://faculty.vassar.edu/lowry/VassarStats.htmlhttp://www.socialresearchmethods.net/kb/statcorr.htmhttp://www.socialresearchmethods.net/kb/statcorr.htmhttp://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.htmlhttp://research.ed.asu.edu/msms/multimedia/multimedia.cfmhttp://research.ed.asu.edu/msms/multimedia/multimedia.cfmhttp://www.aera.net/http://www.naropa.edu/faculty/johndavis/prm2/correl1.htmlhttp://www.surveysystem.com/correlation.htmhttp://faculty.vassar.edu/lowry/VassarStats.htmlhttp://www.socialresearchmethods.net/kb/statcorr.htmhttp://www.stat.uiuc.edu/courses/stat100//java/guess/GCApplet.htmlhttp://research.ed.asu.edu/msms/multimedia/multimedia.cfmhttp://www.aera.net/


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Gosman, E. J., B. A. Dandridge, M. T. Nettles, and A. R. Thoeny. 1983. Predicting

student progression: The influence of race and other student and institutional

characteristics on college student performance.Research in Higher Education, 18,209-236.

Kenny, D. A. 1979. Correlation and causality. New York: Wiley.

Kim, F. J., and C. W. Mueller. 1978.Introduction to factor analysis: What it is and how

to do it. Beverly Hills, CA: Sage.

Liebetrau, A. M. 1983.Measures of association. Beverly Hills, CA: Sage.


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