Ed 603 - Lesson 11 - Correlational Research

Lesson 11 will consist of the following topics

Please Note - This Lesson is Still Being Worked On

· Text Assignment for Lesson 11

· Correlational Research

· The Nature of Correlation

· The Design of Correlational Research Studies

· Prediction Studies

· Lesson 11 Assignment

· Lesson 11 Quiz

Text Assignment for Lesson 11

For lesson 11, read pages 311-334 in Educational Research: Competencies for Analysis and Application, Seventh Edition by L. R. Gay and Peter Airasian (2003, Merrill/Prentice Hall, ISBN 0-13-099463-4)

or read pages 190-204 in Educational Research: Competencies for Analysis and Application, Eighth Edition by Lorrie Gay, Geoffrey Mills, and Peter Airasian (2006, Prentice-Hall, ISBN 0-13-118534-9)

or read pages 355-386 in Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 3^rd Edition by John W. Creswell (2008, Merrill/Prentice Hall, ISBN-13: 978-0-13-613550-0)

Correlational Research

The basic question for descriptive research is - "What are the values of a number of variables for a given sample of subjects.

The basic research question for correlation research is - What is the relationship between two or more variables for a given set of subjects. Notice that we said relationship between variables and not the effect of one variable on another variable.

In descriptive research we are just describing our subjects in terms of one or more variables, while in correlational research we are looking at the relationship between the variables.

In future lessons we will look at research in which we are looking at the effect of one variable (the independent variable) on another variable (the dependent variable). This will be the case for causal-comparative reseaerch (lesson 12) and for experimental research (lesson 13).

The important thing to remember is that for correlational research we are just looking at the degree of relationship between the variables and not the effect of one variable on another variable.

An example of a correlational research study:

One important type of correlational research are studies conducted to provide information about the validity and reliability of tests.

Reliability studies are conducted to demonstrate the consistency with which tests perform their measurement function. In one type of reliability study the same group of subjects is given a test and then at a somewhat later date are given the test again. We thus have two scores for each subject (the test score and the retest score) and the correlation coefficient between the two sets of scores can be calculated.

this kind of correlation coefficient is referred to as a reliability coefficient. The reliability coefficient can also be calculated by using equivalent forms of the test. Many tests used in education, for example, standardized achievement tests, have more than one form. To determine the reliability coefficent, a group of subjects are given both forms of a test (e.g. Form A and form B) thus two scores are obtained for each subject and the correlation coefficient is calculated for the two sets of scores.

The first type of correlation study we referred to is a test-retest reliability study and the second is an equivalent forms reliability study.

To demonstrate the validity of a test we want to show that scores on the test correlate highly with some external measure of what the test purportedly measures. This external measure is referred to as the criterion. To conduct a validity correlational study. We obtain scores for students on some test and also record their scores on the criterion measure. Thus we have two scores for each subject and can calculate the correlation coefficient of the sets of scores. This correlation coefficient is referred to as a validity coefficient.

In the follow table are listed some example tests and criteria that might be used in validity studies.

Test	Criterion
Reading Comprehension	Teachers Rating on Reading Comprehension
Jiffy IQ Test	Wechsler Intelligence Test for Children
Clinical Depression Scale	Psychiatrist's Rating on Depression Checklist
Algebra Prediction Test	Final Grades for Algebra Class

Note that in the first three examples the test and the criteria occurred at about the same time. This type of validity is referred to as concurrent validity. In the last example note that the criteria occurs at some time after the test. This is referred to as predictive validity. In this case we want to show the effectiveness of scores on the test in predicting the subjects' standing on some criteria. Some of the same consideratins for predictive validity studies are true for predition studies in general, which we will discuss later.

The Nature of Correlation

Correlational research studies almost always use the correlation coefficient to indicate the degree of relationship bwtween two variaables. The correlation coefficient is a number ranging from 1 (a perfect positive correlation) through 0 (no relationship between the variables) to -1 (a perfect negative correlation).

It is tempting to think of a correlation coefficient as indicating the proportaion of sameness between the two variables. But this is not true. A correlation of .90 does not mean that the two variables are 90% the same. In fact, the proportion of common variance (an indication of sameness) for a correlation of .90 is .81 or 81%. The proportion of commmon variance is the square of the correlation coefficient. (.90 x .90 = .8100).

If we have a correlation of .50 between two variables the proportion of common variance is only .25 or 25% (.50 x .50 = .2500). We could say that the two variables demonstrate 25% sameness but 75% (100 - 25) differentness (if there is such a word and we can use it in the present context).

The Design of Correlational Research Studies

Prediction Studies

In predictive correlational studies we are using the degree of relationship that exists between two variables to predict one variable from the other. For example if reading and spelling are correlated, then we can use the information to predict a student's score on the spelling test if the student has only taken the reading test. Converseley we could predict the student's score on the reading test given the student's score on the spelling test.

Prediction studies are widely used to predict student academic success in college based on such measures as high school grades, teacher grades, and apptitude test scores. In fact, many such criteria may be used in a multiple correlation prediction study.