1. Correlational Research

2. Researchers try to determine the degree to which, or if at all, a relationship exists between two (or more) non-manipulated variables. Sometimes referred to as Associational Research

3. Variables Can involve two quantitative variables, two categorical variables, or one quantitative and one categorical variable. Examples: Reading Achievement (Q or C) and Interest Level in School (Q or C) Reading Achievement (Q or C) and Method Used for Reading Instruction (Q or C) Student Gender (Q or C) and College Major (Q or C) Mathematical Ability (Q or C) and Career Choice (Q or C)

4. ?Causation? Does not prove causation, however researchers often times make causal statements as a result of their study. Since correlational research often times serves as a springboard to/foundation for additional research, a hypothesis which predicts existence of a relationship is very common. Example: Research Question - Will teaching elementary math through the use of manipulatives result in better math performancace? Hypothesis - Teaching elementary math through manipulatives results in better math performance.

5. Summary Correlational Research --> relationships (how)--> become focus of future investigations --> investigations help us learn (why) variables are related --> detect patterns or connections between variables --> better understand the world in which we live

6. The degree to which two variables are related is noted by using a correlation coefficient Correlations are categorized as Positive, Negative, or None. A positive correlation indicates a direct relationship between the variables, that is, high scores on one variable tend to be associated with high scores on the other variable or low scores on one variable with low scores of the other.

7. Example Education Level in YearsStarting Salary in Dollars 1118000 1230000 1640000 1843000 2050000 Graphing the points in the above table would result in a scatterplot in quadrant 2 which emanates from lower left and travels to the upper right (/).

8. Negative A negative correlation indicates an indirect or inverse relationship exists between the variables. High scores on one variable are associated with low scores on the other variable, or low with high.

9. Example Weight in PoundsLife Expectancy in Years 20080 25073 30068 35060 40052 Graphing the points in this table would result in a scatterplot in quadrant 2 which emanates from the upper left and travels to the lower right (\).

10. Quantifying Degree of Correlation The parameters for the value of the coefficient of correlation are -1< r <+1 with -1 and +1 representing perfect negative and positive correlations respectively. The closer the correlation coefficient gets to 1 the stronger the positive correlation and the closer the correlation coefficient gets to -1 the stronger the negative correlation. Obviously, a correlation of "0" would be interpreted as no correlation exists between the measured variables.

11. Coefficient of Determination Squarring the correltaion coefficient (r 2 ) yields (determines) the percentage of the variability among the dependent variable scores that can be attributed to differences in the scores on the independent variable.

12. Example of r and (r 2 ) Suppose a strong positive correlation exists between High School Grades and College GPA, that is, assume r=.65 Then it follows that r 2 = (.65x.65) = 42% Thus it could be said that 42% of the differences in college GPA's can be attributed to differences in students' High School grades.

13. Cut Scores Here are some suggested cut scores for Correlations. This info was taken from our "Fraenkel and Wallen" class text. rr2r2 Interpretation.3512% Weak relationship, No use for predicting.525% Predictions can be made but will be very crude with huge errors..6542% Prediction said to be reasonably accurate.8572% Close relationship between variables and very useful for predicting

14. Procedures There are different kinds of correlational procedures. The procedure chosen depends upon the type of variables that are involved in the research. For information on specific procedures, refer to our "Huck" class text, chapter 3, pp.58-67.

15. Procedures Correlational ProcedureWhen to Use Pearson's Product-Moment Two Quantitative Variables, Purpose to produce Raw Scores Spearman's Rho (Rank- Order) Two Quantitative Variables, Purpose is to Rank Kendall's Tau Two Quantitative Variables, Purpose is to Rank and Tie in rank exists Point Biserial One Quantitative Variable and One Qualitative & True Dichotomous Variable Biserial One Quantitative Variable and One Qualitative & Artificial Dichotomous Variable PhiBoth variables are true dichotomies TetrachoricBoth variables are aritificial dichotomies Cramer's VTwo Qualitative Variables