1. Correlational Research

2. Correlational Research
The purpose of correlational research is to discover relationships between two or more variables.
Relationship means that an individuals status on one variable tends to reflect his or her status on the other.

3. Correlational Research
Helps us understand related events, conditions, and behaviors.
Is there a relationship between educational levels of parents and children’s learning interest?
To make predictions of how one variable might predict another
Can high school grades be used to predict college grades?

4. Correlational Research
To examine the possible existence of causation
Does physical exercise cause people to lose weight?
CAUTION: In correlational research you CAN NOT absolutely say once variable causes something to happen. This can only be done through experimental research. You can say one variable might cause something else to happen.

5. Warning!
Relationship does not necessarily indicate cause-effect (causal connection)
(it may suggest cause-effect but does not establish one)
“the independent variable DOES PLAY A ROLE in the occurrence of the dependent variable…” (but does not necessarily cause it)

6. Where does the data come from for correlational research?
Surveys
Scores on various tests or rating scales
Demographic information
Judges or expert ratings

7. Correlational Research Process
Variables to be study are identified
Questions and/or hypotheses are stated
A sample is selected (a minimum of 30 is needed)
Data are collected
Correlations are calculated
Results are reported

8. Terminology
“Predictor” variable – the variable(s) that are believed to predict the outcome.
Could be called an independent variable

9. Terminology
“Criterion” variable – the variable to be predicted, the outcome
Could be called the dependent variable

10. Terminology
Is level of education (predictor variable) related to family income (criterion variable)?
Do people who eat more eggs (predictor variable) have higher cholesterol levels (criterion variable)?

11. Correlational research in MI
Research Q?
Variables?
Dependent and independent?
Target
Measure?
Gardner’s MI test
BGFL test

12. Correlation coefficient
Needed to show the
Existence
Degree
Direction
of the correlation
Usually expressed as…
r (simple) or R (multiple) [ to 0 to +1.00]

13. Correlations Correlations can range from –1.00 to 1.00
A 1.00 is a perfect positive correlation
As one variable increases, so does the other
A is a perfect negative correlation
As one variable increases, the other variable decreases
A .00 correlation indicates no correlation
There is no relationship between one variable and another

14. Interpretation of the Strength of Correlations
– Very Weak
– Weak
– Moderate
– Strong
.81 – Very Strong
Different statisticians may have similar but slightly different scales.

15. Correlations Scatter plots are often used to depict correlations
This chart shows a strong positive correlation

16. Correlations Scatter plots are often used to depict correlations
This chart shows a strong negative correlation

17. Correlations Scatter plots are often used to depict correlations
This chart shows virtually no correlation

18. How can I calculate correlations?
Excel has a statistical function. It calculates Pearson Product Moment correlations.
SPSS (a statistical software program for personal computers used by graduate students) calculates correlations.

19. Which correlation to use?
Phi correlation
Pearson Product Moment
Spearman rho
Biserial Correlation
Kendall tau

20. Pearson Product-Moment Correlation
Used when both the criterion and predictor variable contain continuous interval data such as test scores, years of experience, money, etc.

21. Examples of when to use the Pearson Correlation!
Predictor Variable (IV)
Criterion Variable (DV)
Years of Experience in Extension
Job Satisfaction score
Family Income
EOC Test Scores
Distance from Dunkin donut shop.
Weight

22. Point Biserial Correlation
When the predictor variable is a natural (real) dichotomy (two categories) and the criterion variable is interval or continuous, the point biserial correlation is used.

23. Examples of when to use the Point Biserial Correlation!
Predictor Variable (IV)
Criterion Variable (DV)
4-H member or Not
Leadership score
National Board Certified or Not
EOC Test Scores
Male or Female
Salary

24. Biserial Correlation
When the predictor variable is an artificial dichotomy (two categories) and the criterion variable is interval or continuous , the biserial correlation is used.

25. Examples of when to use the Biserial Correlation!
Predictor Variable
Criterion Variable
Tall or short
Leadership score
Good looking or ugly
Salary
More Popular or Less Popular
Self Concept Score

26. Phi Correlation
When the both the predictor and criterion variables are natural dichotomies (two categories), the phi correlation is used.
If the dichotomies are artificial, the tetrachoric correlation is used. This is rarely the case in educational research

27. Examples of when to use the Phi Correlation!
Predictor Variable
Criterion Variable
4-H member or not
On School Honor Roll or Not
Board Certified Teacher or Not
Member of Teachers Organization or Not
Male or Female
Full Professor or Not

28. Spearman rho and Kendall tau
When the both the predictor and criterion variables are rankings, use either the Spearman rho or Kendall tau correlation.
More than 20 cases – Spearman rho
Less than 20 cases – Kendall tau

29. Examples of when to use the Spearman rho or Kendall tau Correlation!
Predictor Variable
Criterion Variable
Ranking of students in high school graduating class
Ranking of students according to number of scholarship offers
Ranking of discipline problems in 1990
Ranking of discipline problems in 2002

30. Correlation Table Predictor Variable Criterion Variable
Correlation to Use
Interval (Continuous)
Pearson
Real Dichotomy
Point Biserial
Artificial Dichotomy
Biserial
Phi
Tetrachoric
Ranking
Spearman rho for 20 or more rankings
Kendall’s tau for less than 20 rankings

31. Other Correlations
You can perform multiple correlations using such approaches as partial correlation, multiple regression, discriminant analysis, and factor analysis.
These are outside the scope of this class.

32. How can I calculate correlations?
Excel has a statistical function. It calculates Pearson Product Moment correlations.
SPSS (a statistical software program for personal computers used by graduate students) calculates correlations.

33. Correlation Principles to Remember
For each individual in the research, there must be at least two measures, or it will be impossible to calculate a correlation.

34. Correlation Principles to Remember
A correlation may be statistically significant (it didn’t happen by chance) but be weak or low which means it is nothing to get excited about. It has no practical significance.

35. More Principles to Remember
A correlation is reported as r such as r=.36.

36. More Principles to Remember
The statistical probability is reported as p.
Some researchers report the probability of the correlation happening by chance was p>.05 (more than 5 out of 100) or p<.05 (less than 5 out of 100) – we hope for the later as researchers
Other researchers report the actual probability; p=.03
The first approach was used before the age of computers
Either approach is acceptable.

37. More Principles to Remember
In reporting correlations in research reports you report both the r value and the p.