correlational research
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Correlational Research. 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. Correlational Research. - PowerPoint PPT PresentationTRANSCRIPT
Correlational Research
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.
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?
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.
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.
Warning!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)
Where does the data come from for correlational research? Surveys Scores on various tests or rating scales Demographic information Judges or expert ratings
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
Terminology
“Predictor” variable – the variable(s) that are believed to predict the outcome. Could be called an independent variable
Terminology
“Criterion” variable – the variable to be predicted, the outcome Could be called the dependent variable
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)?
Correlational research in MI
Research Q? Variables?
Dependent and independent? Target Measure?
Gardner’s MI test BGFL test
Correlation coefficient
Needed to show the Existence Degree Direction
of the correlation
Usually expressed as…
1. r (simple) or R (multiple) [ -1.00 to 0 to +1.00]
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 -1.00 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
Interpretation of the Strength of Correlations
.00 - .20 – Very Weak .21 - .40 – Weak .41 - .60 – Moderate .61 - .80 – Strong .81 – 1.00 - Very Strong
Different statisticians may have similar but slightly different scales.
Different statisticians may have similar but slightly different scales.
Correlations
Scatter plots are often used to depict correlations
0
1000
2000
3000
4000
5000
6000
100 150 200 250 300 350 400
Weight
Cal
orie
s pe
r da
y
This chart shows a strong positive correlation
This chart shows a strong positive correlation
Correlations
Scatter plots are often used to depict correlations
0
20
40
60
80
100
120
140
160
100 150 200 250 300 350 400
Weight
Min
utes
of
Exe
rcis
e pe
r da
y This chart shows a strong negative correlation
This chart shows a strong negative correlation
Correlations
Scatter plots are often used to depict correlations
05
1015202530354045
100 150 200 250 300 350 400
Weight
Mil
es f
rom
Kri
spy
Cre
me
This chart shows virtually no correlation
This chart shows virtually no correlation
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.
Which correlation to use?
Pearson Product Moment
Kendall tau
Biserial Correlatio
n
Spearman rho
Phi correlation
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.
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
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.
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
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.
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
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
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
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
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
Correlation TablePredictor Variable Criterion Variable Correlation to Use
Interval (Continuous) Interval (Continuous) Pearson
Real Dichotomy Interval (Continuous) Point Biserial
Artificial Dichotomy Interval (Continuous) Biserial
Real Dichotomy Real Dichotomy Phi
Artificial Dichotomy Artificial Dichotomy Tetrachoric
Ranking Ranking Spearman rho for 20 or more rankings
Ranking Ranking Kendall’s tau for less than 20 rankings
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.
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.
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.
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.
More Principles to Remember
A correlation is reported as r such as r=.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.
More Principles to Remember
In reporting correlations in research reports you report both the r value and the p.