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

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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

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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.