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Experimental and correlational research Lectures
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Experimental and Correlational Research Study Guide
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Experimental &Correlational Research
Correlations and Measures of Effect Size
Correlation IS NOT Causation
Correlation: Is there an association between two variables?
Causality: Is there an effect?
1. Covariance: Variables have an association.
2. Directionality: Cause precedes effect (in time).
3. Internal Validity: Eliminate alternative explanations.
Scatterplots:
• Direction: positive vs. negative.
• Strength: the more the points are clustered around one (straight) line, the stronger
the relation.
• Shape: linear vs. nonlinear / homogeneous vs. heterogeneous.
Covariance:
= to measure the degree to which two variables vary together.
Covariance provides information on the strength and the direction of the association.
Disadvantage: the range of the covariance is dependent on the unit of measurement of
the variables. Solution: Pearson Product-Moment Correlation Coefficient r.
, Pearson Product-Moment Correlation Coefficient r:
OR
Divide the covariance by the size of the standard deviations.
r also describes the linear relationship between two quantitative variables, and lies
between -1 and 1.
Beware of:
- Non-linear relationships
- Outliers
- Heterogeneous subgroups
- Restriction of range
Alternative Correlation Coefficients
Most commonly used: Pearson r.
But there are more variants, depending on measurement level.
Spearman’s rho
If scores are not ranked yet, convert raw scores into ranks.
Mean and standard deviation:
It is faster to calculate mean and standard deviation for rank orders using the following
formulas than in usual way. Spearman’s rho is a robust alternative to Pearson r in case of
outliers, or weak non-linearity.
, Point-Biserial Correlation:
Describes relationship between quantitative and dichotomous variable. Use Pearson r
formula to calculate Point-Biserial Correlation.
Note: Sign of the correlation (+/-) depends on the way in which 0 and 1 are assigned to
groups.
Dichotomous variable differentiates between groups of observations, each has its own
mean logical that Point-Biserial and t(independent) are related.
Phi Coefficient:
Describes relationship between two dichotomous variables.
Use Person r to calculate Phi.
Also possible to make a 2 X 2 contingency table with two dichotomous variables and use
that to compute phi logical that Phi and Chi-squared are related.
Testing the Significance of r
What do the alternative coefficients say about the correlation in population (p)?
, Testing Difference between Two Independent rs:
Correlation and Significance:
Statistical significance depends on N, r, alpha.
Result:
- Low correlations in large samples become significant.
- High correlations in small samples are not significant.
So, testing only for significance is too limited.
Measures of Effect Size
Measure of effect size:
• r(effect)
• r(squared) (COD, VAF)
• Alternative measures:
o Cohen’s d
o Hedges’s g
r(effect)
Disadvantage
Value of correlation hard to interpret:
- What does r=.60 mean?
- r=.60 does NOT mean relationship twice as large as r=.30.
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