Correlation. Introduction Two meanings of correlation –Research design –Statistical Relationship –Scatterplots.

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Correlation

Introduction Two meanings of correlation –Research design –Statistical Relationship –Scatterplots

Relationship –Scatterplots Quantification of relationship –Correlation coefficient range +1.0 to - 1.0

r =.20

r =.50

r =.80

r = -.10

r = -.60

r = -.90

Pearson Product Moment Correlation

Relationship –Scatterplots Quantification of relationship –Correlation coefficient range +1.0 to - 1.0 –Pearson Product Moment Correlation

Covariance

Assumptions when using Pearson: 1.The relationship is linear. 2.The scale of measurement is interval or ratio 3.That there is a bivariate normal distribution - X and Y scores are normally distributed in the population. 4.Homogeneity of variance - at each X score Y scores in the population are normally distributed and vice versa.

Significance of correlations

Interpreting correlations r2r2 –proportional reduction in error

Effect size and Power Cohen –.10 small effect size –.30 medium effect size –.50 large effect size To get power of.80, number of participants required are: –783 for small effect size – 85 for medium effect size – 28for large effect size

Potential Problems 1.Correlation and causality 2.Restricted range 3.Outliers.

Alternative Correlational Techniques Point - biserial coefficient r pb The Phi coefficient - φ Spearman Rank Order Correlation

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