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Correlation

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

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

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r =.20

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r =.50

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r =.80

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r = -.10

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r = -.60

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r = -.90

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Pearson Product Moment Correlation

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

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Covariance

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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.

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Significance of correlations

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Interpreting correlations r2r2 –proportional reduction in error

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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

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

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

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