🗊Презентация Session 6_Correlation

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Session 6: Correlation Correlation Analysis and Covariance
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Session 6: Correlation Correlation Analysis and Covariance

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Aims Measuring Relationships Scatterplots Covariance Pearson’s Correlation Coefficient Nonparametric measures Spearman’s Rho Kendall’s Tau
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Aims Measuring Relationships Scatterplots Covariance Pearson’s Correlation Coefficient Nonparametric measures Spearman’s Rho Kendall’s Tau

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What is a Correlation? It is a way of measuring the extent to which two variables are related. It measures the pattern of responses across variables.
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What is a Correlation? It is a way of measuring the extent to which two variables are related. It measures the pattern of responses across variables.

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Measuring Relationships We need to see whether as one variable increases, the other increases, decreases or stays the same. This can be done by calculating the Covariance.
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Measuring Relationships We need to see whether as one variable increases, the other increases, decreases or stays the same. This can be done by calculating the Covariance.

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Covariance Calculate the error between the mean and each subject’s score for the first variable (x). Calculate the error between the mean and their score for the second variable (y). Multiply these error values. Add these values and you get the cross product deviations. The covariance is the average cross-product deviations:
Описание слайда:
Covariance Calculate the error between the mean and each subject’s score for the first variable (x). Calculate the error between the mean and their score for the second variable (y). Multiply these error values. Add these values and you get the cross product deviations. The covariance is the average cross-product deviations:

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Problems with Covariance It depends upon the units of measurement. E.g. The Covariance of two variables measured in Miles might be 4.25, but if the same scores are converted to Km, the Covariance is 11. One solution: standardize it! Divide by the standard deviations of both variables. The standardized version of Covariance is known as the Correlation coefficient. It is relatively affected by units of measurement.
Описание слайда:
Problems with Covariance It depends upon the units of measurement. E.g. The Covariance of two variables measured in Miles might be 4.25, but if the same scores are converted to Km, the Covariance is 11. One solution: standardize it! Divide by the standard deviations of both variables. The standardized version of Covariance is known as the Correlation coefficient. It is relatively affected by units of measurement.

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The Correlation Coefficient (Pearson)
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The Correlation Coefficient (Pearson)

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Conducting Correlation Analysis
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Conducting Correlation Analysis

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Things to know about the Correlation It varies between -1 and +1 0 = no relationship Coefficient of determination, By squaring the value of you get the proportion of variance in one variable shared by the other.
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Things to know about the Correlation It varies between -1 and +1 0 = no relationship Coefficient of determination, By squaring the value of you get the proportion of variance in one variable shared by the other.

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Interpretation of Correlation (may vary by discipline) Correlations From 0 to 0.25 (-0.25) = little (weak) or no relationship; From 0.25 to 0.50 (-0.25 to 0.50) = fair (moderate) degree of relationship; From 0.50 to 0.75 (-0.50 to -0.75) = moderate to good (strong) relationship; Greater than 0.75 (or -0.75) = very good to excellent (very strong) relationship.
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Interpretation of Correlation (may vary by discipline) Correlations From 0 to 0.25 (-0.25) = little (weak) or no relationship; From 0.25 to 0.50 (-0.25 to 0.50) = fair (moderate) degree of relationship; From 0.50 to 0.75 (-0.50 to -0.75) = moderate to good (strong) relationship; Greater than 0.75 (or -0.75) = very good to excellent (very strong) relationship.

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Correlation and Causality The third-variable problem: in any correlation, causality between two variables cannot be assumed because there may be other measured or unmeasured variables (i.e., covariates or control variables) affecting the results. Direction of causality: Correlation coefficients say nothing about which variable causes the other to change
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Correlation and Causality The third-variable problem: in any correlation, causality between two variables cannot be assumed because there may be other measured or unmeasured variables (i.e., covariates or control variables) affecting the results. Direction of causality: Correlation coefficients say nothing about which variable causes the other to change

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Partial vs Semi-Partial Correlations
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Partial vs Semi-Partial Correlations

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Nonparametric Correlation Spearman’s Rho, Pearson’s correlation on the ranked data Kendall’s Tau, Better than Spearman’s for small samples
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Nonparametric Correlation Spearman’s Rho, Pearson’s correlation on the ranked data Kendall’s Tau, Better than Spearman’s for small samples

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One-Tailed vs Two-Tailed Tests
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One-Tailed vs Two-Tailed Tests

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Session 6_Correlation, слайд №15
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Session 6_Correlation, слайд №16
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