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# Correlation coefficient

## on Jan 18, 2011

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## Correlation coefficientPresentation Transcript

• Correlation Coefficient ELESTA1
• Correlation
• Measure of relationship between two variables
• Ex. Grades in English tends to be related with Foreign Language
• Height and weight
• Nature of Correlation
• Magnitude/direction of the relationship
• Strength of the relationship
• Variance explained
• Significance of the relationship
• Magnitude of the Relationship
• Positive relationship – as one variable increases the other variable also increases
• Negative relationship – as one variable increases, the other decreases or vice versa
• Ex. procrastination and motivation
• Absence of relationship between variables – denoted by .00
• Strength of Relationship
• A correlation coefficient is computed for a bivariate distribution using a statistical formula
Correlation Coefficient Value Interpretation 0.80 – 1.00 Very strong relationship 0.6 – 0.79 Strong relationship 0.40 – 0.59 Substantial/marked relationship 0.2 – 0.39 Low relationship 0.00 – 0.19 Negligible relationship
• Variance
• How much of Y’s is explained/accounted for by X
• Proportion explained
• Square of the correlation coefficient value
• Conditions in interpreting r
• Linear regression – the points in a scatterplot should tend to fall along a straight line
• The size of the r reflects the amount of variance that can be accounted for by a straight line
• Homosedasticity – tendency of the standard deviation (or variances) of the arrays to be equal.
• Correlational Techniques
• Pearson Product-Moment correlation – (r) used for interval/ratio sets of variables
• Spearman Rank-order correlation – two sets of data are ordinal
• Phi coefficient – each of the variables is a dichotomy