Correlation coefficient
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This document discusses correlation and the correlation coefficient. It defines correlation as a measure of the relationship between two variables. It explains that the correlation coefficient indicates the magnitude and direction of the relationship as well as the strength of the relationship and percentage of variance explained. Values of the correlation coefficient are interpreted as showing no relationship, a low relationship, or a strong relationship. Conditions for interpreting the correlation coefficient include data forming a linear pattern and equal variances.
Correlation coefficient
- 2. Correlation Measure of relationship between two variables Ex. Grades in English tends to be related with Foreign Language Height and weight
- 3. Nature of Correlation Magnitude/direction of the relationship Strength of the relationship Variance explained Significance of the relationship
- 4. Magnitude of the Relationship Positive relationship – as one variable increases the other variable also increases Ex. academic grades and intelligence Negative relationship – as one variable increases, the other decreases or vice versa Ex. procrastination and motivation Absence of relationship between variables – denoted by .00
- 5. 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
- 6. Variance How much of Y’s is explained/accounted for by X Proportion explained Square of the correlation coefficient value
- 7. 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.
- 8. 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