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# Correlation coefficient

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### Correlation coefficient

1. 1. Correlation Coefficient ELESTA1
2. 2. Correlation <ul><li>Measure of relationship between two variables </li></ul><ul><li>Ex. Grades in English tends to be related with Foreign Language </li></ul><ul><li>Height and weight </li></ul>
3. 3. Nature of Correlation <ul><li>Magnitude/direction of the relationship </li></ul><ul><li>Strength of the relationship </li></ul><ul><li>Variance explained </li></ul><ul><li>Significance of the relationship </li></ul>
4. 4. Magnitude of the Relationship <ul><li>Positive relationship – as one variable increases the other variable also increases </li></ul><ul><li>Ex. academic grades and intelligence </li></ul><ul><li>Negative relationship – as one variable increases, the other decreases or vice versa </li></ul><ul><li>Ex. procrastination and motivation </li></ul><ul><li>Absence of relationship between variables – denoted by .00 </li></ul>
5. 5. Strength of Relationship <ul><li>A correlation coefficient is computed for a bivariate distribution using a statistical formula </li></ul>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. 6. Variance <ul><li>How much of Y’s is explained/accounted for by X </li></ul><ul><li>Proportion explained </li></ul><ul><li>Square of the correlation coefficient value </li></ul>
7. 7. Conditions in interpreting r <ul><li>Linear regression – the points in a scatterplot should tend to fall along a straight line </li></ul><ul><li>The size of the r reflects the amount of variance that can be accounted for by a straight line </li></ul><ul><li>Homosedasticity – tendency of the standard deviation (or variances) of the arrays to be equal. </li></ul>
8. 8. Correlational Techniques <ul><li>Pearson Product-Moment correlation – (r) used for interval/ratio sets of variables </li></ul><ul><li>Spearman Rank-order correlation – two sets of data are ordinal </li></ul><ul><li>Phi coefficient – each of the variables is a dichotomy </li></ul>