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- A correlation coefficient is a numerical index that indicates the strength and direction of a relationship between two variables.
- There are a number of different correlation coefficients. In general, the most common and most useful by far is the Pearson correlation coefficient. The phi, point biserial and Spearman's rho correlation coefficients are all merely variants of it.
- It is good practice to draw a scattergram as this represents the data included in a correlation coefficient. Not only will this give you a visual representation of the relationship but it also helps identify a number of problems such as a curved relationship or the presence of outliers. The Pearson correlation coefficient assumes a straight-line relationship between two variables. It is misleading if a curved relationship exists between the two variables. Outliers are extreme and unusual scores that distort the size of the correlation coefficient. Remedies include examining the relationship if the outliers are omitted. Alternatively, a Spearman correlation coefficient is less affected by outliers, and so one could compare the size of the Spearman correlation for the same data.
- A correlation coefficient is a numerical measure or index of the amount of association between two sets of scores. It ranges in size from a maximum of +1.00 through 0.00 to -1.00.
- The '+' sign indicates a positive correlation: that is, the scores on one variable increase as the scores on the other variable increase. A '-' sign indicates a negative correlation: that is, as the scores on one variable increase, the scores on the other variable decrease.
- A correlation of 1.00 indicates a perfect association between the two variables. In other words, a scattergram of the two variables will show that
*all*of the points fit a straight line exactly. A value of 0.00 indicates that the points of the scattergram are essentially scattered randomly around any straight line drawn through the data or are arranged in a curvilinear manner. A correlation coefficient of -0.5 would indicate a moderate negative relationship between the two variables. - Spearman's rho is the Pearson correlation coefficient applied to the scores after they have been ranked from the smallest to the largest on the two variables separately. It is used when the basic assumptions of the Pearson correlation coefficient have not been met by the data – that is especially when the scores are markedly asymmetrical (skewed) on a variable.
- Since correlation coefficients are usually based on samples of data, it is usual to include a statement of the statistical significance of the correlation coefficient. Statistical significance is a statement of the likelihood of obtaining a particular correlation coefficient for a sample of data
*if*there is no correlation (i.e. a correlation of 0.00) in the population from which the sample was drawn. SPSS can give statistical significance as an exact value or as one of the conventional critical significance levels (e.g. 0.05 and 0.01).