1. ©aSup - 2009   Menghitung Korelasi Bivariat menggunakan SPSS Pearson's correlation coefficient, Spearman's rho, and Kendall's tau-b

2. ©aSup - 2009   The Bivariate Correlations  …procedure computes the pair-wise associations for a set of variables and displays the results in a matrix. It is useful for determining the strength and direction of the association between two scale or ordinal variables.

3. ©aSup - 2009    Pairwise: When computing a measure of association between two variables in a larger set, cases are included in the computation when the two variables have non-missing values, irrespective of the values of the other variables in the set.  Scale: A variable can be treated as scale when its values represent ordered categories with a meaningful metric, so that distance comparisons between values are appropriate.  Ordinal: A variable can be treated as ordinal when its values represent categories with some intrinsic ranking; for example, levels of service satisfaction from highly dissatisfied to highly satisfied.

4. ©aSup - 2009   Correlation  … measure how variables or rank orders are related.  Before calculating a correlation coefficient, screen your data for outliers (which can cause misleading results) and evidence of a linear relationship.

5. ©aSup - 2009    Pearson's correlation coefficient is a measure of linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson's correlation coefficient is not an appropriate statistic for measuring their association.  Pearson correlation coefficients assume the data are normally distributed.

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7.   To Obtain Bivariate Correlations From the menus choose: Analyze Correlate Bivariate...  Select two or more numeric variables.

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9.   The following options are also available:  Correlation Coefficients. ○ For quantitative, normally distributed variables, choose the Pearson correlation coefficient. ○ If your data are not normally distributed or have ordered categories, choose Kendall's tau-b or Spearman, which measure the association between rank orders.

10. ©aSup - 2009   The following options are also available:  Test of Significance. You can select two-tailed or one-tailed probabilities. If the direction of association is known in advance, select One-tailed. Otherwise, select Two-tailed.

11. ©aSup - 2009   The following options are also available:  Flag significant correlations. Correlation coefficients significant at the 0.05 level are identified with a single asterisk, and those significant at the 0.01 level are identified with two asterisks.

12. ©aSup - 2009   Result: Pearson’s correlation

13. ©aSup - 2009   Result: Spearman’s rho correlation

14. ©aSup - 2009   The correlations table displays Pearson correlation coefficients, significance values, and the number of cases with non-missing values.

15. ©aSup - 2009   Pearson correlation coefficients  The Pearson correlation coefficient is a measure of linear association between two variables.  The values of the correlation coefficient range from 0 to 1.  The sign of the correlation coefficient indicates the direction of the relationship (positive or negative).

16. ©aSup - 2009   Pearson correlation coefficients  The absolute value of the correlation coefficient indicates the strength, with larger absolute values indicating stronger relationships.  The correlation coefficients on the main diagonal are always 1.0, because each variable has a perfect positive linear relationship with itself.  Correlations above the main diagonal are a mirror image of those below.

17. ©aSup - 2009   In this example, the correlation coefficient for Arimatika and Loneliness is 0.837. Since 0.837 is relatively close to 1, this indicates that Arimatika and Loneliness are positively correlated.

18. ©aSup - 2009   Significance Values  The significance level (or p-value) is the probability of obtaining results as extreme as the one observed.  If the significance level is very small (less than 0.05) then the correlation is significant and the two variables are linearly related.  If the significance level is relatively large (for example, 0.50) then the correlation is not significant and the two variables are not linearly related.

19. ©aSup - 2009    The significance level or p-value is 0.000 which indicates a very low significance.  The small significance level indicates that Aritmatika and Loneliness are significantly positively correlated.

20. ©aSup - 2009   Significance Values  The significance level (or p-value) is the probability of obtaining results as extreme as the one observed.  If the significance level is very small (less than 0.05) then the correlation is significant and the two variables are linearly related.  If the significance level is relatively large (for example, 0.50) then the correlation is not significant and the two variables are not linearly related.

21. ©aSup - 2009   Significance Values As Aritmatika increases Loneliness also increases. And as Aritmatika decreases, Loneliness also decreases.

22. ©aSup - 2009    N is the number of cases with non-missing values.  In this table, the number of cases with non- missing values for both Aritmatika and Loneliness is 23.

23. ©aSup - 2009   Notice  Even if the correlation between two variables is not significant, the variables may be correlated but the relationship is not linear.  So, we use Spearman’s rho or Kendall Tau-b