Report

S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 13: correlation coefficient This week Testing correlation coefficient The interpretation PEARSON Using Excel to calculate correlation coefficient Which test to use Figure 13.1 (p261) The relationship between variables, and not the difference between groups, is being examined. Only two variables are being used The appropriate test statistic to use is the t test for the correlation coefficient Example Quality of Marriage Quality of parent-child relationship 76 81 78 76 76 78 76 78 98 88 76 66 44 67 65 59 87 77 79 85 68 76 77 98 99 98 87 67 78 43 33 23 34 31 51 56 43 44 45 32 33 28 39 31 38 21 27 43 46 41 41 48 56 55 45 68 54 33 Correlation coefficient CORREL() and PEARSON() Same value There is no difference Spearman’s rank correlation coefficient Kendall's tau T test for the significance of the correlation coefficient Step1: A statement of the null and research hypotheses Null hypothesis: there is no relationship between the quality of the marriage and the quality of the relationship between parents and children Research hypothesis: (two-tailed, nondirectional) there is a relationship between the two variables H0 : xy 0 H1 : rxy 0 T test for the significance of the correlation coefficient Step2: setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis 0.05 or 0.01 What does it mean? on any test of the null hypothesis, there is a 5% (1%) chance you will reject it when the null is true when there is no group difference at all. Why not 0.0001? So rigorous in your rejection of false null hypothesis that you may miss a true one; such stringent Type I error rate allows for little leeway T test for the significance of the correlation coefficient Step 3 and 4: select the appropriate test statistics The relationship between variables, and not the difference between groups, is being examined. Only two variables are being used The appropriate test statistic to use is the t test for the correlation coefficient T test for the significance of the correlation coefficient Step5: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic. Table B4 compute the correlation coefficient (r=0.393) Compute df=n-2 (df=27) If obtained value>the critical value reject null hypothesis If obtained value<the critical value accept null hypothesis T test for the significance of the correlation coefficient Step6: compare the obtained value with the critical value obtained value: 0.393 critical value: 0.349 T test for the significance of the correlation coefficient Step 7 and 8: make decisions What could be your decision? And why, how to interpret? obtained value: 0.393 > critical value: 0.349 (level of significance: 0.05) Coefficient of determination is 0.154, indicating that 15.4% of the variance is accounted for and 84.6% of the variance is not. There is a 5% chance that the two variables are not related at all Causes and associations Two variables are related to each other One causes another having a great marriage cannot ensure that the parent-child relationship will be of a high quality as well; The two variables maybe correlated because they share some traits that might make a person a good husband or wife and also a good parent; It’s possible that someone can be a good husband or wife but have a terrible relationship with his/her children. A critique a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be. These examples indicate that the correlation coefficient, as a summary statistic, cannot replace the individual examination of the data. Exercise: S-P267-Q1 n degree of freedom correlation coefficient level tail critical value 20 18 0.567 0.01 one 0.516 80 78 -0.45 0.05 one 0.183 50 48 0.37 0.05 two 0.273