S 519 Evaluation of Information Systems Social Statistics

S 519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 13: correlation coefficient

This week l l Testing correlation coefficient The interpretation PEARSON Using Excel to calculate correlation coefficient

Which test to use l l Figure 13. 1 (p 261) 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 parent-child Quality of Marriage relationship 76 43 81 33 78 23 76 34 76 31 78 51 76 56 78 43 98 44 88 45 76 32 66 33 44 28 67 39 65 31 59 38 87 21 77 27 79 43 85 46 68 41 76 41 77 48 98 56 99 55 98 45 87 68 67 54 78 33

Correlation coefficient l CORREL() and PEARSON() l l Same value There is no difference Spearman’s rank correlation coefficient Kendall's tau

T test for the significance of the correlation coefficient l Step 1: A statement of the null and research hypotheses l l 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

T test for the significance of the correlation coefficient l Step 2: setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis l l 0. 05 or 0. 01 What does it mean? l l 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? l 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 l Step 3 and 4: select the appropriate test statistics l l l 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 l Step 5: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic. l l l Table B 4 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 l Step 6: compare the obtained value with the critical value l l obtained value: 0. 393 critical value: 0. 349

T test for the significance of the correlation coefficient l l Step 7 and 8: make decisions What could be your decision? And why, how to interpret? l l l 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 l Two variables are related to each other One causes another l l l having a great marriage cannot ensure that the parentchild 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 l l 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-P 267 -Q 1 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