2.  Once you know the correlation coefficient for your sample, you might want to determine whether this correlation occurred by chance.  Or does the relationship you found in your sample really exist in the population or were your results a fluke?  Or in the case of a t-test, did the difference between the two means in your sample occurred by chance and not really exist in your population. 2

3.  If you set your confidence level at 0.05  Let’s assume that you collected your data with 100 different samples from the same population and calculate correlation each time. So, the maximum of 5 out of 100 samples might show a relationship when there really was no relationship (r=0) 3

4.  Any relationship should be assessed for its significance as well as its strength  Pearson correlation measures the strength of a relationship between two continuous variables  Correlation coefficient: r  Coefficient of determination: r 2  Significance is measured by t-test with p=0.05 (which tells how unlikely a given correlation coefficient, r, will occur given no relationship in the population)  The smaller the p-level, the more significant the relationship  The larger the correlation, the stronger the relationship 4

5.  You have a sample from a population  Whether you observed statistic for the sample is likely to be observed given some assumption of the corresponding population parameter. 5

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7.  When the test is against the null hypothesis: r xy = 0.0  What is the likelihood of drawing a sample with r xy ­ =0.0?  The sampling distribution of r is  approximately normal (but bounded at -1.0 and +1.0) when N is large  and distributes t when N is small. 7

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9. Quality of Marriage Quality of parent-child relationship 7643 8133 7823 7634 7631 7851 7656 7843 9844 8845 7632 6633 4428 6739 6531 5938 8721 7727 7943 8546 6841 7641 7748 9856 9955 9845 8768 6754 7833 9

10.  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 10

11.  CORREL() and PEARSON() 11 r=0.393

12.  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 12

13.  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 13

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15.  Step5: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic.  From t table, the critical value=2.052 (two tailed, 0.05, df=27)  T=2.22  If obtained value>the critical value  reject null hypothesis  If obtained value<the critical value  accept null hypothesis 15

16.  Step6: compare the obtained value with the critical value  T Distribution Critical Values Table (Critical value r table)  compute the correlation coefficient (r=0.393)  Compute df =n-2 (df=27)  obtained value: 0.393  critical value: 0.367 http://www.gifted.uconn.edu/siegle/research/correlation/corrc hrt.htm 16

17.  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 17

18.  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. 18

19.  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. 19

20.  To investigate the effect of a new hay fever drug on driving skills, a researcher studies 24 individuals with hay fever: 12 who have been taking the drug and 12 who have not. All participants then entered a simulator and were given a driving test which assigned a score to each driver as summarized in the below figure.  Explain whether this drug has an effect or not? 20