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7.2 Correlation Coefficient 7.2.1 Population correlation coefficient
Pearson’s product-moment linear correlation coefficient:
The mean of “product of the two standardized variables”
---- simple correlation coefficient
-- covariance between X and Y
Pearson’s product moment sample correlation coefficient r 7.2.2 Sample correlation coefficient
A measurement of linear relationship: 1) Whether there is a correlation If the correlation coefficient is 0 or not big enough -- no correlation 2) If correlation coefficient is big enough The direction of correlation? -- positive or negative The strength of correlation? high or not? -- Is the absolute value big enough? Complete correlation : +1 or -1,
Example 7.3 Calculate the correlation coefficient between the heights of father and son.
n pairs of observations, (x 1 ,y 1 ), …, (x n ,y n )
Example 7.6 An etiology study on liver cancer has collected data on liver-cancer-specific death rate and the relative content of aflatoxin in certain food for 10 Counties. Putting the ranks into the formula of Spearman’s correlation coefficient
Table 9 Critical value for Spearman’s rank correlation coefficient 7.4.2 Hypothesis test for (1) Checking a special table (Table 9) P <0.02 and it is significant