TAILIEUCHUNG - Statistical Description of Data part 6

Norusis, . 1982, SPSS Introductory Guide: Basic Statistics and Operations; and 1985, SPSSX Advanced Statistics Guide (New York: McGraw-Hill). Fano, . 1961, Transmission of Information (New York: Wiley and MIT Press), Chapter 2 | 636 Chapter 14. Statistical Description of Data Norusis . 1982 SPSS Introductory Guide Basic Statistics and Operations and 1985 SPSS-X Advanced Statistics Guide New York McGraw-Hill . Fano . 1961 Transmission of Information New York Wiley and MIT Press Chapter 2. LinearCorrelation g 2. o Z co cr q 2 o We next turn to measures of association between variables that are ordinal or continuous rather than nominal. Most widely used is the linear correlation coefficient. For pairs of quantities xi yfi i 1 . . N the linear correlation i coefficient r also called the product-moment correlation coefficient or PearsonS o 8 r is given by the formula S 3 3 3 P Xi - x yi - y r i . S JUxi -x 2 JE yi - v ssl V i V i d o where as usual X is the mean of the xi s y is the mean of the yi s. I The value of r lies between -1 and 1 inclusive. It takes on a value of 1 termed - S complete positive correlation when the data points lie on a perfect straight line with positive slope with x and y increasing together. The value 1 holds independent of the magnitude of the slope. If the data points lie on a perfect straight line with negative slope y decreasing as x increases then r has the value -1 this is called a 19 complete negative correlation. A value of r near zero indicates that the variables 1 x and y are uncorrelated. e P z When a correlation is known to be significant r is one conventional way of summarizing its strength. In fact the value of r can be translated into a statement about what residuals root mean square deviations are to be expected if the data are z 5 fitted to a straight line by the least-squares method see especially equations j - . Unfortunately r is a rather poor statistic for deciding whether 8 an observed correlation is statistically significant and or whether one observed 3 3 correlation is significantly stronger than another. The reason is that r is ignorant of t a the individual distributions of x and y so there is no .

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