In scatter diagram one variable is measured on the x

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Unformatted text preview: h by means of dot marks. If plotted points do not show any trend, two variables are not correlated. If the trend shows upward rising movement, correlation is positive. If the trend is downward sloping, correlation is negative. Karl Pearson’s Co-Efficient of Correlation Karl Pearson’s Co-Efficient of Correlation is a mathematical method for measuring correlation. Karl Pearson developed the correlation from the covariance between two sets of variables. Karl Pearson’s Co-Efficient of Correlation is denoted by symbol r. The formula for obtaining Karl Pearson’s Co-Efficient of Correlation is: Direct method r Covariance between x and y SD, x SDy Sikkim Manipal University Page No. 205 Research Methodology Unit 11 xy / N - (x/N X y/N) Covariance between x and y = SDx = standard deviation of x series= (x2 / N) - (x/N) 2 SDy = standard deviation of y series= (y2 / N) - (y/N) 2 Shortcut Method using Assumed Mean If short cut method is used using assumed mean, the formula for obtaining Karl Pearson’s Co-Efficient of Correlation is: Covariance between x and y = dxdy / N - (dx/N X dy/N) SDx = (dx2 / N) - (dx /N) 2 SDy = (dy2 / N) - (dy /N) 2 r dxdy / N (dx / N x dy / N (dx 2 / N) - (dx / N) 2 (dy 2 / N) - (dy / N) 2 Steps in calculating Karl Pearson’s Correlation Coefficient using Shortcut Method Assume means of x and y series Take deviations of x and y series from assumed mean and get dx and dy Square the dx and dy and find the sum of squares and get dx2 and dy2. Multiply the corresponding deviations of x and y series and total the products to get dxdy. If the deviations are taken from the arithmetic mean dx = 0 and dy =0 and the formula becomes r Sikkim Manipal University dxdy dx 2 dy 2 Page No. 206 Research Methodology Unit 11 Shortcut Method using Arithmetic Mean If short cut method is used using actual mean, the formula for obtaining Karl Pearson’s Co-Efficient of Correlation is: r dx dy dx 2 dy 2 Interpreting Co-Efficient of Correlation The Co-Efficient of Correlation measures the correlation between two variables. The value of Co-Efficient of Correlation always lies between +1 and –1. It can be interpreted in the following ways. If the value of Co-Efficient of Correlation r is...
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