. Elementary biophysics: selected topics. Biophysics. TREATMENT OF EXPERIMENTAL DATA 23. Fig. 9. A plot of some experimental data (o); their deviations (---) from the mean, y; and their deviations (—-) from a line proposed to fit the data. The extent to which x and y are said to be correlated is given by the extent to which the line is a better representation of the data than is the value y. The criterion for better representation is the ratio of the sum of the squares of the deviation from the line to the sum of the squares of the deviations from the mean, y. The quantitative use of the crite
. Elementary biophysics: selected topics. Biophysics. TREATMENT OF EXPERIMENTAL DATA 23. Fig. 9. A plot of some experimental data (o); their deviations (---) from the mean, y; and their deviations (—-) from a line proposed to fit the data. The extent to which x and y are said to be correlated is given by the extent to which the line is a better representation of the data than is the value y. The criterion for better representation is the ratio of the sum of the squares of the deviation from the line to the sum of the squares of the deviations from the mean, y. The quantitative use of the criterion is given in the text. Consider the ratio of these two variations: E(y — Vth)2 Z(y - y)2 If there were a perfect correlation between y and x—that is to say, if the line fit the data perfectly—the numerator would be zero. If the line is less than a perfect fit, the numerator becomes increasingly large until, finally, if there is absolutely no connection between y and x, there will be as much variation around the line as around the mean value of y. Then the ratio will be unity. Thus the values of this ratio vary from zero for a perfect correlation to unity for completely unrelated things. Since we wish to speak of the extent to which things are "co-related," the statisticians have chosen to use one minus this ratio as the index of correlation, R. Then perfect relation is unity and complete lack of relation is zero. R 1 E(y - V)2 There is one more complication to be taken care of. The way we have chosen the relationship index, it is always positive. This presents a problem, because it is possible for things to be negatively connected, in that an increase in one variable correlates with a decrease in the Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Epstein, Herman T. (Herman Theo
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