Simple Correlations 



The simple correlation coefficients were determined from the sample 

 n ■ 32o Each simple correlation coefficient was tested for significance 

 using the standard tables at 30 degrees of freedom. The results are shown 

 in table 1, One asterisk indicates that the sample value exceeds the table 

 value at the 5-percent level of significancej 2 asterisks, at the 1-percent 

 level J and 3 asterisks, at the 0,1-percent level. 



Multiple Correlations 



The multiple correlations vary in degrees of freedom, depending on the 

 number of variables included. In general, degrees of freedom " n - p - 1, 

 •vrfiere p is the number of independent variables included. The data are 

 tabulated in tables 2 to 5 inclusive. 



Discussion of Tests for Significance 



The testing of either simple or multiple correlation coefficients 

 using the standard tables and levels of significance is always a test of 

 the null hypothesis that the true correlation in the population is exactly 

 zero. Hence it is frequently observed that "significant" correlations do 

 not always indicate a strong association. Another measure of the strength 

 of the association is the square of the correlation coefficient, which 

 rather roughly expresses the percent variability in the dependent variable 

 associated with the independent variable (or variables). For example, the 

 simple correlation between water insoluble matter and Suitability Factor 

 is -0,1jO86 significantly different from zero at the 5-percent level. Yet, 

 i^ X 100 « 16,7 percent of the variability in Suitability Factor is associ- 

 ated with water insoluble matter leaving 83,3 percent still to be accounted 

 for. The value of r^ or (r2) therefore should always be kept in mind when 

 interpreting the significance of correlation coefficients. 



Analysis of Variance 



The analysis of variance was applied to the information on history of 

 samples, to determine what affect these factors had on sample variability. 

 The technique used was that of a single classification. The data were not 

 extensive enough to allow a cross-classification of areas, processes, and 

 dates. No attempt was made to evaluate the factor plant because so many 

 plants fere represented by only one sample. These data are tabulated in 

 tables 6 to 9, 



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