Correlation coefficient confidence levels

Correlation coefficient confidence limits estimates for selected confidence level are ... 

Data Analysis Because of the danger of false conclusions if only one or two parameters were evaluated, it was deemed better to correlate every parameter with all the others, and to assemble the results in a triangular matrix, so that trends would become more apparent. The program CORREL described in Section 5.2 retains the sign of the correlation coefficient (positive or negative slope) and combines this with a confidence level (probability p of obtaining such a correlation by chance alone). 

A Worksheet for computing the confidence limits for the correlation coefficient at user selected confidence levels. 

In this chapter as a continuation of Chapters 58 and 59 [1, 2], the confidence limits for the correlation coefficient are calculated for a user-selected confidence level. The user selects the test correlation coefficient, the number of samples in the calibration set, and the confidence level. A MathCad Worksheet ( MathSoft Engineering Education, Inc., 101 Main Street, Cambridge, MA 02142-1521) is used to calculate the z-statistic for the lower and upper limits and computes the appropriate correlation for the z-statistic. The upper and lower confidence limits are displayed. The Worksheet also contains the tabular calculations for any set of correlation coefficients (given as p). A graphic showing the general case entered for the table is also displayed. 

The following description and corresponding MathCad Worksheet allows the user to test if two correlation coefficients are significantly different based on the number of sample pairs (N) used to compute each correlation. For the Worksheet, the user enters the confidence level for the test (e.g., 0.95), two comparative correlation coefficients, r, and r2, and the respective number of paired (X, Y) samples as N and N2. The desired confidence level is entered and the corresponding z statistic and hypothesis test is performed. A Test result of 0 indicates a significant difference between the correlation coefficients a Test result of 1 indicates no significant difference in the correlation coefficients at the selected confidence level. 

As can be seen from Table 1, the estimated coefficients b[0] are not equal to zero for different samples, whereas the estimated coefficients b[l] are close to 1 within confidence interval. That means that coefficients b[0] estimated for different points of the territory are generalized relative characteristics of elements abundance at the chosen sampling points. Statistical analysis has confirmed that hypotheses Hi and H2 are true with 95% confidence level for the data obtained by any of the analytical groups involved. This conclusion allowed us to verify hypothesis H3 considering that the estimated average variances of the correlation equation (1) are homogeneous for all snow samples in each analytical group. Hypothesis H3... 

He found a correlation coefficient of r=0.85 and concluded that only four NH3 determinations are necessary to determine the odour level with a confidence of 90 percent. 

As noted earlier, the choice of species for experimentation is critical due to anatomical differences and it may also reflect species, as well as individual, differences in the expression/activity of transporter and metabolic proteins [43, 44], Since the fraction absorbed across buccal mucosa in vivo is not established for many compounds in different species including humans, the potential existence of a correlation between in vitro permeability coefficients in freshly isolated pig, dog, monkey, and human buccal mucosa was investigated (Figure 7.3). The correlation coefficient obtained for porcine and canine tissue was poor (0.65 and 0.67, respectively, at the 95% confidence level). Results for relatively high permeability compounds in porcine tissue resemble those previously reported where permeability coefficients were by an order of magnitude... 

In this equation, n denotes the number of observations (i.e., data points), r is the correlation coefficient, i is the standard deviation of the residuals, F is the value of the Fisher test for the significance of the equation, and the P-value denotes the statistical significance level. The values in parenthesis of this QSPR equation indicate the 95% confidence inferval of fhe estimated coefficients. From the statistical parameters it can be derived that this QSPR model is significant at the 99% confidence level. 

A high correlation coefficient ( r = 0.903, 99 percent confidence level) was found between Y c and polar group concentration ( COO) and relatively high correlation coefficients were obtained between Yc and the metallic elements (Cr and Ni), but carbon (main component of oil), oxygen, hydration degree (n) and covering rate W showed low correlation coefficient. In Fig. 11, Yc versus the polar group concentration is presented. 

Note Problems 3 through 7 and 10 through 14 are, m part, given at two levels of sophistication and expectation The best" answers involve doing the part marked with an asterisk ( ) instead of the immediately preceding part The parts with an involve the use of the method of least squares, correlation coefficients, and confidence intervals for the slopes and intercepts, the preceding parts do not... 

The regression coefficient (r2) for this relationship was 0.8685. The significance of the calculated F(1/3) = 22.2 can be ascertained by consulting tables of F values. From such a table, it is found that the F(13)a0 025 distribution is 17.4. Because the F(13) of 22.2 is greater than 17.4, it can be assumed that the equation is significant at the 2.5% confidence level. This relationship showed that the kinetic rate increases as ELUMO increases. A set of aliphatic compounds was used for the correlation between ELUMO as molecular descriptor and activation energy as a predictive molecular descriptor. The dataset of... 

---