# Innovative Quality Assessment of Pavement Subgrades Using the Glegg Impact Soil Tester
## 3 Verification of the Suitability of CIST Device for Quality Control of Cohesive Soils
In practice, Pearson's correlation coefficients and Spearman's rank correlation coefficients are the most commonly used. Pearson's correlation coefficient is a statistic that measures the linear relationship between a pair of random variables (\(X\),\(Y\)). The formula for the Pearson correlation coefficient \(R(X\),\(Y)\) involves the covariance \(cov(X\),\(Y)\) and standard deviations \(\sigma_{X}\) and \(\sigma_{Y}\), which can be expressed as follows:  
\[R(X,Y)=\frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{\sum_{i=1}^{n}X_{i}Y_{i}-n \overline{XY}}{\sqrt{\left(\sum_{i=1}^{n}X_{i}^{2}-n\overline{X}^{2}\right) \left(\sum_{i=1}^{n}Y_{i}^{2}-n\overline{Y}^{2}\right)}} \tag{5}\]  
where \(n\) is the size of the sample, \(X_{i}\); \(Y_{i}\) represents the individual sample points; \(\overline{X}\) and \(\overline{Y}\) are the sample means. An issue with the Pearson correlation lies in its sensitivity to outliers, potentially resulting in erroneous conclusions depending on the data. Optimal application of the Pearson correlation coefficient requires adherence to specific criteria: the variables are quantitative and normally distributed, the data have no outliers, and the relationship is linear [14]. The coefficient of determination, symbolized as \(R^{2}\), stands as the square of the correlation coefficient. Its range consistently falls between 0 and 1, frequently presented as a percentage. It provides insights into how well the regression model fits the observed data, with a higher \(R^{2}\) indicating more variability. When dealing with small samples, the coefficient of determination is often more reliable than the correlation coefficient [15]. The Spearman rank correlation coefficient is a nonparametric measure of rank correlation, assessing the statistical dependence between the rankings of two variables. Unlike the Pearson correlation, Spearman focuses on monotonic relationships, whether linear or not, making it suitable for variables that are ordinal, not normally distributed, include outliers, or exhibit a non-linear but monotonic relationship. A perfect Spearman correlation of \(+1\) or \(-1\) materializes when each variable constitutes a purely monotonic function of the other; the formula is as follows:  
Figure 3:0  
Figure 3:1 Laboratory-objectified dependence of Clegg CBR values on clay soil moisture. where \(d_{i}\) is the difference between the \(X\)-variable rank and the \(Y\)-variable rank for each pair of data, and \(n\) is the size of the sample [16]. The Spearman correlation coefficient proves to be a superior option when at least one of the following conditions applies: the variables are ordinal, do not adhere to a normal distribution, outliers are present in the data, or the relationship between variables is not linear but exhibits monotonic patterns [14]. Table 1 shows the range of correlation coefficient values (rounded to two decimals) proposed in the literature [17] for the level of correlation. According to the presented facts, we can conclude that there is a very strong (\(R=0.9625\)) correlation dependence (Figure 6) of the \(CBR_{Clegg}\) values [%] on the moisture of fine-grained soils \(w\) [%]. Figure 3:2  
Another hypothesis was to verify whether the CIST device provides a compatible output with the determination of the CBR value according to STN 72 1016 [13]. Since STN 72 1016 yields lower values than the Clegg device CBR determination, correlation relationships of STN 72 1016 CBR values to Clegg CBR values were worked out (Figure 7). From Figure 7, it is evident that the \(CBR_{Clegg}\) values are significantly different from the \(CBR_{STN21016}\) values. On average, they are 1.8-fold higher. Therefore, the \(CBR_{Clegg}\) values cannot be used directly in the pavement construction design.