# Advancements in Data Analysis for the Work-Sampling Method
## 4 Upgrade of the Analysis of Work-Sampling Results  
We usually report the results of work-sampling study observations in the form of percentages of individual activities (or grouped) by hours, days, and work shifts [27]. We also calculate the achieved accuracy of the results and their control limits [28]. Many unplanned losses can be caused by certain superficially insignificant events, which in turn trigger new events in a chain, leading to extensive time losses. Since the work-sampling method gives us an insight into the activity proportions at the finest level in the workday hours, we can consider using the data from the activity plot by hour and comparing them with each other to identify possible correlations. The most used measure of the linear relationship between two quantitative variables (two sets of data) is Pearson's correlation coefficient \(r\), which assumes at least one interval type of the two variables analyzed and a linear relationship between the variables. The coefficient can assume values between \(-1\) and \(1\). [PERSON]'s correlation coefficient answers two questions, namely:  
1. Is there a linear relationship between the variables at all? and
2. How strong is the linear relationship between the variables? When we examine the existence of a linear relationship, we speak of two types of relationships. A positive correlation exists when the values of the first (\(x\)) and second (\(y\)) variables are high or low. In this case, the coefficient is positive and close to \(1\). If one variable changes, the other variable also changes in the same direction. A negative correlation exists if the values of the first (\(x\)) variable are high and the values of the second (\(y\)) variable are low or vice versa. The coefficient is then negative and close to \(-1\). To determine the strength of the interdependence between the activities, we use a modified coefficient value scale, which is presented above in Table 1.  
It should also be emphasized that [PERSON]'s correlation coefficient indicates the relationship between two variables, but not the influence of one variable on another. Therefore, the judgment of the analyst is necessary in accordance with their knowledge of the performance of the observed activities and the possible causes of the correlation. Therefore, we calculate the correlations between the percentages of all activities by hour and find the correlation coefficient for all possible pairs within an \(8\) h work shift. A sample size \(n=8\), values of pairs of variables are as follows: \((x_{1},y_{1})\), \(\ldots\), \((x_{8},y_{8})\). \begin{table}
\begin{tabular}{c c} \hline
**Coefficient Value \(r\)** & **Strength of Interdependence** \\ \hline
0.00 & None \\
0.01–0.19 & Very weak (negligible) \\
0.20–0.39 & Weak \\
0.40–0.69 & Moderate \\
0.70–0.89 & Strong \\
0.90–0.99 & Very strong \\
1.00 & Perfect (functional) \\ \hline \end{tabular}
\end{table} 
Table 1: Strength of interdependence according to the value of the correlation coefficient. Correlation value equation, adjusted for \(n=8\) (universal for all studies), is:  
\[r=\frac{8\cdot\Sigma xy-(\Sigma x)\cdot(\Sigma y)}{\sqrt{\left(8\cdot\Sigma x^{2}- \left(\Sigma x\right)^{2}\right)\cdot\left(8\cdot\Sigma y^{2}-\left(\Sigma y \right)^{2}\right)}}, \tag{5}\]  
In our methodological development, we use the \(t\)-test for two independent samples (independent-samples \(t\)-test, two-tailed) and determine whether there are statistically significant differences in the average value of the two samples. It is a standard method to determine whether the correlation coefficient is statistically significant or not [29]. A 95% confidence interval can be defined as the interval spanning from the 2.5 th to the 97.5 th percentiles of the resampled \(r\) values (Figure 1). This corresponds to a significance level of 0.05. The sampling distribution of the studentized Pearson's correlation coefficient follows the Student's \(t\)-distribution with degrees of freedom (DOF) \(n-2\).