# Revisiting Problem-Solution Co-Evolution in the Context of Team Conceptual Design Activity
## 3 Results
### Relationship between ASE and Problem/Solution Exploration  
The first set of hypotheses concerns the correlation between performing ASE state-transitions and exploring the problem and the solution space. It was assumed that the intensity of performing analysis is positively correlated with the intensity of problem space exploration, whereas the intensities of performing synthesis and evaluation are positively correlated with the intensity of solution space exploration. For this reason, simply counting the instances of ASE within the problem space vs. ASE in the solution space is not sufficient for testing the hypotheses. Namely, it is evident in the data (as reported in [43]) that the total number of all three types of state transitions was higher within the solution space than in the problem space. However, this data does not provide insight into the  
Figure 4: Triangular proportion visualisation of ASE transitions and the associated proportions of problem-related verbalisations throughout ideation (I1-I2-I3) and concept review (CR1-CR2-CR3) activities for all four teams.  
relationship that might exist between a particular type of state transition and problem vs. solution space exploration. Hence, additional analyses were made as described hereafter.  
First, the data points sampled from all fragments and teams were mapped within a single triangular visualisation of ASE proportions across the activities and the associated proportions of problem-related verbalisations (Figure 5). Such representation gives an overview of the problem space focus that was associated with different proportions of ASE state transitions. Ideation activity fragments (diamonds in Figure 5) are associated with higher proportions of problem-related verbalisations and spread towards the synthesis corner of the triangle when compared to the concept review fragments (circles in Figure 5), which gravitate towards the analysis/evaluation side and exhibit higher proportions of solution-related verbalisations.  
Given the hypothesis H1a, one would assume that the closer the markers are to the analysis corner, the more problem-focused transitions they should exhibit. Moreover, according to the hypotheses H1b and H1c, the closer the markers are to the synthesis/evaluation side, the more solution-focused transitions they should exhibit. This initial, qualitative analysis shows that this is not necessarily the case. In fact, markers closer to synthesis describe higher proportions of problem-related verbalisations than those closer to analysis and vice versa. Hence, in order to further investigate the assumed relationships, the hypothesised correlations were tested using [PERSON]'s rank-order correlation coefficient as a measure of correlation.  
The reason for using [PERSON]'s instead of [PERSON]'s correlation was that it does not assume the normality, the homoscedasticity, or the linear relationship of the measurement data. Namely, the data were first tested for normality using the Shapiro-Wilk test [89], and the measures of problem and solution proportions were rejected concerning the normality assumption at the significance level of 0.05. Moreover, the scatter plots of the proportions (see Table 3) revealed issues concerning the homoscedasticity and linear relationship. Hence, [PERSON]'s rank-order correlation coefficient was selected as the most appropriate measure of the correlation between the proportions of ASE state transitions and the associated proportions of problem/solution-related transitions.  
One important note is that the following analysis assumes that the observations (measured proportions) are independent. This is an important and debatable assumption, given that the data for each team is sampled from a series of subsequent fragments of two activities. Hence, one could argue that each observed fragment depends on the prior one. However, given the Markov processes  
Figure 5: Triangular proportion visualisation of ASE transitions and the associated proportions of problem-related verbalisations sampled from sessions of all four teams.