#### 6.2.2. Comparison between Two Participants for Poster 7

Here, we show first in

Figure 8 the results for poster 7 for all participants and then we compare more finely for participants 2 and 5. Observe from

Figure 8a that the AOIs more visited by all participants are AOI5 (results section), AOI6 (conclusions section), and AOI3 (method section), although the most visited area depends on the participant. The majority of participants prefer, or visit it often, AOI5 (results section), others AOI6 (conclusions section), and finally others AOI3 (method section).

Figure 8b shows the main measures of the channel for each participant, some of them are similar for several participants, although from

Figure 8c,d, we can conclude that the exploration strategy can be in general different for each participant.

Next,

Table 3 shows the transition probabilities of the participants 2 and 5 for the poster with more areas of interest, poster 7 with six AOIs. See

Figure 9 for an illustration of the gaze channel for participant 5. Observe that, in

Table 3, the values of

${p}_{ii}$ are the highest transition probabilities, which is consistent with the above transition matrix analysis. This is similar to

The tempest painting example presented in [

44]. As observed before, this means that, before switching to another AOI, the observer firstly moves the gaze within the current AOI. As shown in

Table 3, we can clearly find that there is no direct transition between AOI 2 and AOI 6 when viewing the tested poster. The reason might be that the AOI 2 (introduction section of the poster) is far apart from AOI 6 (the conclusion section of the poster).

Table 4 and

Figure 10 show the values for the equilibrium distribution,

${H}_{s}$,

${H}_{t}$,

$H\left(Y\right|x)$,

$H(X,Y)$,

$I(X;Y)$ and

$I(x;Y)$, for the gaze information channel for participants 2 and 5. The gaze entropy

${H}_{s}$ is the entropy of the equilibrium distribution

$\pi $, which indicates how frequently each AOI is visited. Note that currently in our gaze channel model, as in Markov chain model, we do not support fixation time, thus number of visits does not directly translate into spent time, although it can be considered as an approximation. From

Table 4 and

Figure 10, we can find that the AOIs that the participants prefer, AOI 5 (results section) for participant 2, and AOI 3 (method section) and AOI 6 (conclusions section) for participant 5, have the larger equilibrium distribution

${\pi}_{i}$ value. This is consistent with

Figure 7 charts for poster 7. A higher value of

${H}_{s}$ means that the participant visited more equally each AOI. A lower value of

${H}_{s}$ is obtained when the number of visits in each AOI is not balanced, possibly because the participant spent more time concentrated on a certain region. It can be seen from

Table 4 and

Figure 10 that the entropy

${H}_{s}$ of the participant 5 is greater than for the participant 2. This means that the participant 5 pays more attention to overall reading and spent time more equally among AOIs than the participant 2. This conclusion is consistent with the previous scanpath analysis from

Figure 4.

${H}_{t}$ reflects the randomness of gaze transition among the different AOIs. Higher

${H}_{t}$ values mean that there are frequent transition among AOIs, while lower

${H}_{t}$ values indicate more careful observation of AOIs [

44].

$H\left(Y\right|i)$ measures the randomness of the gaze transfer from the

i-th AOI. A lower value of

$H\left(Y\right|i)$ indicates that the observer is more clear about the next AOI in the following view. It may also represent that the

i-th AOI provides the observer with significant clues to understand the test poster. From

Table 4 and

Figure 10, we can find that, for participant 2,

$H\left(Y\right|1)$ has the highest value, which means that when in AOI1 (title section of the poster), the observer moves randomly (or evenly) towards any of the other neighbour AOIs. For participant 5,

$H\left(Y\right|2)$ has the highest value, which indicates that this participant moves evenly from AOI 2 (intro section) to any AOI of the poster. Moreover, we can also see that

$I(3;Y)$ has the lowest value, which represents that the information shared between AOI3 (method section) and all the AOIs is minimum.

$H(X,Y)={H}_{s}+{H}_{t}$ measures the total uncertainty, or total randomness of fixations distribution and gaze transition. The lowest value of

$H(X,Y)$ is obtained when the participant 2 views the poster. Compared with the participant 5’s scanpath in

Figure 4, the scanpath with lowest

$H(X,Y)$ has higher fixation length and less gaze transitions.

As expected, we can observe in

Table 4 and

Figure 10 that

$I(i;Y)$ and

$H\left(Y\right|i)$ show in general opposite behavior. Higher values of

$I(i;Y)$ correspond to lower values of

$H\left(Y\right|i)$ and viceversa. The values of

$I(4;Y)$ for participant 2 and

$I(1;Y)$ for participant 5 are higher than the other values of

$I(i;Y)$. This indicates that next AOIs when leaving AOI4 (algorithm section) for the participant 2, and leaving AOI1 (title section) for participant 5, were well defined, as a high value of

$I(i;Y)$ means that the next AOI is known with high probability. This behavior can be re-confirmed in the corresponding scanpaths in

Figure 4. Furthermore, from

Table 4 and

Figure 10 we can see that participant 5 has the highest

$I(X;Y)$ value. Mutual information

$I(X;Y)$ expresses the degree of dependence between the AOIs. It might mean that participant 5 has a more precise strategy or more clues in exploring the tested poster. However, this is in apparent contradiction to the fact that total uncertainty of participant 5 is higher than for participant 2. To be able to compare the mutual information between the two participants, we should first normalize it. Several normalization proposals exist in the literature [

54]. If we consider for instance the one defined in [

47] as a correlation coefficient

$\rho =\frac{I(X;Y)}{H\left(X\right)}=\frac{I(X;Y)}{{H}_{s}}$, the value of

$\rho $ for participant 2 is

$0.643$, and for participant 5 is

$0.644$, practically the same. Thus, in this case, we can not discover any difference based on mutual information.

#### 6.2.3. Averaging Results for All Posters and Participants

We can find in the Appendix the

Table A1,

Table A2,

Table A3,

Table A4,

Table A5 and

Table A6, with the values for all participants and posters of

$I(X;Y)$,

${H}_{s}$,

${H}_{t}$ and

$H(X,Y)$, and

$I(X;Y)$ normalized by

${H}_{s}$ and

$H(X,Y)$, respectively. For instance,

Table A1 lists the mutual information

$I(X;Y)$ of all participants when they view all tested posters, the average value and standard deviation for each poster is given in the last two rows. It can be observed clearly that the MI values for tested poster 7 (with six AOIs) are much larger for all participants in general than for the other posters, which may indicate that the degree of dependence or correlation between AOIs of poster 7 is much stronger. We observe also that, although values of MI for different posters might be significantly different, the differences are reduced when considering the average MI value. These facts are confirmed looking at the normalized MI (see

Table A5 and

Table A6).

We have summarized

Table A1,

Table A2,

Table A3 and

Table A4 in

Figure 11 and

Figure 12. This allows readers to more intuitively observe the quantitative gaze collection of all participants.

Figure 11 shows the stacked

${H}_{t}$,

${H}_{s}$,

$H(X,Y)$ and

$I(X;Y)$ in the gaze information channel from all participants when they view all tested posters. From the stacked

${H}_{s}$ and

${H}_{t}$ bar chart in

Figure 11a, we see that, for every participant, the values of joint entropy

$H(X,Y)$ (marked in gray color) approximately equal the total of

${H}_{s}$ and

${H}_{t}$. Their total is equal for each separated transition matrix,

Figure 11 shows that using averages is a valid approach. The joint entropy

$H(X,Y)$ measures the total uncertainty, which gives the uncertainty when every participant views the tested poster. At the same time, we can find that the values of the conditional entropy or transfer entropy

${H}_{t}$ (given by the crimson color bar) are close for all participants. This phenomenon illustrates, for all participants, when they begin to reading the test poster, they always like to switch between the different AOIs to better understand the context of the poster. This is consistent with the property of

${H}_{t}$ which reflects the randomness of gaze transition among the different AOIs.

From the right stacked

${H}_{t}$ and

$I(X;Y)$ chart in

Figure 11, we can see that

${H}_{s}$ (as marked in blue color) is approximately equal to the

${H}_{t}$ plus

$I(X;Y)$ (see previous remark about totals). Mutual information (MI)

$I(X;Y)$ in gaze information channel represents the degree of dependence or correlation between the set of AOIs. Furthermore,

${H}_{s}$, which is the entropy of the equilibrium distribution

$\pi $, measures how much equally the AOIs have been visited. From the blue bars in

Figure 11a, it is clear that the participants 3, 5, 8, 9 spent more balanced time in each AOI when they read the tested poster since their

${H}_{s}$ is larger compared with the participants 1, 7, 10. This means that the participants 1, 7, 10 possibly spent more time concentrated on certain regions of the tested poster.

Figure 12 also shows the stacked

${H}_{t}$,

${H}_{s}$,

$H(X,Y)$ and

$I(X;Y)$ in gaze information channel for all tested posters. According to

Figure 12, we could consider the posters into three groups, the first one with poster 1, with the lowest value of

$H(X,Y)$ and

${H}_{s}$, a second group with posters 2–6, with similar value of

$H(X,Y)$ and

${H}_{s}$, and a third one with poster 7, with highest value of

$H(X,Y)$ and

${H}_{s}$. Looking at

Figure 1, we observe that poster 1 has one AOI that does not practically include relevant information, AOI3, this explains the lower values for this poster, as this AOI will be mostly ignored by participants. On the other extreme, poster 7 with six areas of interest is the more complex of all them. It also has the highest mutual information, and also, from

Table A5 and

Table A6, the highest normalized mutual information. It might mean that, although it is a more complex poster than the other ones, it is well structured and readers establish a coherent reading strategy.

Looking now at

Figure 12b, we can observe the differences between the posters in the second group, from 2 to 6. All of them have similar

${H}_{s}$ value, but, in poster 2, the distribution is different. For poster 2, the mutual information

$I(X;Y)$ is higher (and correspondingly the entropy

${H}_{t}$ is lower) than for posters 3–6. This is further checked by taking a look at

Table A1. It means that this poster is easier to read or to interpret than posters 3–6. It can also be seen from

Table 5, where we have classed the results of the explaining the core idea stage after the experiment into two groups: expressing the core ideas basically (called basic group), and saying only some keywords (called keywords group),

Table 5 gives the participants from both groups for all tested posters. Although due to the low number of participants we can not draw any conclusive result, it seems that higher mutual information in posters 2 and 7 is related to a higher cognitive comprehension. It might work in an indirect way, that is, higher MI means more coherent exploration strategies that facilitate the comprehension of the poster.

Having a look at

Figure 1, we see that poster 2 contains just text in the middle AOI, being probably easier the flow from graphics to text and graphics again than in the other posters. In addition, we see that posters 4–6, although they contain four areas of interest, one of them contains very little relevant information to understand the posters, thus, although we should in principle expect more information and uncertainty with four areas than with three, the results are similar. Observe that, for the analysis of posters 2–6, we do not need to consider the normalized mutual information, as we had to do in

Section 6.2.2, as we compare posters with similar values of

${H}_{s}$.