CALVI: Critical Thinking Assessment for Literacy in Visualizations

2.1 Visualization Misinformation

In general, misinformation can happen as a result of carelessness during communication, but it could also come from deliberate manipulation. More specifically, several aspects of visualization misinformation have been studied previously. For instance, some have looked at line charts and addressed deception in line charts by adding annotations [22]. Others have studied misalignment between a visualization and its title and how this impacts trust and recall of information [27]. When visualizations violate important design principles, they can become hallucinators (i.e., different representations of data causing a different impression) or confusers (i.e., ambiguous visualizations such that changes to the data makes no difference in the visual representation) [26]. McNutt et al. studied visualization mirages, which are visualizations that might appear to support a certain claim, but actually are not upon a closer examination [32]. McNutt et al. also compiled categories of errors that can lead to visualization mirages, such as missing records in the data curating process, overplotting, concealing uncertainty, or manipulating scales in the visualization phase [32]. More recently, Lo et al. developed a taxonomy of misinformative visualizations that included errors or issues that could be present on poorly designed visualizations [30]. Previous work on visualization misinformation has informed us ways of manipulation that can result in misleading visualizations. However, more work is required to understand how well the public can identify and interpret misleading visualizations, which is a first step in developing effective interventions to combat visualization misinformation.

2.2 Visualization Literacy

Previously, researchers have studied visualization literacy under varying definitions. Boy et al. focused on line charts, bar charts, and scatterplots and defined visualization literacy to be “the ability to confidently use a given data visualization to translate questions specified in the data domain into visual queries in the visual domain, as well as interpreting visual patterns in the visual domain as properties in the data domain” [7]. Börner et al. designed a study specifically looking at the visualization literacy of a target audience that is also interested in science and museums [10]. Although this audience group encounters visualizations in their everyday lives and have a higher interest in math and science, Börner et al. found that most of the participants still struggled to interpret the visualizations presented in the study [10]. Differing from Boy et al., Börner et al. defined visualization literacy to be “the ability to make meaning from and interpret patterns, trends, and correlations in visual representations of data” [10]. Their study results also showed an urgent need in the educational space to better teach students about visualizations. In a later work, Börner et al. proposed a framework aiming to assess visualization literacy and teach visualizations; the ability to construct visualizations was also included in their definition of visualization literacy [9]. In order to provide a more tailored instruction on visualizations, it is important to better understand the students’ current abilities in visualization interpretation. Lee et al. developed a Visualization Literacy Assessment Test (VLAT) that measures people’s visualization literacy, which they defined as “the ability and skill to read and interpret visually represented data in and to extract information from data visualizations” [29]. However, every visualization in VLAT is assumed to be correct, and we argue that this assumption does not transfer to the real world because the public will likely encounter erroneous visualizations as well.

As discussed above, not every visualization is guaranteed to be correctly or effectively designed. Thus, only measuring visualization literacy with correctly designed visualizations is not comprehensive enough. To be able to identify visualization misinformation, one needs the ability to critically think about what is given, which could be referred to as the ability to judge the accuracy of the information presented [21]. This aspect related to critical thinking has been studied in other domains such as statistical literacy [23, 43], where researchers have also looked at graph interpretation related to statistical literacy, some specifically targeting the critical aspect [2, 3, 33]. However, this critical thinking aspect has not been studied extensively in the context of visualization literacy. Camba et al., focusing on misleading or deceptive visualizations in the education space, identified deception recognition as an important part of visualization literacy [13], but studied only one type of deception (i.e., inappropriate y-axis range) out of the many ways a chart can mislead. This presents an opportunity to put the existing taxonomies of misleading visualizations we discussed in section 2.1 into practice to more comprehensively understand people’s ability to identify visualization misinformation.

2.3 Systematic Procedure for Test Development

We will follow the procedure outlined in Psychological Testing and Assessment [14] to systematically develop our test. Here, we describe each phase with its core considerations.

The Test Conceptualization phase lays the foundation of the test by identifying a need for it and considering questions such as what the test intends to measure, what contents should be included in the test, who will be administering and taking the test, and how the test will be administered [14]. An item is a question in the test, and the main tasks in Test Construction include deciding the format of the items and designing the items. During Test Tryout, the developer tries out the test on a sample of the target audience [14]. The necessary sample size depends on the analysis method planned for the next phase, Item Analysis, where data from test tryout will be used to evaluate how well different questions separate participants of different ability levels [14]. Classical test theory (CTT) and IRT can both be used for item analysis, and both methods have been used in prior work for measuring visualization literacy (e.g., Lee et al. [29] used CTT; Boy et al. [7] used IRT). Depending on the IRT model, different samples sizes are recommended [19]. We opted for IRT because it can be extended further to develop computer adaptive testing (CAT) [5, 19]. We selected the 2-parameter logistic (2PL) model to conduct item analysis, because we are most interested in the item easiness and item discrimination parameters. These parameters will be used in the Test Revision phase to determine whether certain items should be removed or rewritten. There are no standard ways of revising the test; developers must decide on the criteria and revise based on the aim of the test [14].

3.1 Test Construction: CALVI Format

We chose to create our items in a selected-response format, which includes multiple-choice and true-or-false questions. This format provides a convenient and efficient way to aggregate results and conduct quantitative item analysis and is easy to use for large-scale testing [24]. Henceforth, we will use items to refer to selected-response questions in our test that are associated with visualizations. We conducted an initial pilot study to qualitatively try out our test with members in our lab and observed that 30 items is a reasonable set for people to complete in one sitting. Thus, we limited the test to contain 30 items with an estimated completion time of 30 minutes.

In the real world, people likely encounter misleading visualizations mixed in with correctly construed visualizations, making it harder to identify and reason about the potentially misleading ones. To simulate this reality, CALVI contains two categories of items: (1) trick items using misleading and erroneous visualizations and (2) normal items using well-formed visualizations inspired by VLAT. Each participant sees 15 items from each category. We use only the trick items to assess their critical thinking ability in visualization interpretation. To be able to analyze a large bank of items, the 15 trick items each participant sees are randomly drawn from our item bank, which we describe below. The 15 normal items are fixed.

3.2 Test Construction: Visualization Content Design Space

To systematically generate the items in the bank, we constructed a design space that consisted of combinations of possible ways a chart can become misleading (we refer to these as misleaders) and chart types. Below, we describe the process of distilling the set of misleaders and chart types used to construct the design space (also shown in Figure 3).

Figure 3:

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Misleaders. To compile an initial set of ways a visualization can mislead, we drew from two main prior works: categorizations from McNutt et al. and Lo et al. [30, 32]. We reviewed each category from McNutt et al., extracted relevant categories based on main criteria such as visually detectable (we cannot test for misleaders that people cannot detect visually) and not cognitive biases (cognitive biases from readers do not fit in the definition of misleader as they are not part of the visualization construction process³), and further categorized them into higher-level or lower-level categories ( in Figure 3). The same process is repeated with categorizations from Lo et al.⁴ Then, we merged the two sets by mapping the lower-level categories from Lo et al. to the higher-level categories from McNutt et al. ( in Figure 3). During the merge, we mapped 17 lower-level categories to the Manipulation of Scales higher-level category, making it the largest category. We then split it into four subcategories: Inappropriate Order, Inappropriate Scale Range, Inappropriate Use of Scale Functions, and Unconventional Scale Directions, resulting in 14 misleaders ( in Figure 3).

In order to systemically apply the misleaders to different chart types, the misleaders have to be generalizable across chart types. Thus, misleaders with an inability to generalize cannot be applied to a variety of chart types to populate the design space. Additionally, the items need to be self-contained, so they cannot require domain-specific knowledge. Three high-level categories from McNutt et al. [32] were removed from the set of 14 based on these two criteria ( in Figure 3). Namely, within-the-bar-bias and misunderstanding area as quantity categories were removed because of their inability to generalize to chart types without bars and without area encodings, respectively. Assumptions of causality category was removed due to it requiring domain-specific knowledge: e.g., to decide whether or not a correlation in a visual representation reflects a causal relationship requires knowing the causal structure of the domain, and is not a property of the visualization itself. Thus, the result is a set of 11 misleaders, whose descriptions are shown in Table 1.

Chart Types. We started with the 12 chart types from VLAT surveyed by Lee et al. [29] ( in Figure 3). Because we want the combinations of chart types and misleaders to create misinformative visualizations we might expect people to see in the wild, we remove chart types that are less likely to appear in reality (i.e., realism criteria). Hence, treemap was removed: it was ranked in the bottom half in the list of chart types in data visualization authoring tools and news outlets by Lee et al. [29]. In addition, to run an experiment in which each item is seen by a reasonable number of people, we need an item bank that is not too large. Yet we still want it to be diverse (i.e., diversity criteria). Thus, we removed histogram due to its similarities with bar chart after applying the misleaders. Additionally, we merged bubble chart into scatterplot as it is essentially a type of scatterplot with an additional dimension ( in Figure 3). The result is a set of 9 chart types.

Design Space Structure. To construct the skeleton of the design space, we generated a matrix with misleaders as rows and chart types as columns ( in Figure 3).⁵ This matrix helped us explore how misleaders can be applied across chart types to systematically construct misleading visualizations, and we refer a cell in this matrix as an item type.

Designing Visualizations. Next, we filled out the design space by applying misleaders to different chart types. We want to note one important consideration during the design process: visualizations alone are not necessarily misleading. To be misled means that the conclusion drawn from the visualization deviates from the correct conclusion, requiring a correct answer or conclusion to exist in the first place. Thus, a visualization can only be misleading when there is a specific question or task that viewers need to answer or perform using the visualization. We acknowledge that certain types of visualization are implicitly associated with specific tasks because they are designed in such a way to highlight certain aspect of information from data, so those visualizations can be misleading even without explicitly asking viewers to perform a task based on them. Therefore, a misleading visualization cannot be divorced from its visualization task, and this is crucial to keep in mind while designing the visualizations in the design space (and writing the question text afterwards).

While filling out the design space, we also designed visual modifications that we believed would make some items easier or harder than others, and we systematically applied the alterations across chart types ( in Figure 3). This is only our attempt to have items with varying levels of easiness, a property of items ultimately measured by IRT (see section 5). We show another example alteration in Figure 4, which stemmed from applying the misleader Manipulation of Scales - Inappropriate Scale Range on bar charts. The base version of this is simply truncating the y-axis, and the alteration of adding an axis break should make it easier to identify the truncated axis. This specific item type (i.e., bar chart with Manipulation of Scales - Inappropriate Scale Range) has two variations. With the variations in each item type, a total of 128 candidate items were generated after applying misleaders across chart types, as shown in in Figure 3.

Figure 4:

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Within the set of 128 candidate items, there were redundancies due to generating up to three variations within each item type. Thus, to arrive at a diverse bank of items, we reviewed and eliminated misleading visualizations in the design space by following the same two criteria as before: realism and diversity ( in Figure 3). By the realism criterion, if an item type is not likely to appear in a real world setting, then it is eliminated. For instance, inconsistent grid lines and an arrow next to them were less likely to appear in reality for the Manipulation of Scales - Inappropriate Use of Scale Functions misleader, so such items were removed ( in Figure 3). Per the diversity criterion, we removed item types that are redundant. One such example was Manipulation of Scales - Unconventional Scale Directions for stacked bar chart: including this item type would not add variety as it is essentially the same outcome design as a regular bar chart, so we eliminated it. After removing item types based on the realism and diversity criteria, we are left with a total of 35 item types that stemmed from 11 misleaders and 9 chart types. Along with the variations within each item type, the resulting bank contained 52 items associated with erroneous and misleading visualizations ( in Figure 3). An overview of our final design space is in Figure 5.

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3.3 Test Construction: Writing Trick Items

Again, it is important to note that whether a visualization is misleading depends on the underlying visualization task one is asked to perform. Take the example of a line chart with an inverted y-axis: this visualization can be very misleading if one were asked to identify the trend of the line and did not notice the inverted axis. However, if the viewer was asked to retrieve the y value of the line at a specific x value, then it is not misleading because they would simply identify the point of interest on the x-axis and look up its corresponding y value. When we wrote the question text for each visualization in the design space, we ensured that the visualization task associated with each question is a relevant task for the visualization to be misleading. For example, Concealed Uncertainty is most salient in prediction-making, so all items in this category ask test takers to make predictions; to test whether people can detect Inappropriate Aggregation, the items must ask them to aggregate values from the visualization, such as finding the average. There are also misleaders that have multiple relevant tasks: in Manipulation of Scales - Unconventional Scale Directions, it is appropriate to ask people to find correlations/trends from a line chart with an inverted y-axis or to make comparisons of two regions in a choropleth map where the color scale is inverted. The items in our bank involve a total of six tasks: retrieve value, find extremum, find correlations/trends, make comparisons, make predictions, and aggregate values, all of which are visualization tasks rooted in literature [1, 8, 39].⁶ The first four tasks were taken from VLAT [29], and the latter two were added to support the Concealed Uncertainty and Inappropriate Aggregation misleaders. For further discussion on the relationship between tasks and misleaders, see section 9.5.

To further increase the diversity of the items, we created a total of 52 different contexts (background stories), covering topics from the prevalence of a plant species to the market share of cell phone brands. Representative item examples from each of the 11 misleaders in our design space are shown in Figure 6. The contexts were intentionally made fictional in order to limit participants’ use of prior knowledge. Thus, every item is self-contained and participants should be able to select the best answer solely based on what is given in the question text, answer choices, and the associated visualization. To isolate the effect of the specific visualization misleader of each item, we designed the choices for the items to be such that there is at least one correct (best) answer and at least one wrong but seemingly correct answer due to the misleader (i.e., wrong-due-to-misleader). Any other incorrect answers are more obviously wrong and are unrelated to the misleader (i.e., wrong-but-unrelated-to-misleader). The wrong-due-to-misleader answer(s) are needed to measure susceptibility to the misleader (see Figure 6).

Figure 6:

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For items with visualizations that do not present enough information for the test taker to choose a reasonable answer, such as the items in the Inappropriate Aggregation misleader category, we considered two ways of phrasing the correct answer: “Cannot be inferred” and “Inadequate information”. After trying both in pilots, we decided to keep it consistent throughout the test and used “Cannot be inferred / inadequate information” for these answers. Additionally, we added this option to items where the correct answer is not “Cannot be inferred / inadequate information” to ensure that this option is not the correct answer every time it appears in an item, so that the answer choices did not hint at the correct answer.

One difficulty while writing the items was to not make the question text and answer choices too long. The concern with long question text is that reading and parsing it might interfere with the goal of measuring the ability to identify the misleader (i.e., answering incorrectly due to errors in reading the question text or answer choices instead of not noticing the misleader). An example technique we used to shorten the texts is to label the points of interest on a chart to avoid using long descriptions to pinpoint those points.

3.4 Test Construction: Designing Normal items

In order to construct a diverse set of 15 normal items on well-formed visualizations that cover all chart types, we ensured that there is at least one item from each of the 9 chart types and created additional normal items for the chart types that appear more frequently in the item bank. As a result, 6 chart types have 2 items and 3 chart types have 1 item. We also kept the visualization tasks of the normal items consistent with those of the trick items, which mainly include comparing values and identifying trends. Most of the 15 normal items are essentially versions of trick items but with the misleaders removed. We did so to ensure the similarity and consistency between trick and normal items, so that participants would not be able to distinguish them just by looking at the style of the items. For the same reason, when writing the question text and answer choices for the normal items, we followed the same general principles as writing the trick items, including keeping the text concise and adding the option of “Cannot be inferred / inadequate information” to items where it is not the correct answer.

3.5 Test Construction: Preliminary Study

The goal of the preliminary study is twofold: (1) to qualitatively identify sources of ambiguity and misunderstanding in the question text and the visualizations in the test and (2) use the preliminary data to help determine the sample size needed for the test tryout phase. Therefore, in addition to asking each participant to answer 30 items, we also asked them to complete a set of open-ended questions related to the set of items that were randomly assigned to them. The open-ended questions asked participants to explain why they selected their answers for the items that they answered incorrectly (participants were oblivious to this logic). Thus, along with 3 attention check questions, each participant received 33 selected-response items and a subset of open-ended questions depending on their responses in the selected-response section. There was no time limit.

Participants. We recruited 30 participants⁷ from Prolific for the preliminary study, whose average approval rate is 99.57%. All of the participants are located in the U.S. and speak fluent English. In addition, participants whose ages do not fall between 18 and 65 or who do not have normal or corrected-to-normal vision are excluded from the study. We collected a balanced sample of 15 males and 15 females with age ranging from 19 to 64.

Procedure. First, we presented participants with a consent form and information page describing the structure of the study.⁸ They were instructed that they are required to select an answer for the current item/question before moving on to the next one, and once they moved on, they could not return to previous ones.

Figure 7:

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Method. Because one of the goals of the preliminary study was to uncover any confusion in the question text or visualizations, for each selected-response item, we reviewed participants’ responses to the corresponding open-ended question to understand their reasoning behind their incorrect choices and whether their decision was due to the intended misleader or problems with our question text or visualization.

Qualitative Results. The text responses revealed a few sources of ambiguity and inconsistency in the design of items. Two such items are on pie chart and Manipulation of Scales - Inappropriate Use of Scale Functions; in these items, the sizes of the pie slices are inconsistent with the percentages written on the slices. For both items, we initially designated the option of “Cannot be inferred / inadequate information” as the correct answer, because this inconsistency should suggest that the visualizations do not convey any reliable information. However, some participants expressed that they noticed this conflict between the percentages and the sizes of the pie slices, but they decided to trust one over the other nonetheless. Another item on line chart and Misleading Annotations has a similar quality: the title of the chart disagrees with the trend of the line. We were curious about how people understand such visualizations when there is conflicting information present, so we decided to implement an open-ended questions section in the test tryout phase and asked participants who received the corresponding trick item(s) in the selected-response section to justify their answers for these three items (shown in Figure 7).

Another (slightly ironic) ambiguity came in the interpretation of stacked bar charts and stacked area charts. The key ambiguity for these charts is whether the chart was constructed using a position encoding or length encoding. If a position encoding is used, then the quantity of each segment of the bar (or area) should be the corresponding number on the y-axis. If a length encoding is used, then the quantity of each segment should be the difference between the top of the segment and the bottom of the segment (i.e., the top of the segment immediately below). We had disagreement ourselves during item construction: two different authors had used both types of interpretations in the construction of stacked bar charts and area charts, and many participants were able to understand both interpretations and make correct choices based on them. This reflected the ambiguous nature of stacked charts. To resolve this inconsistency, we unified our interpretation to using length encoding, which is the more common interpretation, and we designed the choices of the items in such a way that the “correct” answer for the position-encoding interpretation do not appear in the choices of most items related to stacked bar charts and area charts. To further reduce the ambiguity, we added visual cues with the goal of making the use of length encoding more obvious, such as add transparency to the stacked area charts as well as grid lines in the background to emphasize the interpretation should be based on length encoding.

For the rest of the items, there were no major ambiguities. We made stylistic modifications to a small subset of visualizations to improve their presentations, such as adding strokes to state and country borders in choropleth maps and making the colors more distinct from each other for certain visualizations with color encoding. Through reading the open-ended responses, we also noticed that the vast majority of participants who answered the wrong-due-to-misleader answers continued to explain their reasoning without recognizing the misleader.

Test Tryout Sample Size Determination. The data from the 30 participants were used to fit a preliminary model that was then used to simulate 500 participants, which is the sample size that would likely be sufficient for the 2PL IRT model [19]. We fit the simulated 500 participants to our preregistered model (details in section 5.2) and checked that our model converged with a sample size of 500, posterior predictive checks were reasonable, and we could estimate the correlation between trick and normal items to a resolution of approximately ± 0.1.⁹ Thus, we chose 500 as our sample size for test tryout.

4.1 Descriptive Statistics

We calculated some basic statistics on participant level raw correctness and completion times.

Participant Correctness. Participants’ correctness (proportion of correct answers) for the 15 trick items ranged from 0 to 0.93 (M = 0.39, SD = 0.16). Participants’ correctness for the 15 normal items ranged from 0.27 to 1 (M = 0.80, SD = 0.13).

Completion Time. We examined the completion time for the selected-response section of the test, which included 15 trick items, 15 normal items, and 3 attention check questions. The total time in minutes (the complete distribution can be found in supplemental materials) ranged from 4.62 to 89.60 (M = 19.80, SD = 10.25). This suggests that 30 minutes is reasonable to complete the test.

5.1 2-Parameter IRT Model

We selected the 2PL IRT model, which characterizes each item in two dimensions: item easiness and item discrimination. Item easiness can be interpreted as the easiness (or negation of difficulty) of correctly answering the item. Item discrimination can be understood as an item’s ability of differentiating participants of different levels of ability. The model is described by Equation (1): the left-hand side is the probability of a participant with ability θ answering item i correctly given item easiness b_i and item discrimination a_i; the right-hand side is the formula of how to compute this probability given the values of θ, a_i, and b_i. Equation (1) is often referred to as the item response function, and the curve of this function is called the item characteristic curve (ICC). (1) \(\begin{equation} p_i(\theta) = \frac{1}{1 + \exp (-a_i(\theta + b_i))} \end{equation} \)

Item Easiness. To understand item easiness, consider the case where θ = −b_i. Then by Equation (1), the probability of a person with ability θ = −b_i answering item i correctly is \(\frac{1}{2}\). For example, the dot on the ICC curve of item A in Figure 8 has θ = −b_A and probability of correctness of 0.50. In other words, if a person’s ability is the same as an item’s difficulty, which is the negative of its easiness, then that person has a 50% chance of answering that item correctly. Therefore, the higher the person’s ability θ is above the item difficulty − b_i, the more likely they will answer the item correctly.

Item Discrimination. To gain intuition for the discrimination parameter, observe that the maximum slope of Equation (1) is \(\frac{a_i}{4}\) at θ = −b_i. For instance, Figure 8 shows the slope of the tangent line at the point on the ICC curve of item B where θ = −b_B, which is \(\frac{a_B}{4}\). As a result, a_i is associated with the rate at which the probability of answering the item correctly changes with ability values, hence interpreted as item discrimination. If an item has high discrimination, then people with higher ability should have a much greater chance of answering the item correctly than people with lower ability.

Figure 8:

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5.2 Bayesian IRT

We estimate the parameters of our IRT model using Bayesian modeling. In Bayesian IRT, we are interested in obtaining the posterior distribution of the parameters given the observations. This contrasts traditional IRT where methods such as maximum likelihood estimation are used to find the best point estimates of the parameters. We chose to use Bayesian IRT because it has better modeling flexibility and provides more informative results [11].

After we obtain the posterior distributions of the ability, item easiness, and item discrimination parameters, we take the medians of these distributions as our point estimates.

For our analysis, we used the R package brms, which provides flexible ways to conduct Bayesian IRT modeling [11], which was preregistered on OSF (see https://osf.io/pv67z/).

5.3 Results

Figure 10 contains the analysis results of each item, including the item easiness and discrimination estimates, correctness, rate_wm (see section 7.1), chance_wm (see section 7.1), and the content validity index (CVI) (see section 7.2).

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Item Easiness and Discrimination. The median item easiness parameter estimates for all trick items range from -5.32 to 4.12, with an average of -1.12. The median item discrimination parameter estimates for all trick items range from 0.45 to 1.26, with an average of 0.76. Figure 10 shows the coefficient plots displaying the median easiness and discrimination of each item with 95% and 66% credible intervals (CI).

In Figure 9, we show the average item easiness and discrimination estimates for each misleader. Overplotting, Missing Data, and Missing Normalization are the most difficult misleaders, while Misleading Annotations and Manipulation of Scales - Inappropriate Order are the easiest. The most discriminating misleaders include Misleading Annotations, Concealed Uncertainty, Manipulation of Scales - Inappropriate Use of Scale Function, while Overplotting and Manipulation of Scales - Inappropriate Scale Range have relatively weak discriminating power.

Performance on trick vs. normal items. In addition to analyzing the items, we also investigated the relationship between the performance of participants on trick items and normal items. Their performance on the normal items can be considered as a rough proxy of their basic visualization interpretation ability. The correlation coefficient is 0.63 with 95% CI: [0.48, 0.76], showing a moderately strong correlation. However, these abilities are still qualitatively different, as participant correctness for normal items is generally much higher than that for trick items.

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6.1 Revision from IRT Analysis

Results from section 5.3 were used to revise the items in the item bank. The revision process is necesssarily holistic with many factors to balance [14], such as considering item discrimination, item easiness, and preserving the diversity of the item bank. The two most difficult items have very low discriminating power, namely items T7 and T41: T7 is the second most difficult and the least discriminating item, and T41 is the most difficult item with only 8 items that are less discriminating than it. In addition, both of these items have variations in the design space matrix (T6 for T7 and T40 for T41) that are easier and more discriminating than themselves, so removing them does not reduce the diversity of the item bank.

6.2 Revision from Qualitative Analysis of Open-ended Questions

As described in section 3.5, we included open-ended questions for items T28 and T29 (pie charts where numbers and pie slices mismatch) to investigate whether “Cannot be inferred / inadequate information” is the only reasonable correct answer by examining the justifications of participants who did not select that option as their answer.

For both items, most participants answered according to the percentage labels on the charts. For item T28 shown in Figure 7.A, 124 participants were asked “Does cell phone brand A have more than half of the total market share?”, and

For item T29 shown in Figure 7.B, 146 participants were asked “Are there more households with exactly 1 car than households with exactly 2 cars?”, and

We found that only a small fraction of such participants acknowledged the conflict between the percentage labels and pie slice sizes in their responses, and out of these people, no one provided a clear and convincing argument for why an alternative choice should be correct. This suggests that there is insufficient evidence that percentage label-based or size of pie slices-based answers should be correct. Therefore, the best answers are still “Cannot be inferred / inadequate information” for both items. This also suggests that the misleader Manipulation of Scales - Inappropriate Use of Scale Functions can be hard to detect and reason about. We decided to keep these two items in the bank because they have good item discrimination and reasonable easiness.

The third item we included an open-ended question for was a line chart with a contradicting title, as shown in Figure 7.C (T51). Out of 141 participants who were asked “What is the trend of the number of new tourists in Town Z from 1880 to 1891?”,

We observed that the majority of participants answered this item based on the visual representation rather than the title. Upon examining the justifications of participants who chose “Generally increasing”, we found that most of them did not even notice that the title contained conflicting information at first. Since the aim of this item is to study how people make decisions when reading misleading annotations in visualizations and the majority of participants did not even notice the annotation, this suggests that T51 was not measuring susceptibility to misleadingness. Thus, we decided to remove it from the bank.

Interestingly, a previous study that directly investigated trust and recall when titles contradict the visual representation, found that people tend to recall the visualization title more [27]. Perhaps the salience of titles differs when people are asked to recall information from a visualization versus making a decision on the spot (i.e., choose a correct answer).

7.1 Wrong-due-to-misleader Score

We constructed (section 3.2) and wrote the items (section 3.3) to have three types of answer choices: correct answers, wrong-but-unrelated-to-misleader answers, and wrong-due-to-misleader answers. The wrong-due-to-misleader answers were specifically designed for people who did not recognize or correctly reason about the associated misleader (see Figure 6). Thus, if the majority of people who get an item incorrect are choosing a wrong-due-to-misleader answer rather than a wrong-but-unrelated-to-misleader answer, this is evidence that people have been misled (i.e., that the item measures susceptibility to the misleader). We see evidence of this in responses from the qualitative preliminary study (section 3.5): in explaining their reasoning, participants who chose the wrong-due-to-misleader answers generally continued to justify their answers without recognizing the misleader.

For the test tryout study, we use a wrong-due-to-misleader score, RR_wm, as one measure of validity. We define RR_wm of each item to be \(\frac{{rate}_{wm}}{{chance}_{wm}}\), where rate_wm is the proportion of wrong answers that people chose that are wrong-due-to-misleader and chance_wm is the probability of choosing the wrong-due-to-misleader answer among all wrong answers if one were to choose randomly. We consider items with a rate_wm greater than chance_wm to be valid, meaning the RR_wm is greater than 1. Items with a RR_wm below 1 are candidates for revision.

7.2 Content Validity Index

We also evaluated items using CVI. The CVI of an item is the proportion of domain experts who rated the item a 3 (quite relevant) or 4 (highly relevant) on a 4-point relevance scale [35]. We invited five domain experts to rate the 49 items in our bank on a scale of 1 (not relevant) to 4 (highly relevant) [35]. Each domain expert has a doctorate and actively conducts research in Information Visualization; three are in academia, and two are in industry. We calculated the CVI for each item based on the expert ratings, and items below 78% are candidates for revision (i.e., should be re-examined for whether they will be retained in the final bank) [35].

7.3 Revision from Wrong-due-to-misleader Score and Content Validity Index

We used both RR_wm and CVI to evaluate the items:

This leaves 45 items in the final bank (indicated with the leftmost dots in Figure 10).

8.1 Finalized Bank of Items

The finalized bank of items spans a wide range of difficulty and discrimination (as shown in Figure 11 (top)), which is appropriate for a general audience for which we initially designed the test. Moreover, test administrators can also conveniently customize their tests based on their target audience by selecting the appropriate items from the item bank (see section 9.1.2).¹⁰

Figure 11:

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As we mentioned in section 2.3, there is no strict criteria or gold standard for selecting the final set of items. Test administrators should select items most suited to the purpose of the test [14]. It is also worth noting that the test development process we applied in this paper is an iterative process: over time, as the test gets deployed in practice, the item bank may need to be revised to fit its purpose when new data arrives or related research emerge in the field [14].

8.2 Reliability

Reliability is a fundamental concept in psychometrics, and its basic idea is simple: observed test results are a combination of signal and noise. The higher the proportion that is due to signal rather than noise, the more reliable the test. Psychometricians have developed many measures of reliability, such as ω and Cronbach’s coefficient α [18]. However, Dunn et al. pointed out some difficulties with using α and outlined advantages for using ω [20]. Revelle and Condon also showed that ω is a more reliable measure because it does not consistently underestimate reliability like α and captures total variance common to all test items [37]. There are several forms of ω, and ω_t is the total reliable variance of the test, representing the overall reliability of the test. Thus, we used ω_t to measure reliability, and our analysis demonstrated that our finalized item bank with 45 items has a high reliability score (ω_t = 0.81).

9.1 Recommendations for Using CALVI

To make our test easily accessible without the need to use an item bank, we provide a set of 15 items that can be used to cover a wide range of abilities. These 15 trick items would be combined with the 15 fixed normal items to construct a test of 30 items. To select a representative set of 15 trick items, we adopt the following method. For each of the 11 misleaders, we select the item with the highest item discrimination. For the remaining 4 items, we prioritize the misleaders that have a large representation in the bank and items with high discrimination at ability levels not covered by the previously-selected 11 items. The resulting 15 trick items cover all misleaders and 8 out of 9 chart types in the design space (colored item IDs in Figure 10); the 1 absent chart types is stacked area chart, an acceptable compromise since the similar 100% stacked bar chart, stacked bar chart, and area chart are in our selected set. The ICC curves of the 15 items are shown in Figure 11 (middle), and compared to the ICC curves of all 45 items in Figure 11 (top), we conclude that this recommended set of items covers a wide range of ability levels and is appropriate for a general audience. This selected set of 15 items also shows high reliability (ω_t = 0.82).

9.2 Applications of CALVI in Future Research

CALVI has many interesting applications beyond assessing the ability to reason about misleading visualizations of the general public. In educational settings, CALVI could be used to investigate when students learn to identify visualization misinformation by studying changes in that skill over time (e.g., from high school through college). Similarly, one could use CALVI to investigate whether consumers of different types of news have different critical thinking abilities for visualization interpretation (e.g., are people who read data journalism better at this skill?). Moreover, CALVI can also be used to test the effectiveness of an intervention on visualization misinformation by asking participants to take the test before and after the intervention to observe change in their performance. The item bank offers a resource to construct a pre- and post-test without asking the participants the same items (see section 9.1).

9.3 Is Attention All We Need to Detect Visualization Misinformation?

We believe attention is indispensable in identifying visualization misinformation. Some misleaders involve direct manipulations to emphasize or distort certain visual features, such as y-axis inversion that gives an opposite visual impression (see Figure 6.G). Thus, for these manipulations, paying attention to the right part of the visualization matters. As with most tests, if one pays more attention to the right part of the question, one is likely to perform better. In the case of CALVI, adding salient features to draw people’s attention to the misleading part of the visualization design, such as adding a downward arrow next to the inverted y-axis, seem to make it easier for people to detect and interpret the visualization.

While attention appears to be a key component of the ability to detect visualization misinformation, we want to emphasize that only attention is not enough. For about 20 items in the bank of CALVI (e.g., from Missing Data, Concealed Uncertainty, Overplotting), merely paying attention to the misleading part of the visualization is insufficient — reasoning about them requires thinking critically about the visualization construction process beyond just reading the visual representations. Therefore, the ability to detect and reason about visualization misinformation is not equivalent to the amount of attention one pays in viewing visualizations. We saw evidence in our data that suggests a positive relationship between attention and the ability to read, interpret, and reason about erroneous and potentially misleading visualizations; the connection between the two seem to exist in some real-world examples too: in Figure 2.B, if one paid more attention to the x-axis, then it would be easier to identify the inappropriate ordering of the dates. Future work is needed to further investigate the relationship between attention and the ability to detect visualization misinformation.

9.4 Context of Use May Affect Interpretation and Misleadingness

In reality, visualizations are rarely consumed alone in media: they are often accompanied by written text or verbal commentaries, which influence viewers’ interpretations of the visualizations. Therefore, studying and understanding the interplay between visualization and text is crucial to advance our knowledge of visual reasoning and visualization literacy. In the context of developing a test, an interesting consideration is if we were to ask the question in a different way on the same visualization, would that have a noticeable effect on how people understand and reason about the visualization? Is a particular misleader always misleading, or is it only misleading in the face of certain tasks or questions?

9.5 Are All Misleaders Actually Misleading?

As we explained in section 3.2, to what extent a visualization can be misleading depends highly on the visualization task. Existing literature lacks clear guidelines connecting misleading visualizations to visualization tasks. Thus, we did so using our best judgment and knowledge of the literature. A taxonomy mapping misleading visualizations to visualization tasks would be a useful direction for future research, and new findings may yield different items in the test.

There may also be disagreement on whether every potential misleader should be considered as a visualization error. For instance, some evidence suggests that whether a truncated y-axis is “deceptive” or “truthful” is domain-specific and depends on what effect sizes are meaningful in that domain [15]; so some may deem a truncated axis an error while others may not, or may disagree on when it is an error. In our case, if an item was found to be easy, then it may suggest that the associated misleader is not really a misleader at all. Our design space and item bank offer a starting point for determining what putative misleaders are actual misleaders: future work could start from the easiest misleaders in our item bank, and conduct studies specifically examining their effect on interpretation across a range of chart types. Such an effort would help systematize the study of visualization misinformation, and could generate more empirically-grounded guidelines for visualization construction.