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The authors have declared that no competing interests exist.

Misleading graphs are a source of misinformation that worry many experts. Especially people with a low graph literacy are thought to be persuaded by graphs that misrepresent the underlying data. But we know little about how people interpret misleading graphs and how these graphs influence their opinions. In this study we focus on the effect of truncating the y-axis for a line chart which exaggerates an upgoing trend. In a randomized controlled trial, we showed participants either a normal or a misleading chart, and we did so in two different contexts. After they had seen the graphs, we asked participants their opinion on the trend and to give an estimation of the increase. Finally we measured their graph literacy. Our results show that context is the only significant factor in opinion-forming; the misleading graph and graph literacy had no effect. None of these factors had a significant impact on estimations for the increase. These results show that people might be less susceptible to misleading graphs than we thought and that context has more impact than a misleading y-axis.

Graphs can misrepresent the underlying data in many ways, and this worries experts in different fields, from health communication [

Misleading graphs were omnipresent in the media during the covid pandemic, both in (social) media and governmental communications [

There are many ways for a graph to be ’wrong’. For example, there can be inconsistencies within a graph, such as a

Graph literacy is the individual’s ability to read, process, and comprehend data visualisations [

Individuals with higher graph literacy can process graphs with greater ease and have an expected higher comprehension of the graph’s content [

There are multiple tests available to determine the level of graph literacy of an individual. For example, the objective graph literacy scale [

A few studies have studied the interpretation of conflicted graphs or other types of misleading graphs, which usually covered only bar charts. For instance, [

Experiments showed that individuals with high graph literacy have a more accurate interpretation of self-conflicting graphs [

In real-life situations, graphs are used in a context, and we know that prior knowledge about a subject influences the reader’s interpretation of graphs [

It is known that people who do not have a strong opinion on a subject are more susceptible to persuasion using charts [

In this paper, we study the interpretation of line graphs. Specifically, we study whether and how truncating the

The current study uses a quantitative survey-based research design with four distinct surveys. The surveys can be separated on two between-person factors, namely, context and graphical representation.

The contextualisation presents the participants a narrative that focuses on the fictional ’Bluebeak’, a non-native bird in Denmark. One story about the ’Bluebeak’ is that the bird is endangered, whereas the other story focuses on the disruption the ’Bluebeak’ causes to Denmark’s eco-system. Both narratives are provided in

The graphical design element accompanies the ’Bluebeak’ contextualisation, where one group of each contextualisation gets a different graph presented. The first possible graph being a line graph at which the

Data collection is done through Prolific (

Participants provided written informed consent. The Ethics Committee Psychology of the University of Groningen has approved this study (PSY-1920-S-0441).

The study uses two grouping factors, contextualisation and graphical representation. Additionally, we ask the participants to make a judgement call about the displayed situation, with scores ranging from 1 (very bad) to 5 (very good).

Participants are asked to estimate the proportional increase of the number of ’Bluebeaks’ in the previously presented graph to determine which type of graph the participants give the most accurate proportional increase estimation. Graph literacy is measured using the SGL scale (see: Instruments) to determine whether varying levels of graph literacy influence their judgement and estimation of Denmark’s ’Bluebeak’ situation.

Finally, a set of demographics are included to have options for control and evaluations of sample balance. The demographics are age, gender, and educational level. Age is measured on a categorical scale ranging from 1 (18–25) to 7 (66 +), and is assumed to be continuous within the analysis. Gender has options male, female and other. Education level is measured on a 7-point scale.

The short graph literacy scale consists of four items with different types of graphs displayed [

Descriptive statistics for all variables are provided. Outliers are detected and removed based on two criteria. To avoid non-serious participants, all those with a participation duration exceeding the mean duration plus three times the standard deviation are excluded. Furthermore, outliers are detected using the MAD (median absolute deviation) on the percentage estimation variable since this is the sole variable that took manual input from the participant. For the MAD, the threshold of 2.5 is chosen, which is classified as a mildly conservative criterion [

The relation between axis type, context, judgement and interpretation is analysed via multiple linear regression. Two sets of models are built, one using judgment and the other using estimated proportional increase as the dependent variable. The percentage variable is centred around the correct answer; this way, the estimates received by the model are interpretable as the amount which the given estimates diverge from the correct answer.

For both sets of models, we make versions with (i) the main effects of axis-type and context, (ii) as (i) but with the inclusion of SGL as moderation variable, (iii) as (ii) but including the interaction between axis type and context. In all three models, age, education level, and gender will be included as covariates.

A posthoc power analysis is conducted for 247 participants, at which the multiple regression with ^{2} = .05 with a power of .968.

In total, 313 people started with the questionnaire. A total of 66 participants were excluded due to the following reasons: not completing the questionnaire (13), not providing consent (1), exceeding our participation duration threshold (5), not specifying gender (6) and providing scores exceeding the MAD-threshold (41). Data for 247 participants were included. Descriptive statistics are provided in Tables

Variable | Normal graph | Shifted graph | ||
---|---|---|---|---|

Age | 4.14 (1.92) | 4.41 (1.78) | 3.53 (1.84) | 3.90 (1.99) |

Education | 3.56 (1.80) | 4.20 (2.27) | 3.43 (1.87) | 3.95 (2.21) |

Male | 48% | 47% | 60% | 47% |

63 | 71 | 53 | 60 |

Variable | Normal graph | Shifted graph | ||
---|---|---|---|---|

Judgement | 2.21 (0.70) | 4.07 (0.76) | 2.43 (0.95) | 4.28 (0.78) |

Percentage | 21.52 (11.10) | 17.31 (10.31) | 29.21 (15.13) | 28.37 (13.42) |

SGL | 1.65 (0.48) | 1.80 (0.40) | 1.72 (0.50) | 1.77 (0.46) |

63 | 71 | 53 | 60 |

None of the bivariate Pearson correlations between pairs of the variables in

Two multiple regression models are fitted to assess the possible association between variables, one with judgment and the other with the centred percentage estimate as the dependent variable. For both models, the underlying statistical assumptions have been checked, and there were no reasons to abandon the choice for multiple linear regression. The results are given in Tables

Estimate | 95% CI | ||
---|---|---|---|

^{A} |
0.38 | [-0.43; 1.19] | .359 |

^{B} |
1.86 | [1.64; 2.07] | |

^{C} |
|||

-0.28 | [-0.98; 0.42] | .430 | |

-0.06 | [-0.75; 0.62] | .861 | |

0.06 | [-0.67; 0.79] | .872 | |

-0.30 | [-1.20; 0.59] | .504 | |

-0.37 | [-1.52; 0.77] | .523 | |

0.01 | [-0.71; 0.73] | .974 | |

^{D} |
|||

0.13 | [-0.27; 0.53] | .527 | |

0.04 | [-0.37; 0.45] | .836 | |

-0.01 | [-0.40; 0.38] | .948 | |

0.03 | [-0.34; 0.41] | .857 | |

0.05 | [-0.37; 0.46] | .820 | |

0.05 | [-0.37; 0.47] | .825 | |

0.05 | [-0.16; 0.26] | .643 | |

-0.07 | [-0.39; 0.26] | .690 | |

-0.07 | [-0.53; 0.38] | .745 | |

^{2} |
.596 | ||

^{2} |
.566 | ||

247 |

^{A} normal graph is the reference group

^{B} Invasive is the reference group

^{C} No formal education is the reference group

^{D} 18–25 is the reference group

Estimate | 95% CI | ||
---|---|---|---|

^{A} |
5.68 | [-6.86; 18.22] | .373 |

^{B} |
-2.78 | [-6.04; 0.48] | .095 |

^{C} |
|||

1.14 | [-9.73; 12.00] | .837 | |

-3.05 | [-13.64; 7.54] | .571 | |

-1.94 | [-13.20; 9.32] | .734 | |

-0.90 | [-14.71; 12.91] | .898 | |

-10.83 | [-28.56; 6.90] | .230 | |

0.64 | [-10.47; 11.74] | .910 | |

^{D} |
|||

-1.09 | [-7.31; 5.14] | .731 | |

-4.84 | [-11.16; 1.49] | .133 | |

-4.11 | [-10.16; 1.93] | .181 | |

-6.09 | [-11.86; -0.32] | ||

-5.47 | [-11.89; 0.96] | .095 | |

-2.29 | [-8.77; 4.19] | .487 | |

-0.04 | [-3.25. 3.17] | .979 | |

0.46 | [-4.54; 5.46] | .857 | |

1.96 | [-5.03; 8.91] | .582 | |

^{2} |
.184 | ||

^{2} |
.123 | ||

247 |

^{A} normal graph is the reference group

^{B} Invasive is the reference group

^{C} No formal education is the reference group

^{D} 18–25 is the reference group

As predictor variables, the model has the type of graph (shifted vs non-shifted), the type of context (invasive vs endangered), the score on the short graph literacy (SGL) test and its interaction with the type of graph, and the demographic variables education level, age and gender.

When looking at the model with judgment as the dependent variable, context clearly is significant, with the average score in the endangered group 1.86 points higher than the ecosystem group (95% CI [1.64, 2.07], p < .001). None of the other variables is significant. When SGL is not included in the model, graph type is significant (with shifted graphs scoring, on average, 0.25 higher than normal graphs (95% CI [.03, .46], p = .023), but this effect vanishes when graph literacy is included.

A similar picture arises when looking at the model with the percentage estimate centred around the correct answer (approximately 16%) as the dependent variable. Here none of the variables is significant. (The age group 46–55 differs (p = .039) from the reference group, but this effect is non-significant when correcting for multiple comparisons.) When SGL is excluded from the model, the variable graph does become significant, with shifted graphs scoring 9.12 percentage points higher than non-shifted graphs (95% CI [5.86, 12.39], p < .001) but also here, the effect vanishes when SGL is included in the model.

This study looks at how a truncated y-axis, context, graph literacy and demographics influence the judgment and interpretation of graphs.

When participants are required to make a judgement call based on a displayed graph, it becomes apparent that the story itself matters more in the decision-making process than the shape of the graph’s

For the interpretation of the graph, truncating the y-axis does have a significant impact on percentage estimates, which is in line with [

All in all, our randomized experiment on a representative sample of the US population confirms the hypothesis by [

One limitation of our study is that some of the participants did not seem to be used to working with percentages and gave unreasonably high estimates (for instance, one participant estimated 3,000% for an increase that was, in reality, 19.4%). An explanation for these very high estimates could be that the upper bound of the line graphs was 3,000. Maybe these participants thought the exercise was to state to which value the number of ‘bluebeaks’ had increased. These outliers did not influence our conclusions, and we kept them in our data set, but it might be good to realise that there might be a deeper misunderstanding hidden between the variables we measure.

Another limitation is that in our study large groups of participants had the same level of graph literacy. Even though the Short Graph Literacy test graphs are very basic graphs, 75% percent of the participants answered only 1 or 2 questions correctly. This either means that many people do not know how to read and interpret simple graphs, which is in line with [

For future research on this subject, it would also be interesting to see which kinds of contextualization lead to under or overestimating the correct answer. Furthermore, it might be good to see if these results hold for other graph types, such as bar charts.

Finally, we want to emphasize that although truncating the y-axis seems to have less influence on people’s judgement and understanding than previously thought, it is in no way an excuse to make or use misleading graphs.

Misleading graphs in context: less misleading than expected

PONE-D-21-36742

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Reviewer #1: This is a straightforward study on an important practical issue in science communication. The authors use a representative sample of participants from the prodigy platform to examine the effect of what they call "context" (which in other fields in the social sciences is usually called "framing") and y-axis graph manipulation of people's quantitative estimates and goodness/badness judgments of a hypothetical scientific finding. The authors find that framing matters (people tend to judge the increase of bluebeaks as good when it is framed as an endangered species and bad when it is framed as a predator) but that neither graph literacy nor graph manipulation have an effect on qualitative judgment or relative accuracy of quantitative estimates.

Overall, the paper is well done, and it is based on reasonable hypotheses and expectations. The null finding regarding graph literacy and y-axis manipulation is a bit surprising. I commend the authors for making their data and code available which allows curious reviewers like myself to poke around. One thing I noticed when running exploratory models separate by gender is that there is a possible three-way interaction between y-axis manipulation, gender, graph literacy and judgment, such that graph literacy has a negative effect on the judgments of women in the shifted condition, but has a positive effect on men. Of course, this is a post hoc finding and the sample is small, but it could be something worthwhile to study in a more principled way in future work.

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PONE-D-21-36742

Misleading graphs in context: less misleading than expected

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