Framing Risk with Numbers: The Framing Effects of Risk Assertions and Number Formats on Emotions and Risk Perceptions

Abstract

This study examines how risk assertions and relevant statistics presented in different number formats interact to influence emotional and cognitive outcomes. Experimental news stories present risk assertions that highlight either safety from or vulnerability to violent crime; these assertions are accompanied by crime statistics in absolute frequency, simple fraction, or percentage format. Although it may be tempting to assume that national statistics in absolute frequency format create a greater impression due to the sheer size of the numbers, our results show that only probability formats, including simple fractions and percentages, interact with assertions to generate amplified emotions. Furthermore, we find that negative emotions play a mediating role in producing pessimistic risk assessments. Our findings reveal how people process numerical information and its impact on emotional and cognitive responses. This article also discusses the empirical and methodological implications for framing research, as well as cognitive aspects of emotional reactions and the nature of emotional effects on risk perceptions.

Notes

¹ They summarized their findings as follows: “Fear increased risk estimates and plans for precautionary measures; anger did the opposite” (p. 144). However, the mean of the perceived likelihood of future terror attacks on U.S. soil was 3.38 for anger and 3.62 for fear on a 9-point scale ranging from 0 (extremely unlikely) to 8 (extremely likely). The mean estimated probability of future terror attacks was 30.5% for anger and 35.2% for fear. We believe, therefore, that it is more correct to interpret these results as pointing to similar effects of anger and fear, with the latter having a slightly stronger effect.

² Although we expect emotions of the same valence produce similar results, we test each emotion separately just in case emotions have different effects because (a) we cannot ascertain the true nature of violent crime risk and (b) positive emotions may have different appraisals.

³ The experiment was approved by the Institutional Review Board at the University of Wisconsin–Madison on October 25, 2016.

⁴ We examined the interaction between risk assertions and number formats by treating each number format separately (i.e., a 2 × 3 factorial design). The results show that percentages interacted with risk assertions for all of the six emotions and simple fractions interacted for four emotions: anger, fear, sadness, and hopefulness. By contrast, risk assertions presented in absolute frequency format failed to produce corresponding levels of emotional reactions regardless of the kind of emotions. We believe that these results further justify merging the percentage and simple fraction conditions for a powerful test given the exploratory nature of the current study. The detailed analytical procedure and estimates can be obtained from the corresponding author upon request.

⁵ A post hoc power analysis based on the largest effect size in the interaction effects (i.e., anger, partial η² = .03) yielded a power level of .70 at α = .05, suggesting an insufficient sample size (Cohen, 1992). Along with Rosnow and Renthal’s (1989) argument, this result may further justify using a .10 significant level.

⁶ A model with multiple mediators is possible only when those mediators are “conceptually distinct and not too highly correlated” (Kenny, 2016, Multiple mediators section, para. 1). The emotions we tested, however, are strongly correlated with one another (r = .64–.86) and not conceptually distinct.

Additional information

Notes on contributors

ByungGu Lee

ByungGu Lee (M.S., Syracuse University, 2009) is a Ph.D. student in the School of Journalism and Mass Communication at the University of Wisconsin–Madison. His research interests include media effects and audience psychology in the context of political decision making.

Jiawei Liu

Jiawei Liu (M.S., University of Illinois at Urbana-Champaign, 2013) is a Ph.D. student in the School of Journalism and Mass Communication at the University of Wisconsin–Madison. His research interests include media effects and communication technologies with an emphasis on framing effects in digital contexts.

Hyesun Choung

Hyesun Choung (M.A., Yonsei University, 2013) is a doctoral student in the School of Journalism and Mass Communication at the University of Wisconsin–Madison. Her research focuses on the psychological underpinnings of media effects in political and health communication contexts.

Douglas McLeod

Douglas McLeod (Ph.D., University of Minnesota, 1989) is the Evjue Centennial Professor in the School of Journalism and Mass Communication at the University of Wisconsin—Madison. His research interests include social conflicts and the media, media framing effects, and public opinion.