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People frequently encounter numeric information in medical and health contexts. In this paper, we investigated the math factors that are associated with decision-making accuracy in health and non-health contexts. This is an important endeavor given that there is relatively little cross-talk between math cognition researchers and those studying health decision making. Ninety adults (M = 37 years; 86% White; 51% male) answered hypothetical health decision-making problems, and 93 adults (M = 36 years; 75% White; 42% males) answered a non-health decision-making problem. All participants were recruited from an online panel. Each participant completed a battery of tasks involving objective math skills (e.g., whole number and fraction estimation, comparison, arithmetic fluency, objective numeracy, etc.) and subjective ratings of their math attitudes, anxiety, and subjective numeracy. In separate regression models, we identified which objective and subjective math measures were associated with health and non-health decision-making accuracy. Magnitude comparison accuracy, multi-step arithmetic accuracy, and math anxiety accounted for significant variance in health decision-making accuracy, whereas attention to math, as illustrated in open-ended strategy reports, was the only significant predictor of non-health decision-making accuracy. Importantly, reliable and valid measures from the math cognition literature were more strongly related to health decision-making accuracy than were commonly used subjective and objective measures of numeracy. These results have a practical implication: Understanding the math factors that are associated with health decision-making performance could inform future interventions to enhance comprehension of numeric health information.

How do people make health decisions involving trade-offs between costs and benefits (see

People might receive disease risk information from medical providers, risk tools, genetic tests, and the media, and the hypothetical problem in

Another individual difference, the strategies that people use as they compare and estimate ratios and complete fraction arithmetic problems, has illuminated common errors that children and adults make as they reason about rational numbers in neutral, non-health contexts. Such errors have been identified by examining trial-by-trial, self-reported strategies as people solve math problems (

Our overarching goal in the current paper is to determine whether individual differences in math skills, math attitudes and anxiety, and math strategies that account for variance in performance accuracy in pure numerical contexts

Furthermore, to our knowledge, there is very little work in which open-ended strategy reports are collected as adults make hypothetical or real-world health decisions (cf.

To summarize our rationale, math problems concerning one’s own or others’ personal health, even if the problems are hypothetical, have the potential to engage the processes typically involved in math problem solving as well as additional processes that might influence the selection and use of math strategies compared to more neutral, “pure” numerical contexts. For example, people may possess pre-existing strategies when it comes to their health, such as an aversion to taking medication. Or, it is possible that the emotional salience of thinking about serious health concerns may use up cognitive resources that would be otherwise devoted to solving a problem involving complex health statistics. The primary goal of the present study was

We explored whether key individual differences in math cognition – math anxiety, measures of magnitude understanding (e.g., number-line estimation and magnitude comparison), arithmetic fluency, calculation accuracy on multi-step arithmetic tasks, math attitudes, math anxiety, and strategy use – were associated with performance accuracy on health decision-making problems given our own and others’ previous research in pure numerical contexts. Specifically, we anticipated that higher math anxiety and lower magnitude understanding would negatively predict decision-making accuracy.

Further, we included measures of objective and subjective numeracy (

The sample included 90 participants recruited through Amazon Mechanical Turk’s online panel (MTurk) (

In an attempt to obtain data from high-quality responders, we included only MTurk participants in the parent study who had previously completed at least 100 Human Intelligence Tasks (HITs) and had at least 95% approval from other requestors. Only three participants from the parent study were excluded for poor quality data (i.e., random responding). The study was approved by the Kent State University IRB, and consent was provided by each participant prior to beginning the survey. Prior to launching data collection for the parent study, we conducted an a priori power analysis for a 3 (between subjects: number type) x 2 (between subjects: health vs. non-health) design to detect a small effect size with 80% power and alpha level of .05.

Upon launching the survey on MTurk, participants informed us that the study took longer than advertised, resulting in underpayment based on length of time and difficulty of the math tasks. We increased the pay to 10 cents/minute for those who had already completed the survey and decided to stop data collection before obtaining the desired sample size.

As part of the study design, we included an experimental manipulation in which we presented the numerical information with different formats (e.g., fractions, whole number frequencies, or percentages) because number type is a well-established factor that influences risk comprehension and decision-making accuracy (

See the Appendix for the survey flow of objective and subjective math tasks, health and non-health decision-making tasks, and demographic questions. Note that these measures were included to meet the main goal of the parent study (

We operationalized magnitude understanding as the precision of adults’ number-line estimation skill as indicated by percent absolute error (PAE;

Estimation tasks are strongly correlated with concurrent standardized math achievement scores (

In this task (adapted from

In the 36 trials of the magnitude comparison task, participants saw two fractions and had to choose which fraction was the largest. The largest fraction appeared an equal number of times on the left and right sides of the screen. Fraction comparison is strongly correlated with other measures of magnitude knowledge, like number-line estimation (

Arithmetic accuracy was averaged across a fraction arithmetic task and a whole number fluency task involving addition, subtraction, and multiplication.

We measured participants’ fraction arithmetic performance across 24 problems: six problems blocked by addition, subtraction, multiplication, and division operation type. Participants were given three minutes to solve each set of six problems. Two problems in each section involved two fraction operands (

We measured participants’ whole-number arithmetic fluency with the Calculation Fluency Test (

Participants solved four multi-step fraction arithmetic problems in which the correct steps involved finding common denominators (for two problems), adding sets of fractions, and subtracting the resulting fractions. If participants solved these problems correctly, they should also correctly complete the procedural steps necessary to solve the health and non-health decision-making problems (

Participants completed the Rasch-based objective numeracy scale (

The subjective numeracy scale (

Participants answered 20 questions (MAQ:

Although we asked participants to rate their math emotions on seven-point Likert scales anchored by opposites (e.g., bad vs. good; sad vs. happy;

Participants rated their overall math anxiety on a 10-point scale with higher scores indicating greater anxiety (

Health Decision-Making Problem 1 (adapted from |
---|

Imagine that you are talking to your doctor about your risk of getting cancer. Your doctor says that your risk of getting stomach cancer is |

Health Decision-Making Problem 2 |

Imagine you are hospitalized for a severe allergy, and you are thinking about transferring to a new hospital with special allergy doctors. Your doctor tells you that your risk of your severe allergy symptoms getting worse in the current hospital is |

Health Decision-Making Problem 3 |

Imagine that you're considering surgery, and the surgery will affect two systems in your body. The surgeon says that your current risk of heart failure in the future is to |

Health Decision-Making Problem 4 |

Imagine that you have found radon (a natural radioactive gas) in your home, and you are thinking about having it removed. If you do nothing, then your risk of developing cancer because of radon is |

Non-Health Decision-Making Problem |

Imagine that your home floods every year and you are thinking about getting a flood-resistant treatment for your floor. If you do nothing, then your risk of needing to repair your floor is |

Participants typed their strategy report (

Strategy | Definition | Example | Non-Health Problem | Waters Problem | Four Health Problems |
---|---|---|---|---|---|

Attention to Math | Any attention to math including comparison (e.g., smaller, bigger), estimation (e.g., about 3%), calculation (e.g., adding or subtracting risks), specific references to numbers, or magnitudes (e.g., drastically, miniscule). | 54.84% | 54.44% | 50.56% | |

Specific Numeral | Referenced a specific numeral. | 15.05% | 13.33% | 9.44% | |

Percentage | Referenced a specific percentage, or used the word “percentage.” | 12.90% | 13.33% | 9.17% | |

Fraction | Referenced a specific fraction, or used the word “fraction.” | 2.15% | 4.44% | 4.17% | |

Whole Number | Referenced a specific whole number. | 1.08% | 2.22% | 1.11% | |

Restated Prompt | Restated the strategy report prompt (e.g., risk would increase or decrease) without additional description of why, how, or in what manner this would occur. | 11.83% | 25.56% | 13.61% | |

Non-Math | Exhibited at least one of the non-math subcategories below. | 23.66% | 25.56% | 24.17% | |

Prior Experiences and Beliefs | Mentioned personal prior experiences or beliefs, such as opinions. | 19.35% | 8.89% | 11.94% | |

Severity | Referenced the potential danger or harm of cancer. | 4.30% | 5.56% | 8.06% | |

Emotions | Used emotional language. | 0.00% | 5.56% | 2.50% | |

Doctor | Mentioned doctors. | 0.00% | 3.33% | 1.39% | |

Difficulty | Problem was difficult or confusing. | 0.00% | 2.22% | 2.22% | |

Wants More Information | Expressed a desire for additional information. | 0.00% | 2.22% | 2.50% | |

None | No explanation provided. | 8% | 2% | 5% |

We used a grounded theory approach (

For each participant, the order of the objective math skills tasks (i.e., number-line estimation, magnitude comparison, whole number and fraction arithmetic, multi-step arithmetic, and objective numeracy) was randomized. The math attitudes, subjective numeracy, math anxiety, and math emotions tasks were completed in that order by all participants because the main goal of the parent study was to assess math attitudes with a new researcher-generated measure. Half of the participants completed the math skills tasks before they completed the math attitudes, subjective numeracy, math anxiety, and math emotions tasks.

Participants in each study were randomly assigned to one of three number-type conditions: whole number frequencies (41 out of 100), fractions (41/100), or percentages (41%). The numbers that participants saw in their decision-making problems corresponded to their randomly assigned experimental condition (see

All participants completed the decision-making problems at the very end of the experimental session because, as mentioned above, analyses related to these decision-making problems were largely exploratory given that they were peripheral to the main goal of the parent study. Prior to completing the decision-making questions, participants rated their emotions and perceptions of severity with the scenarios/diseases mentioned in the questions. For example, on the health decision-making problem adapted from

Problem | min | max | skew | kurtosis | ||||
---|---|---|---|---|---|---|---|---|

Health Problems | ||||||||

Emotion Ratings | ||||||||

Health 1 Emotion 1 | 1.84 | 0.82 | 2.00 | 1.00 | 4.00 | 0.53 | -0.70 | 0.09 |

Health 1 Emotion 2 | 1.77 | 0.78 | 2.00 | 1.00 | 4.00 | 0.56 | -0.73 | 0.08 |

Health 2 Emotion 1 | 1.90 | 0.82 | 2.00 | 1.00 | 4.00 | 0.54 | -0.46 | 0.09 |

Health 2 Emotion 2 | 1.87 | 0.86 | 2.00 | 1.00 | 5.00 | 0.88 | 0.67 | 0.09 |

Health 3 Emotion 1 | 1.41 | 0.72 | 1.00 | 1.00 | 4.00 | 1.75 | 2.55 | 0.08 |

Health 3 Emotion 2 | 1.50 | 0.75 | 1.00 | 1.00 | 4.00 | 1.40 | 1.27 | 0.08 |

Health 4 Emotion 1 | 1.76 | 0.85 | 2.00 | 1.00 | 4.00 | 0.91 | 0.04 | 0.09 |

Health 4 Emotion 2 | 1.69 | 0.89 | 1.00 | 1.00 | 5.00 | 1.29 | 1.32 | 0.09 |

Severity Ratings | ||||||||

Health 1 Severity 1 | 4.53 | 0.74 | 5.00 | 1.00 | 5.00 | -2.03 | 5.42 | 0.08 |

Health 1 Severity 2 | 4.50 | 0.74 | 5.00 | 2.00 | 5.00 | -1.57 | 2.34 | 0.08 |

Health 2 Severity 1 | 4.01 | 0.85 | 4.00 | 1.00 | 5.00 | -0.77 | 0.64 | 0.09 |

Health 2 Severity 2 | 3.97 | 0.84 | 4.00 | 1.00 | 5.00 | -0.61 | 0.43 | 0.09 |

Health 3 Severity 1 | 4.69 | 0.77 | 5.00 | 1.00 | 5.00 | -2.87 | 8.20 | 0.08 |

Health 3 Severity 2 | 4.63 | 0.73 | 5.00 | 1.00 | 5.00 | -2.64 | 8.29 | 0.08 |

Health 4 Severity 1 | 4.50 | 0.71 | 5.00 | 2.00 | 5.00 | -1.23 | 0.76 | 0.07 |

Health 4 Severity 2 | 4.53 | 0.67 | 5.00 | 2.00 | 5.00 | -1.32 | 1.27 | 0.07 |

Non-Health Problem | ||||||||

Emotion Ratings | ||||||||

Non-Health 1 Emotion 1 | 1.59 | 0.76 | 1.00 | 1.00 | 4.00 | 1.11 | 0.63 | 0.08 |

Non-Health 1 Emotion 2 | 1.50 | 0.81 | 1.00 | 1.00 | 4.00 | 1.50 | 1.34 | 0.08 |

Severity Ratings | ||||||||

Non-Health 1 Severity 1 | 3.75 | 0.96 | 4.00 | 1.00 | 5.00 | -0.73 | 0.15 | 0.10 |

Non-Health 1 Severity 2 | 4.12 | 0.95 | 4.00 | 1.00 | 5.00 | -1.35 | 1.96 | 0.10 |

We determined that random assignment to the health and non-health conditions was successful: Demographic factors, including participants’ age, ^{2}(1) = 1.06, ^{2}(1) = 0.04, ^{2}(1) = 0.44,

Measure | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

1. PAE 0-1 | 0.70* | 0.50* | -0.22* | 0.23* | -0.41* | -0.32* | -0.30* | -0.44* | -0.36* | |

2. PAE 0-5 | 0.62* | 0.47* | -0.46* | 0.33* | -0.52* | -0.49* | -0.38* | -0.57* | -0.56* | |

3. Whole Number PAE | 0.33* | 0.11 | -0.33* | 0.38* | -0.38* | -0.19^{†} |
-0.35* | -0.42* | -0.44* | |

4. Math Attitudes | -0.18^{†} |
-0.34* | -0.16 | -0.54* | 0.44* | 0.21* | 0.40* | 0.48* | 0.76* | |

5. Math Anxiety | 0.25* | 0.42* | 0.18^{†} |
-0.64* | -0.46* | -0.23* | -0.27* | -0.45* | -0.58* | |

6. Fraction Arithmetic | -0.56* | -0.65* | -0.27* | 0.45* | -0.50* | 0.44* | 0.39* | 0.63* | 0.51* | |

7. Multi-step Arithmetic | -0.33* | -0.45* | -0.16 | 0.26* | -0.32* | 0.46* | 0.16 | 0.29* | 0.37* | |

8. WN Fluency | -0.38* | -0.40* | -0.22* | 0.36* | -0.21^{†} |
0.53* | 0.38* | 0.37* | 0.43* | |

9. Objective Numeracy | -0.47* | -0.48* | -0.35* | 0.40* | -0.31* | 0.62* | 0.34* | 0.40* | 0.49* | |

10. Subjective Numeracy | -0.32* | -0.37* | -0.22* | 0.68* | -0.57* | 0.50* | 0.29* | 0.42* | 0.58* |

^{†}

Problem Type | Health 1 | Health 2 | Health 3 | Health 4 | Health Average | Non-Health |
---|---|---|---|---|---|---|

Accuracy | 78% | 58% | 62% | 78% | 2.74 ( |
82% |

The overarching goal of our analytic plan was to determine which objective and subjective variables accounted for significant variance in health and non-health decision-making accuracy. We conducted a logistic regression for the non-health problem and a linear regression for the four health decision-making problems. To avoid overfitting our model, we aggregated some variables that were highly correlated so that our final model included nine predictors, in line with suggestions for sample size to predictor ratios (

Whether people attended to math, as measured by their open-ended strategy reports, was the only variable that accounted for significant variance in non-health decision making accuracy (

Predictors | Odds Ratio | ||
---|---|---|---|

Attention to Math | 10.89 | 8.29 | .003** |

Number Line PAE (combined) | 0.72 | 0.42 | .519 |

Magnitude Comparison | 0.67 | 0.70 | .403 |

Arithmetic | 1.33 | 0.32 | .571 |

Multi-step Arithmetic | 0.94 | 0.04 | .834 |

Objective Numeracy | 1.27 | 1.13 | .288 |

Math Anxiety | 0.84 | 1.34 | .246 |

Math Attitudes | 1.07 | 0.01 | .912 |

Subjective Numeracy | 0.89 | 0.06 | .812 |

**

Predictors | ||||
---|---|---|---|---|

Attention to Math | 0.05 | 0.08 | 0.66 | .512 |

Number Line PAE (Combined) | -0.04 | 2.44 | -0.23 | .822 |

Magnitude Comparison | 0.35 | 0.94 | 2.08 | .041* |

Arithmetic (Combined) | -0.17 | 0.19 | -0.86 | .395 |

Multi-step Arithmetic | 0.27 | 0.11 | 1.49 | .015* |

Objective Numeracy | -0.03 | 0.08 | -0.41 | .684 |

Math Anxiety | -0.14 | 0.06 | -2.42 | .018* |

Math Attitudes | -0.32 | 0.28 | -1.11 | .270 |

Subjective Numeracy | 0.26 | 0.19 | 1.36 | .177 |

*

Why might these particular math measures be associated with decision-making performance? Magnitude comparison and fraction arithmetic are strongly related to estimation precision (i.e., PAE:

Math anxiety is likely associated with decision-making performance because it interferes with math reasoning and problem solving. Math anxiety is positively related to PAE (see

The primary goal of the current study was to test the hypothesis that math-related factors that have been associated with accurate math performance in pure numerical contexts would also be associated with numeric decision-making performance in health contexts. Although health-related decisions are likely to be influenced by a variety of cognitive and affective processes that do not pertain to pure math decisions devoid of context, we anticipated that the same

These results align with previous research that points to the important role of objective mathematical competence for accurate decision making (e.g.,

Magnitude comparison and multi-step fraction arithmetic accuracy were significantly associated with health decision-making performance. Magnitude comparison (

Note that only one of the health decision-making questions used in our study was adapted from prior literature (see

Typically, in pure numerical contexts, researchers craft strategy report prompts that are very targeted (i.e.,

As with many psychology experiments, our final sample of over 180 participants was essentially a convenience sample of participants who were willing to sign up for our study through the MTurk platform. We were as vague as possible about the purpose of the study in our IRB-approved consent form. However, it is true that participants knew that our study dealt with numerical decisions, and that may have attracted a certain type of participant, namely participants who were willing to solve math problems. But, we did not disclose that participants would be asked to make decisions about rational numbers. Results from the parent study (

As indicated in

Finally, it is an open empirical question as to whether some participants reported non-math strategies in their open-ended reports because they did not want to expend the “mental effort” needed to carry out a mathematical calculation because they were fatigued at the end of the study. Non-math strategies were reported by about half of our participants; however, we did not have a formal way to assess participants’ expended effort on the decision-making task. It is possible that “mental effort” could be operationalized as the amount of time that it takes for a participant to solve each decision-making problem. However, response times may not be an unambiguous measure of mental effort. Previous research (

We cannot underscore enough that objective math skills accounted for a significant amount of variance in decision-making performance. Thus, known math misconceptions identified in “cold,” purely numerical contexts should be remediated to facilitate participants’ attempts at comprehending their risks in “hot,” real-world health contexts. For example, consider recent work by

With growing interest in precision medicine (

The R code, data file, and supplemental analyses that support the findings of this study are available on OSF:

In the supplemental logistic regression analysis, we investigated which objective and subjective math variables were associated with accurate performance on the

Half of participants completed the objective measures (in randomized order) first, and the other half of participants completed the subjective math measures first. The subjective math measures were always completed in the same order. All decision-making problems were completed at the end of the experiment prior to participants reporting their demographic information. As noted in

Objective math measures

Whole number estimation (0 to 1 billion)

0-1 fraction estimation

0-5 fraction estimation

Fraction magnitude comparison

Whole number fluency (addition, subtraction, multiplication)

Fraction arithmetic

Multi-step fraction arithmetic

Math attitudes questionnaire (MAQ)

Objective numeracy

Subjective math measures

Math attitudes

Subjective numeracy

Math anxiety

Math emotions

Emotions/seriousness ratings of health and non-health scenarios

Decision making problems (either health or non-health)

Strategy report completed after each problem

Demographics questions

The authors would like to thank Jessica Kotik and Samantha Choi for helping with the creation of the strategy coding scheme and for their help with coding a portion of the data.

The writing of this report was supported in part by U.S. Department of Education, Institute of Education Sciences Grant # R305A160295 and R305U200004.

The authors have declared that no competing interests exist.