# About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Participants

#### 2.2. Procedure

## 3. Data Analysis

^{2}statistic [40]. In the third phase (Multivariate Effects) we explored the combined effects of the two experimental factors (i.e., group effect and strategy of reasoning), by means of a logistic regression analysis [41]. In the fourth phase we ran a discriminant analysis [42], linking the narrative dimensions taken by means of the LIWC software analysis to the group effect, the expressed strategy of reasoning and the answer correctness. Finally, a t test [43] has been carried out in order to predict the group effect, comparing the individual group discussion. All the analysis has been carried out adopting the SPSS Version 22.0 software [44].

## 4. Results

^{2}= 0, 06; p = 0, 80; Gender: χ

^{2}= 0, 16; p = 0.69; Education: χ

^{2}= 6.82; p = 0.08) and on the mode of thought expressed in the narrative format of the answer conditions (Age: χ

^{2}= 1.22; p = 0.27; Gender: χ

^{2}= 1.57; p = 0.21; Education: χ

^{2}= 2.80; p = 0.42). Once we assessed such a fact, not excluding that such no significant effects are due to the sample size (in particular for what concerns Education), we proceeded with the inferential analysis studying the experimental condition effects on the answers correctness.

#### 4.1. Experimental Conditions Effect

^{2}analysis, thus considering in this first approximation just the main effects (i.e., without considering the combined effects) (Table 2).

^{2}= 22.653, p < 0.01), with the group factor explaining a smaller portion of variance (χ

^{2}= 9.189, p < 0.01). The subsequent analysis investigated the relation between the experimental conditions and the adopted strategy of reasoning. Of course, the sample used to assess such strategies, which is a property measurable only with the open format of response, was composed by the half of the sample (60ss).

#### 4.2. Narrative Strategy: Group Factor vs Correctness

^{2}= 4.57, p < 0.05), in particular again the group condition (correctness of 38.1%) appears to be more efficient than the individual condition (11.5%).

#### 4.3. Multivariate Analysis

#### 4.4. T Test LIWC vs Individual/Group Discussion

#### 4.5. Discriminant Analysis

#### 4.5.1. Model 1: Prediction of the Narrative Style of the Answer (Narrative vs Paradigmatic Strategy of Reasoning)

^{2}= 58.32) and a canonical correlation of 0.80 as described in Table 5. For each parameter, the table reports Wilks Lambda in order to show its significance and its coefficient in the discriminant function. The parameters emerged from the LIWC analysis (Table 6) show a significant effect in predicting a paradigmatic strategy for: Use of numbers, use of words expressing tentative, anxiety or feelings and the use of conditional verbs (e.g., “I choose the “A” option: In the text provided there are no specification on Linda’s job. The probability of option “A” to be right is higher because that option has just one hypothesis, while option “B” has two”). LIWC analysis also show a significant effect for the use of 3rd singular verbs, words expressing positive emotions and words referred to act of seeing (i.e., in the Italian language the verb to see is frequently used in a figurative form indicating the evidence of something) in predicting the use of a narrative strategy (e.g., “Linda is a professor at the faculty of Philosophy. She also had a political role in her city. She chose not to marry to maintain her role in defending woman’s rights and the ecologist cause”). The degree of accuracy of the discriminant function correctly identifies the 97.9% of the paradigmatic answers, and the 87.5% of the narrative answers, providing both a way to identify the “cognitive style” used to answer the question, as well as some antecedents of the answers.

#### 4.5.2. Model 2: Prediction of the Correctness of the Answer (Individual Mode)

^{2}=8.767) and a canonical correlation of 0.503 as described in Table 7.

#### 4.5.3. Model 3: Prediction of the Correctness of the Answer (Group Elaboration Mode)

^{2}= 21.149) and a canonical correlation of 0.741 as described in Table 9.

#### 4.5.4. Model 4: Prediction of the Correctness of the Answer (Narrative Mode of Thought)

^{2}= 4.821) and a canonical correlation of 0.320 as described in Table 11.

#### 4.5.5. Model 5: Prediction of the Correctness of the Answer (Paradigmatic Mode of Thought)

^{2}= 19.472) and a canonical correlation of 0.888 as described in Table 13.

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The subfigures reported show the absolute frequencies of right and wrong answers with. respect to the three main order parameters defined by our study. In particular: The subfigure (

**a**) highlights the difference in subjects performance with respect to the experimental condition “group factor” and 231 in the subfigure (

**b**) with respect to the adopted strategy of reasoning.

**Figure 2.**In figure is reported the relation between the answers correctness and the group factor, Only for the narrative strategy (n = 60).

**Table 1.**Table are reported the subsamples size, showing the number of different subjects assigned to each experimental condition.

Format of Answer | |||
---|---|---|---|

Multiple C. | Open | Tot. | |

Group factor Alone | 30 | 30 | 60 |

Group | 30 | 30 | 60 |

Total | 60 | 60 | 120 |

**Table 2.**Table are reported the χ

^{2}tests assessing the significant differences in the relations between the order parameter (i.e., the answers correctness) and the control parameters of our study: The social condition (i.e., alone vs group of three subjects) in which the answer was elaborated/discussed, and the strategy of reasoning expressed in the open-ended answers.

General Effect | Condition | % of Corr. | χ^{2} | Sig. |
---|---|---|---|---|

Group | Alone | 12.1% | 9.189 | p < 0.01 |

Group | 46.7% | |||

Strategy of reasoning | Paradigmatic | 75% | 22.653 | p < 0.01 |

Narrative | 12.8% |

**Table 3.**Reports the parameters of the best multiple logistic model, describing the effects due to the group factor combined with the strategy of reasoning factor (i.e., only for the open-ended answer), on the answers correctness, (n = 60).

Factor | β | Wald | Sig. |
---|---|---|---|

Group | −2.867 | 6.675 | p < 0.05 |

Strategy of reasoning | −3.899 | 12.230 | p < 0.01 |

**Table 4.**Test LIWC vs group discussion/individual elaboration. *: The statistic is significant at a level of p < 0.05, **: The statistic is significant at a level of p < 0.01.

Group Factor | Mean | Std. Dev. | t |
---|---|---|---|

WC Individual | 47.85 | 19.43 | −2.257 * |

Group | 62.07 | 29.92 | |

SixItr Individual | 28.21 | 6.91 | −2.608 ** |

Group | 32.70 | 6.75 | |

IIndividual | 1.43 | 2.04 | 2.507 * |

Group | 0.41 | 0.90 | |

Possib Individual | 1.97 | 1.84 | −2.812 ** |

Group | 3.81 | 3.22 |

**Table 5.**Table is reported the general statistics for the first discriminant model (Model 1). In this phase we wanted to predict the Narrative/Paradigmatic strategy by the data emerged from the LIWC analysis.

Wilks Lambda | χ^{2} | Sign. | Canonical Correlation | |
---|---|---|---|---|

Model 1 | 0.359 | 58.32 | p < 0.01 | 0.80 |

**Table 6.**Table is reported the best discriminant function linking the the variables representing narrative dimensions taken by means of LIWC software analysis with the strategy of reasoning (i.e., narrative vs paradigmatic answer). *: The statistic is significant at p < 0.01.

Parameter | Wilks Lambda | Coefficient |
---|---|---|

Number | 0.831 * | 0.538 |

Tentative | 0.698 * | 0.810 |

Anxiety | 0.559 * | 0.676 |

Feel | 0.504 * | 0.513 |

3rd Singular Verb | 0.467 * | −0.531 |

Pos. Emotion | 0.420 * | −0.378 |

See | 0.390 * | −0.415 |

Conditional verb | 0.359 * | 0.379 |

**Table 7.**Table is reported the general evaluation of the third discriminant model. In this phase we wanted to predict the correctness of the answer (Right vs. Wrong answer) by the data emerged from the LIWC analysis on the individual elaboration game mode.

Wilks Lambda | χ^{2} | Sign. | Canonical Correlation | |
---|---|---|---|---|

Model 3 | 0.747 | 8.767 | p < 0.01 | 0.503 |

**Table 8.**In table is reported the best discriminant function linking the variables representing the narrative dimensions taken by means of LIWC software analysis with the correctness of the answer (i.e., right vs wrong) on the individual elaboration game mode. *: The statistic is significant at p < 0.01.

Parameter | Wilks Lambda | Coefficient |
---|---|---|

Social | 0.747 | −0.792 |

Self | 0.858 | 1.037 |

**Table 9.**Table is reported the general evaluation of the fourth discriminant model. In this phase we wanted to predict the correctness of the answer (Right vs. Wrong answer) by the data emerged from the LIWC analysis on the group discussion game mode.

Wilks Lambda | χ^{2} | Sign. | Canonical Correlation | |
---|---|---|---|---|

Model 4 | 0.450 | 21.149 | p < 0.01 | 0.741 |

**Table 10.**Table is reported the best discriminant function linking the variables representing the narrative dimensions taken by means of LIWC software analysis with the correctness of the answer (i.e., right vs wrong). *: The statistic is significant at p < 0.01.

Parameter | Wilks Lambda | Coefficient |
---|---|---|

Present | 0.563 | −0.860 |

Future | 0.450 | 0.640 |

Transitive | 0.745 | 0.892 |

**Table 11.**Table is reported the general evaluation of the fourth discriminant model. In this phase we wanted to predict the correctness of the answer (Right vs. Wrong answer) by the data emerged from the LIWC analysis on answers using a narrative mode of thought.

Wilks Lambda | χ^{2} | Sign | Canonical Correlation | |
---|---|---|---|---|

Model 5 | 0.897 | p < 0.05 | 0.320 |

**Table 12.**Table is reported the best discriminant function linking the variables representing the narrative dimensions taken by means of LIWC software analysis with the correctness of the answer (i.e., right vs wrong) on the answers provided using a narrative mode of thought. *: The statistic is significant at p < 0.01.

Parameter | Wilks Lambda | Coefficient |
---|---|---|

Future | 0.914 | 0.787 |

Conditional | 0.822 | 0.762 |

**Table 13.**Table is reported the general evaluation of the fourth discriminant model. In this phase we wanted to predict the correctness of the answer (Right vs. Wrong answer) by the data emerged from the LIWC analysis on answers using a paradigmatic mode of thought.

Wilks Lambda | χ^{2} | Sign. | Canonical Correlation | |
---|---|---|---|---|

Model 6 | 0.211 | 19.472 | p < 0.01 | 0.888 |

**Table 14.**In table is reported the best discriminant function linking the variables representing the narrative dimensions taken by means of LIWC software analysis with the correctness of the answer (i.e., right vs wrong). *: The statistic is significant at p < 0.01.

Parameter | Wilks Lambda | Coefficient |
---|---|---|

Future | 0.914 | 0.787 |

Conditional | 0.822 | 0.762 |

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## Share and Cite

**MDPI and ACS Style**

Donati, C.; Guazzini, A.; Gronchi, G.; Smorti, A.
About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy. *Future Internet* **2019**, *11*, 210.
https://doi.org/10.3390/fi11100210

**AMA Style**

Donati C, Guazzini A, Gronchi G, Smorti A.
About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy. *Future Internet*. 2019; 11(10):210.
https://doi.org/10.3390/fi11100210

**Chicago/Turabian Style**

Donati, Camillo, Andrea Guazzini, Giorgio Gronchi, and Andrea Smorti.
2019. "About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy" *Future Internet* 11, no. 10: 210.
https://doi.org/10.3390/fi11100210