Table 3.
Means and median probability estimates in Experiment 2
| Probability estimates | ||
|---|---|---|
| Itemsa | Mean (%)b | Median (%) |
| Group 1 (N = 104 c): | ||
| Linda is a bank teller. (T) | 13.3 (1.2) | 10 |
| Linda is active in the feminist movement. (F) | 78.1 (1.8) | 80 |
| Linda takes Yoga classes. (Y) | 42.0 (2.2) | 50 |
| Linda is a teacher in elementary school. (P) | 17.7 (1.5) | 15 |
| Linda is a bank teller and is active in the feminist movement. (T ∧ F) | 30.2 (2.5) | 30 |
| Linda takes Yoga classes and is a teacher in elementary school. (Y ∧ P) | 22.3 (2.1) | 15.5 |
| T ∧ F interpreted as an intersection.c (n = 54) | 27.9 (2.9) | 30 |
| T ∧ F interpreted as two separations.c (n = 9) | 12.3 (4.3) | 10 |
| T ∧ F interpreted as neither an intersection nor two separations.c (n = 40) | 41.7 (4.5) | 40 |
| Group 2 (N = 37): | ||
| Linda is a bank teller. (T) | 32.2 (4.2) | 30 |
| Linda is active in the feminist movement. (F) | 67.5 (3.8) | 70 |
| Linda is an executive. (D) | 39.9 (4.3) | 40 |
| Linda subscribes to a popular liberal magazine. (M) | 72.0 (3.8) | 80 |
| Linda is a bank teller and is active in the feminist movement. (T ∧ F) | 38.6 (4.2) | 40 |
| Linda is an executive and subscribes to a popular liberal magazine. (D ∧ M) | 49.8 (4.1) | 50 |
| T ∧ F interpreted as an intersection.c (n = 23) | 35.7 (6.1) | 20 |
| T ∧ F interpreted as two separations.c (n = 6) | 31.7 (7.9) | 35 |
| T ∧ F interpreted as neither an intersection nor two separations.c (n = 7) | 21.4 (5.5) | 10 |
| Group 3 (N = 41): | ||
| Linda is an avid reader. (R) | 72.1 (2,8) | 80 |
| Linda is active in the feminist movement. (F) | 72.2 (2.9) | 80 |
| Linda is an executive. (D) | 40.0 (3.0) | 40 |
| Linda subscribes to a popular liberal magazine. (M) | 68.6 (3.5) | 75 |
| Linda is an avid reader and is active in the feminist movement. (R ∧ F) | 66.9 (3.1) | 70 |
| Linda is an executive and subscribes to a popular liberal magazine. (D ∧ M) | 44.5 (3.3) | 50 |
| R ∧ F interpreted as an intersection.c (n = 24) | 70.4 (3.9) | 80 |
| R ∧ F interpreted as two separations.c (n = 6) | 73.3 (8.4) | 75 |
| R ∧ F interpreted as neither an intersection nor two separations.c (n = 10) | 77.5 (3.9) | 80 |
| Group 4 (N = 42): | ||
| Linda is a bank teller. (T) | 24.3 (3.2) | 20 |
| Linda is very shy. (S) | 11.7 (2.3) | 7 |
| Linda is a teacher in elementary school. (P) | 43.7 (4.5) | 50 |
| Linda is active in crafts like needlepoint. (C) | 31.2 (3.7) | 20 |
| Linda is a bank teller and is very shy. (T ∧ S) | 15.2 (2.8) | 10 |
| Linda is a teacher in elementary school and is active in crafts like needlepoint. (P ∧ C) | 31.4 (3.6) | 30 |
| T ∧ S interpreted as an intersection.c (n = 25) | 17.1 (3.7) | 10 |
| T ∧ S interpreted as two separations.c (n = 11) | 14.6 (6.4) | 0 |
| T ∧ S interpreted as neither an intersection nor two separations.c (n = 4) | 10.0 (5.4) | 7.5 |
aIn the version given to participants, the labels P, F, T, Y, R, S, M, C, D, T ∧ F, Y ∧ P, D ∧ M, R ∧ F, T ∧ S and P ∧ C were omitted
bStandard errors with 95 % confidence intervals are in parentheses. Boldface indicates a significant difference, relative to the conjunctions and their corresponding unlikely constituents (p < .05)
cBased on respondents’ choices in the Venn diagram task. Respondents were regarded as providing an intersection, a disjunction, or neither an intersection nor a disjunction interpretation when they chose respectively Option C, B, or any other option except for Option C and B in Fig. 2. There are so many more participants in Group 1 because Experiment 2 was conducted firstly through Group 1, however, the likelihood types of the Group 1’s statements are mostly the likelihood type of “Unlikely ∧ Likely” and have not enough data in relation to the types of “Likely ∧ Likely” and “Unlikely ∧ Unlikely”. On the other hand, some studies indicate that the conjunction fallacies are related to the likelihood types (e.g., Fantino et al. 1997; Nilsson et al. 2009; Tversky and Kahneman 1983; Yates and Carlson 1986) and that more conjunction fallacies should be happened in the likelihood type of “Unlikely ∧ Likely” rather than the likelihood types of “Unlikely ∧ Unlikely” and “Likely ∧ Likely” (e.g., Fisk 1996; Yates and Carlson 1986). Thereof, in order to examine the second prediction of the current paper, “Likely ∧ Likely” and “Unlikely ∧ Unlikely” combinations of likelihood types of the statements through latter three Groups are thereafter included. Needed numbers of the latter three Groups’ participants are employed to generate much more needed likelihood types