13.39 Trust of individuals and groups. Trust is an essential element in any exchange of goods or services. The following trust game is often used to study trust experimentally:
A sender starts with $X and can transfer any amount x ≤ X to a responder. The responder then gets $3x and can transfer any amount y ≤ 3x back to the sender. The game ends with final amounts X − x + y and 3x − y for the sender and responder, respectively.
The value x is taken as a measure of the sender’s trust, and the value y/3x indicates the responder’s trustworthiness. A recent study used this game to study the dynamics between individuals and groups of three.23 The following table summarizes the average amount x sent by senders starting with $100:
| Sender | Responder | n | s | |
|---|---|---|---|---|
| Individual | Individual | 32 | 65.5 | 36.4 |
| Individual | Group | 25 | 76.3 | 31.2 |
| Group | Individual | 25 | 54.0 | 41.6 |
| Group | Group | 27 | 43.7 | 42.4 |
(a) Find the pooled estimate of the standard deviation for this study and its degrees of freedom.
(b) Is it reasonable to use a pooled standard deviation for the analysis? Explain your answer.
(c) Compute the marginal means.
(d) Plot the means. Do you think there is an interaction? If yes, describe it.
(e) The F statistics for sender, responder, and interaction are 9.05, 0.001, and 2.08, respectively. Compute the P-values and state your conclusions.
| Type of pot | Meat | Legumes | Vegetables | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Aluminum | 1.77 | 2.36 | 1.96 | 2.14 | 2.40 | 2.17 | 2.41 | 2.34 | 1.03 | 1.53 | 1.07 | 1.30 |
| Clay | 2.27 | 1.28 | 2.48 | 2.68 | 2.41 | 2.43 | 2.57 | 2.48 | 1.55 | 0.79 | 1.68 | 1.82 |
| Iron | 5.27 | 5.17 | 4.06 | 4.22 | 3.69 | 3.43 | 3.84 | 3.72 | 2.45 | 2.99 | 2.80 | 2.92 |