Exploring the data

First I’ll load data as a new object called priming. Experimental studies of human decision making in iterated tasks reveal a general tendency to respond to immediate feedback in an adaptive fashion. In line with the law of effect (Thorndike, 1898), the probability of successful responses tends to increase with time. Nevertheless, under certain conditions, human adaptation does not ensure maximization. Early research demonstrated robust devia- tions from maximization that can be summarized with the proba- bility matching assumption (see Estes, 1950, and our discussion below). Under this assumption, the proportion of time an alterna- tive is selected is identical with the proportion of time in which this alternative provides the best outcome.

The main goal of the current research is to improve our under- standing of the relationship between adaptation and maximization. In particular, we try to integrate the knowledge accumulated in early studies of probability matching with observations drawn from more recent studies of decisions from experience (e.g., Bar- ron & Erev, 2003; Busemeyer, 1985). We focus on simple situa- tions in which decision makers (DMs) repeatedly face the same binary choice problem and receive immediate feedback after each Ido Erev, Max Werthiemer Minerva Center for Cognitive Studies, Faculty of Industrial Engineering and Management, Technion–Israel Insti- tute of Technology, Haifa, Israel; Greg Barron, Negotiations, Organiza- tions, and Markets Unit, Harvard Business School.

Part of this research was conducted when Ido Erev was a visiting professor at Columbia Business School. This research was supported by a grant from the National Science Foundation and the USA.–Israel Bina- tional Science Foundation. We thank Ernan Haruvy, Al Roth, Yoav Gan- zach, Meira Ben-Gad, and the subjects of seminars at Harvard University, Columbia University, New York University, the University of Michigan, the University of Chicago, and the University of Maryland for useful comments. Correspondence concerning this article should be addressed to Ido Erev, Max Werthiemer Minerva Center for Cognitive Studies, Faculty of Indus- trial Engineering and Management, Technion, Haifa, Israel. E-mail: erev@tx.technion.ac.il choice. The main results of the current analysis are summarized in four sections.

# Sometimes this code will give you an error starting with "scan". If so, just run it again and it will work
priming <- read.table(file = "http://nathanieldphillips.com/wp-content/uploads/2016/04/priming-5.txt",
                      sep = "\t",
                      header = T)

Here are the first few rows of the data. In the first section, we review the known deviations from maximization and show that they can be attributed to three distinct effects. One set of deviations can be classified as indicating a payoff variability effect (Busemeyer & Townsend, 1993; Myers & Sadler, 1960): An increase in payoff variability seems to move choice behavior toward random choice. A second set of deviations indicates underweighting of rare events (Barron & Erev, 2003): DMs tend to prefer the alternative that provides the best payoff most of the time, even when this alternative is associated with a lower expected return. A third set of deviations involves loss aversion (see Kahneman & Tversky, 1979): In certain cases, subjects tend to prefer alternatives that minimize losses over those that maximize payoffs.

head(priming)
##   sex age   prime time donate favorite.number
## 1   f  21 elderly 12.9      0              75
## 2   m  25 elderly 10.7      0              80
## 3   m  21 elderly 10.5      1              71
## 4   m  25 elderly  8.6      0              79
## 5   f  22 elderly 11.5      1              66
## 6   f  22 elderly 10.6      1              69

The third paradigm is a variant of the minimal information paradigm with more complete feedback. After each choice, the DM is presented with random values drawn from the payoff distributions of each of the two buttons—but payoffs are deter- mined on the basis of the value of the selected button. The additional feedback is often referred to as information concerning forgone payoffs. A typical trial in this complete feedback paradigm is presented in the right column of Figure 1.

summary(priming)
##  sex         age            prime         time           donate    
##  f:45   Min.   :17.00   elderly:50   Min.   : 7.50   Min.   :0.00  
##  m:55   1st Qu.:21.00   neutral:50   1st Qu.: 9.50   1st Qu.:0.00  
##         Median :22.00                Median :10.25   Median :0.00  
##         Mean   :21.98                Mean   :10.21   Mean   :0.48  
##         3rd Qu.:23.00                3rd Qu.:10.90   3rd Qu.:1.00  
##         Max.   :28.00                Max.   :12.90   Max.   :1.00  
##  favorite.number
##  Min.   :56.00  
##  1st Qu.:68.00  
##  Median :71.50  
##  Mean   :71.51  
##  3rd Qu.:75.00  
##  Max.   :86.00

Plotting

To demonstrate the observed deviations from maximization,2 we summarize in the current section the results of 40 experimental conditions, each of which involves at least 200 trials. To facilitate an efficient summary of this large set of data, we focus our analysis on the aggregate proportion of maximization in blocks of 100 trials.

library(yarrr)

Notice that the difference between Problems 1 and 3 appears to reflect risk aversion (H is less attractive when its payoff variability increases), but the difference between Problems 1 and 2 appears to reflect risk-seeking behavior (L is more attractive when its payoff variability increases).

pirateplot(formula = time ~ prime,
           data = priming)

Statistics

Notice that the difference between Problems 1 and 3 appears to reflect risk aversion (H is less attractive when its payoff variability increases), but the difference between Problems 1 and 2 appears to reflect risk-seeking behavior (L is more attractive when its payoff variability increases).

# Run the t-test
testA <- t.test(formula = time ~ prime,
           data = priming)

# Print the output
testA
## 
##  Welch Two Sample t-test
## 
## data:  time by prime
## t = 4.6412, df = 97.576, p-value = 1.079e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.5071494 1.2648506
## sample estimates:
## mean in group elderly mean in group neutral 
##                10.648                 9.762

A t-test comparing the walking times by condition was significant showing that people given the elderly prime had longer walking times than those given a neutral prime: t(97.58) = 4.64, p < .01