Next, we evaluate the efficacy of the PIN reward task that exogenously imposed cognitive load on the High cognitive load treatments. In our pilot experiment sessions, we tested the treatment effect with both 6-digit PIN task and 7-digit PIN task given 20 seconds for subjects to memorize. When the PIN reward task is too simple, participants always collect the reward without taking up a sufficient part of the available cognitive resource that actually affects the performance on the inventory management task. When the PIN reward task is too difficult, participants could either decide to forgo the mental costs of trying to commit the PIN to short term memory or forgo effort in the inventory management tasks. A second concern is that raw intelligence is an omitted variable in our analysis which would manifest itself in a strong positive correlation between a participant’s performances in the PIN reward and the inventory management task. Therefore, we adjusted our design to balance the effort spent on the two concurrent tasks. In the High cognitive load treatments, participants were given 15 seconds to memorize a 6-digit PIN code. The success rates of correctly recall the PIN is at 49% for the Unrestricted treatment and 72% for the Zero Only treatment; the difference between the two treatments is significant under both t-test (p = 0.037) and non-parametric Wilcoxon rank-sum test (p = 0.038). Further, participants indicate in the post-experiment survey that they cared equally about the PIN task and the inventory management task (mean equal to 2.87 on a 1-5 scale) with no statistical differences between the two treatments (t-test, p = 0.355; Wilcoxon rank-sum test, p = 0.511). To clarify, our result is not driven by subjects’ rational allocation of attention. Firstly, as discussed in the introduction section of the current chapter, previous studies proposed that the PIN task as the instrument to impose cognitive stress in laboratory experiments. We have also discussed about our design of avoiding the PIN code being too simple or too difficult. Further, we will provide statistical analysis around the independence of PIN and inventory management task performance in the following paragraphs.
We present subjects’ total profits made in the inventory management task conditional on the
number of PIN rewards earned inFigure 7. The numbers on the top are the number of subjects
who earned the corresponding to number of PIN rewards. First, we can observe that only 3 out of 77 subjects earned less than two PIN rewards while 33 out of 77 subjects collected all five PIN rewards. Second, there is no clustering of poor inventory management performance on either high or low numbers of PIN rewards earned. This is indicating that the raw intelligence of participants is irrelevant to the performance on the PIN task and subjects are balancing the effort spent between the two concurrent tasks. Third, there is little evident difference in the conditional means of total profits; suggesting the PIN and inventory management tasks performance are independent.
We quantify the evidence of the independence of PIN and inventory management task perfor-
mance by statistically measuring their correlation and testing its statistical significance. Table 8
reports the test results of the independence of the performance on the PIN reward task and the inventory management task where the null hypotheses assume that the correlation is zero. The left portion of the table presents the correlation between the success of a PIN reward task in the year and the corresponding annual inventory profit. We find mixed evidence that
Figure 7: Participants’ total inventory management task profits conditional on the number of PIN rewards earned and the corresponding whisker plots for the 50, 75, and 95% quantiles.
1 22 10101010101010101010 999999999 22222222222222222222222222222222222222222222 333333333333333333333333333333333333333333333333333333333333333333 500 1000 1500 2000 2500
Total Inventory Task Profit
0 1 2 3 4 5
The number of correct PIN rewards earned
the correlation is not significantly from zero in all five years separately, but highly significant positive correlation when we pool all five years together. However, this part of the analysis does not allow for differences in terms of subjects’ performances on the PIN task. To address the problem, we test the correlations between the total numbers of PIN reward earned by a subject and the subject’s annual profits as well as the subject’s total profits in the inventory management task. The results are reported in the right portion of the table. From the tests results we can conclude that there is no significant correlation between the two tasks.
Table 8: Spearman correlations between PIN reward earned in a Year and the corresponding Inventory task profit; Spearman and Pearson Rank correlations between a participant’s total number of earned PIN rewards and their Inventory task profits
PIN reward eared in Year a Number of PIN reward earned Spearman Rank Corr. Pearson Corr. Spearman Rank Corr.
Annual Profit Year 1 0.08 0.13 0.11 (0.512) (0.248) (0.324) Year 2 0.12 0.08 0.11 (0.315) (0.507) (0.338) Year 3 0.21 0.10 0.04 (0.072) (0.391) (0.750) Year 4 0.09 0.15 0.04 (0.459) (0.182) (0.725) Year 5 0.14 0.10 0.14 (0.226) (0.379) (0.218)
All Years 0.18 N/A N/A
(0.001) N/A N/A
Total Profit N/AN/A (0.120)0.179 (0.114)0.182
1. The p-values of the respective tests are reported in the parenthesis.
2. We don’t report the correlations for Total Profit in column three because the calculation will include multiple repetitions of a participant’s total inventory profit.
3. We don’t report the correlations for all Years in columns for and five because the calculation will include multiple repetitions of a participant’s total number of PIN rewards.