3.2.1. Method
Participants. Ninety-seven undergraduate students (32 males, 65 females) enrolled in General Psychology at Mississippi State University who had not participated in the previous experiment participated in Experiment II. All students were native English speakers and received course credit upon completion of the experiment. The number of participants was again chosen via a power analysis with the goal of achieving a power of 0.80 for detecting medium-to-large effect sizes using multiple linear regression with three predictor variables (
Cohen, 1992) and represented a convenience sample. This study was reviewed and approved by the Mississippi State University IRB. All participants volunteered and provided written consent to participate.
Materials. Participants completed five tasks, all of which were presented on desktop computers, with the total running time for all tasks lasting up to an hour and a half. In addition to a more elaborate sentences task, participants completed a creative problem-solving task (the anagrams task), an analytic problem-solving task (the modular arithmetic task), a gF task (figural analogies), and a complex WMC span task (symmetry span). Participants completed each task in the fixed order described, and items within each task were randomized and varied in difficulty. Accuracy and response times were recorded for all items in each task.
The Sentences Task. The sentences task in Experiment II included both locally and globally ambiguous sentences, as well as control sentences matched in structure to each of these two types of ambiguity (see
Table 4 for examples). Locally ambiguous and locally non-ambiguous sentence comprehension were assessed using an abbreviated Garden Path Task from Experiment I—participants provided truth-value judgments for 12 locally ambiguous garden path sentences and a randomly chosen, counterbalanced subset (24) of the previously used non-ambiguous control sentences (garden path control). Comprehension was assessed using the same truth-value statements and judgment process used in Experiment I.
Also embedded within the sentences task were 12 globally ambiguous sentences, as measured by relative clause (RC) ambiguous sentences (adapted from
Swets et al., 2007), in which a relative clause can correctly attach to one of two preceding noun phrases and thus result in two correct, but different, interpretations of the sentence. In accordance with the good-enough model of comprehension, readers should therefore consider their initial interpretations of these RC ambiguous sentences acceptable and should not require resolution processes, as locally ambiguous garden path sentences do. Finally, a set of non-ambiguous control sentences (24) matched in structure to the RC ambiguous sentences were also included. For these RC control sentences, a verb phrase was presented between two noun phrases before the relative clause, making it clear which of the two noun phrases the following relative clause referenced.
Because the ambiguous RC sentences maintained two viable interpretations, the truth-value comprehension measure used for locally ambiguous sentences would be inappropriate. Therefore, after reading and fully comprehending a sentence of this type, participants were shown a multiple-choice style statement with three response options from which to choose the correct answer. Six of these multiple-choice statements asked about which noun phrase the relative clause should attach to, with the first two options referring to each of the two noun phrases and the third option suggesting that both of the first two options could be correct. For example, for the sentence, “The sister of the schoolgirl who burned herself the other day was usually very careful,” the comprehension measure stated “___ burned herself the other day? 1. Sister 2. Schoolgirl 3. Both 1 and 2 could be correct.” For these six “RC-True” ambiguous sentences, the third option was considered the correct answer, as the relative clause could relate to either the sister or the schoolgirl. The remaining six multiple-choice statements provided a counterbalanced condition, in which the comprehension measure asked which noun phrase a non-ambiguous part of the sentence—the final verb phrase—referenced. For example, for the sentence, “The sister of the actress who shot herself on the balcony was under investigation,” the comprehension measure was “___ was under investigation? 1. The sister 2. The actress 3. Both 1 and 2 could be correct.” For these six “RC-NP1” ambiguous sentences, the multiple-choice statements emphasized the role of the first noun phrase, so the first option was considered the correct answer for these sentences. Counterbalancing the comprehension measure in this way therefore allowed for a better understanding of a person’s ability to not only notice true global ambiguities (RC-True) but also to correctly attach non-ambiguous parts of the globally ambiguous sentences (RC-NP1), providing a robust measure of a person’s ability to appropriately grapple with the multiple meanings within a globally ambiguous sentence. Accuracies on all 12 of these sentences were combined into a single score and were analyzed together for this reason. For the 24 RC control sentences, the multiple-choice questions were counterbalanced, such that half of the questions referred to the first noun phrase and the other half referred to the second noun phrase.
In all, participants viewed 72 test sentences, divided among four conditions: locally ambiguous garden path sentences (12), globally ambiguous RC sentences (12), non-ambiguous garden path control sentences (24), and non-ambiguous RC control sentences (24). Items within all four conditions were randomized in the sentences task, so participants were prompted to respond differently for the garden path sentences than for the RC sentences. Participants viewed and responded to five example sentences (one garden path, two garden path control, one RC ambiguous, and one RC control) before starting the task to familiarize themselves with the procedure.
The Anagram Task. The anagram task’s materials and procedure were identical to that in Experiment I, with the exception of correcting an item with a typo.
The Modular Arithmetic Task. The modular arithmetic task used adapted materials and procedures from
Beilock and DeCaro (
2007). The modular arithmetic task assesses mathematical problem-solving ability and is novel to most participants. The goal of the task is to determine whether the remainder of a modular equation (e.g., 42 = 20(
mod 11)) is a whole number. A simple algorithm can be used to derive the solution and make a validity judgment: first, the second number should be subtracted from the left-hand side (42 − 20 = 22); next, the difference from the first step should be divided by the modular number (22/11 = 2). If the remainder is a whole number, as in the example provided, the participant would respond with “T” for “true.” For equations resulting in remainders (e.g., 59 = 15(
mod 8) = 5.5), participants would respond with “F” for “false.” Problems represented a range of difficulty and were counterbalanced for validity judgments. Participants solved six practice problems and 48 test problems and were scored for the proportion of correct items.
The Figural Analogies Task. The figural analogies task used materials and procedures from
Lohman and Hagen (
2001) and served as a measure of gF for this study. Participants solved 25 test problems of the form “A is to B as C is to ___,” where A and C are figures of relatively simple shapes that undergo various transformation rules (e.g., rotation, flip, change in size, etc.) to produce B and D. The solver must determine the transformation rule that is demonstrated by A:B and apply it to the relationship between C and the unknown figure. Participants then chose the correct answer from five possible response options presented in a response bank next to the problem. Participants had 10 min to solve as many of the 25 problems as possible before the task timed out.
The Symmetry Span Task. The symmetry span task used materials and procedures from
Unsworth et al. (
2009). The task consisted of two intervening components within a single trial: a processing task and a memory task. The processing task required participants to determine whether a pattern of shaded squares in an eight-by-eight array was vertically symmetrical. Afterwards, the memory task required participants to remember a single shaded square in a four-by-four array. At the end of a trial, which ranged between two and five items, participants clicked the to-be-remembered squares in a blank four-by-four array in the correct serial order in which they were presented. The entire task consisted of three iterations of each trial length. The task was scored as the average proportion of squares recalled in the correct serial position (regardless of item size) across all trials (i.e., partial-credit unit scoring;
Conway et al., 2005).
Procedure. Participants were seated in a testing room at a desktop computer. After providing written informed consent, the experimenter provided participants with general instructions about the tasks to be completed. The experimenter also loaded and started each of the tasks for every participant. Upon completion of the experiment, participants were individually thanked, debriefed, and dismissed.
3.2.2. Results
Initial Analyses. See
Table 5 for descriptive statistics and
Table 6 for Pearson’s correlations of task accuracy. Accuracy on the anagrams task and the figural analogies task significantly correlated with all tasks administered, including each of the four sentence types in the sentences task. Modular arithmetic significantly correlated with all tasks except symmetry span and all sentence types except for garden path sentences. Symmetry span did not significantly correlate with any tasks except for figural analogies and anagrams. Once again, there was lower reliability for garden path sentences (both control and ambiguous versions). This may suppress correlations with those variables.
Initial analyses indicated that garden path and RC sentences behaved similarly.
Table 6 demonstrates that the correlations between garden path and RC sentences were comparable in predicting anagram accuracy. Though unexpected, this may be attributable to the way comprehension was assessed for RC sentences. It is likely that the third response option on the RC comprehension measure (i.e., “Both a and b could be correct”) highlighted the fact that two interpretations of a sentence were possible. This in turn altered participants’ reading strategies, forcing them to restructure rather than accept their initial interpretation to make the most well-informed response. Because participants seemed to restructure on RC sentences, garden path and RC sentence comprehension scores were normalized and averaged into a composite ambiguous sentence comprehension score for each person. Similarly, garden path control and RC control sentences were combined into a composite control sentence comprehension score. For simplicity of reporting results, analyses will focus on these composite sentence comprehension scores. However, it is worth noting that these variables were combined primarily as a data-reduction technique, to provide simplified analyses that may be easier to interpret. A major concern is that these measures do, in fact, interact differently with problem-solving. As such, abbreviated analyses separating by sentence type are highlighted and briefly discussed as well.
Creative Problem Solving. As a manipulation check, a partial correlation between anagram accuracy and composite ambiguous sentence accuracy was conducted, controlling for modular arithmetic performance. When controlling for modular arithmetic performance, anagram accuracy significantly correlated with composite ambiguous sentence accuracy, r(95) = 0.41, p < .001. When correlating ambiguous sentence comprehension with modular arithmetic performance and controlling for anagram accuracy, there was no significant correlation, r(95) = 0.05, p = .66. This suggests that anagram performance is indeed measuring variance related to ambiguous sentence comprehension, over and above performance on a standard analytic problem-solving task.
To address the question of whether ambiguous sentences uniquely predict creative problem solving, two hierarchical linear regressions were conducted with anagram performance as the dependent variable. The first model included WMC in the first step, and the second model included gF in the first step. Composite control and ambiguous sentences were entered into the second and third steps (respectively) for both models. This ordering of variables provides the strictest test of the hypotheses, in that the general constructs’ variance is accounted for first, followed by the control variable, and only then is the variable of interest entered into the equation. Thus, a significant R
2 change represents significant variance being explained by ambiguous sentence processing after controlling for all other variables. The results of the first model, which accounted for WMC in the first step, are presented in
Table 7. The results of the second model, which accounted for gF in the first step, are presented in
Table 8. VIF indices of all variables in each model were less than 1.5, suggesting no issues due to multicollinearity.
As
Table 7 and
Table 8 demonstrate, after controlling for a person’s WMC and propensity for understanding non-ambiguous sentences, the ability to recognize and overcome ambiguity was a unique predictor of creative problem solving, explaining 9% additional variance in the model (ΔR
2 = 0.09; a moderate increase). Similarly, when controlling for a person’s gF and ability to understand non-ambiguous sentences, the ability to recognize and overcome ambiguity was uniquely predictive of creative problem solving, explaining 5% additional variance (ΔR
2 = 0.05; a small increase).
Variants of these models were re-run with the composite sentence variables separated by sentence type (garden path and RC), and the results mirror those of the composite models almost exactly. Indeed, both garden path sentence resolution (ΔR2 = 0.06, B = 0.26, t (96) = 2.64, p = .010, 95% CI = [0.064, 0.458]) and RC sentence comprehension (ΔR2 = 0.10, B = 0.90, t (96) = 3.48, p = .001, 95% CI = [0.388, 1.416]) uniquely predicted creative problem-solving performance, even after accounting for WMC and the ability to understand the control sentences of each type. Similarly, RC sentence comprehension uniquely predicted creative problem-solving performance, after accounting for gF and RC control sentences (ΔR2 = 0.05, B = 0.66, t (96) = 2.60, p = .011, 95% CI = [0.156, 1.162]). However, garden path sentence resolution was no longer a unique predictor of creative problem solving when accounting for gF and garden path control sentences (ΔR2 = 0.02, B = 0.18, t (96) = 1.83, p = .070, 95% CI = [−0.015, 0.369]).
To further elucidate these results, models were re-run with RC-True sentence accuracy (which required addressing ambiguity to respond) or RC-NP1 sentence accuracy (which did not) entered in the final step. When accounting first for WMC and then RC control accuracy, RC-True sentences predicted unique variance in creative problem-solving (ΔR2 = 0.05, B = 0.23, t (96) = 2.42, p = .017, 95% CI = [0.040, 0.409]) but RC-NP1 sentences did not (ΔR2 = 0.00, B = −0.007, t (96) = −0.08, p = .941, 95% CI = [−0.203, 0.189]). The same result was found when accounting for gF: RC-True sentences predicted unique variance in creative problem-solving (ΔR2 = 0.03, B = 0.17, t (96) = 2.02, p = .046, 95% CI = [0.003, 0.345]), but RC-NP1 sentences did not (ΔR2 = 0.001, B = −0.03, t (96) = −0.30, p = .765, 95% CI = [−0.207, 0.153]).
Analytic Problem-Solving. Although the models above demonstrate that ambiguous sentence comprehension uniquely predicts creative problem solving even after accounting for individual difference variables known to be important for reading comprehension, it is necessary to demonstrate that ambiguous sentence comprehension is not predictive of
all types of problem solving. Because restructuring should not be involved in routine, analytic problem solving (
DeCaro et al., 2016;
Fleck, 2008;
Lavric et al., 2000;
Schooler et al., 1993;
Wiley and Jarosz, 2012), the data must also be able to demonstrate that ambiguous sentence comprehension is predictive of
only creative problem solving and not of analytic problem solving. Thus, two hierarchical linear regressions were again conducted, but with modular arithmetic performance as the dependent variable, and with composite control sentence comprehension and composite ambiguous sentence comprehension as the second and third steps (respectively). Congruent with the prior analyses, the first model included WMC in the first step, and the second model included gF in the first step. The results of the first model, which accounted for WMC in the first step, are presented in
Table 9. The results of the second model, which accounted for gF in the first step, are presented in
Table 10.
As
Table 9 and
Table 10 demonstrate, after controlling for a person’s WMC and propensity for understanding non-ambiguous sentences, the ability to recognize and overcome ambiguity was not predictive of analytic problem solving. Similarly, when controlling for a person’s gF and ability to understand non-ambiguous sentences, the ability to recognize and overcome ambiguities was again not predictive of analytic problem solving. In both cases, the ΔR
2 was less than 0.01, suggesting virtually no additional variance was explained. Because the hypotheses relating to these analyses predicted a null result, a Bayesian analysis was also conducted. WMC and control sentence accuracy were added to the null model predicting modular arithmetic performance, with the final model adding in the composite ambiguous sentence comprehension variable. Results indicated that the data were 3.31 times more likely under the null model (BF
10 = 0.30). A similar analysis with gF also supported the null model as 3.45 times more likely (BF
10 = 0.29).
Variants of these models were re-run with the ambiguous and control sentences separated by sentence type (garden path and RC), and the results mirror those of the composite models exactly. Indeed, neither garden path sentence resolution (ΔR2 = 0.00, B = 0.01, t (96) = 0.12, p = .904, 95% CI = [−0.205, 0.232]) nor RC sentence comprehension (ΔR2 = 0.02, B = 0.41, t (96) = 1.47, p = .146, 95% CI = [−0.144, 0.956]) uniquely predicted analytic problem-solving performance, after accounting for WMC and the ability to understand the control sentences of each type. Similarly, neither garden path sentence resolution (ΔR2 = 0.003, B = −0.06, t (96) = −0.58, p = .562, 95% CI = [−0.273, 0.149]) nor RC sentence comprehension (ΔR2 = 0.004, B = 0.20, t (96) = 0.73, p = .470, 95% CI = [−0.347, 0.746]) uniquely predicted analytic problem-solving performance, after accounting for gF and control sentence comprehension of both types. Together, these findings demonstrate that overcoming ambiguities in language are uniquely related to creative problem solving but not analytic problem solving.
Models were again re-run with RC-True sentences or RC-NP1 sentences entered in the final step. When accounting for WMC and RC control sentences, RC-True sentences predicted unique variance in modular arithmetic performance (ΔR2 = 0.05, B = 0.22, t (96) = 2.35, p = .021, 95% CI = [0.034, 0.409]), but RC-NP1 sentences did not (ΔR2 = 0.02, B = −0.13, t (96) = −1.32, p = .189, 95% CI = [−0.329, 0.066]). The same result was found when accounting for gF: RC-True sentences predicted unique variance in analytic problem solving (ΔR2 = 0.04, B = 0.19, t (96) = 2.09, p = .039, 95% CI = [0.009, 0.368]) but RC-NP1 sentences did not (ΔR2 = 0.02, B = −0.15, t (96) = −1.63, p = .107, 95% CI = [−0.339, 0.034]).
Combined WMC and gF. A final analysis repeated the earlier analyses, but combined WMC and gF in the first step simultaneously as a stronger test of the current predictions. As noted in
Table 11 and
Table 12, gF (but not WMC) predicted both creative and analytic problem solving, as did control sentence performance. However, adding ambiguous sentence performance to the model only improved model fit when predicting creative problem solving, and not analytic problem solving. A Bayesian model with WMC, gF, and control sentence processing predicting analytic problem solving as the null model, and adding ambiguous sentence processing in the final model, suggested the data were 2.91 times more likely under the null model (BF
10 = 0.34).
Exploratory Analyses. As in Experiment I, response time analyses were conducted (though no a priori hypotheses were made regarding the results). For both garden path and RC sentences, combined WMC and gF models were conducted to see if results replicated findings from the accuracy analyses. In models predicting anagram response time, garden path sentence reading time did not improve model fit over and above a model with WMC scores, gF scores, and control sentence reading time (ΔR2 = 0.03, p = .05). The same was true for a model using RC reading time in lieu of garden path sentence reading time, ΔR2 = 0.001, p = .70. When predicting modular arithmetic performance, adding garden path sentences to the model improved model fit over and above a model with WMC scores, gF scores, and control sentence reading time (ΔR2 = 0.09, p = .003). In the final model, control sentence reading speed negatively related to solution speed on modular arithmetic problems, β = −0.28, p = .046, while garden path sentence reading time related positively, β = 0.44, p = .003. Using RC reading time in lieu of garden path sentence reading time led to a null result, ΔR2 = 0.002, p = .67.
A final exploratory analysis conceptually replicated the analyses in
Table 11 and
Table 12. Using anagram accuracy as an outcome, and utilizing WMC, gF, and garden path ambiguous and control sentence accuracy as predictors, the analysis was repeated with the inclusion of garden path ambiguous sentence-processing time as a control variable. As seen in
Table 13, including garden path sentence response time as a control variable resulted in the same pattern of results witnessed previously, with ambiguous garden path sentence accuracy predicting anagram solution over and above all other variables. In contrast, as seen in
Table 14, this pattern does not appear for modular arithmetic performance.