Begum Luleciler, Department of Psychology, Loyola University Chicago.
This research is conducted for the Lab in Experimental Psychology: Cognition (Psych 314) course.
Effects of Problem Space on Anagram Problem Solving
The world we live in today is not only highly complex but also dynamic. The average person has to make hundreds of decisions everyday right from the time he or she wakes up. For instance, whereas our forefathers had only one cereal to choose from, today we have thousands of brands and varieties. Similarly, the nature of the problems keep changing rapidly due to technological advancements. We can conjure that the problem space has been increasing over the years and the situations is likely to persist in the future. Corporate competition spurs innovations and invention creating more diversity and changes to our day to day lives. This study seeks to assess the effects of problem space on problem solving. The study uses an anagram to conduct laboratory experiments to test problem solving. Using anagrams to measure dimensions of problems solving is not a new phenomenon. It can be traced to as early as 1916.
In this experiment, we are interested in assessing how the time taken to solve an anagram changes under different problem space. Therefore, we manipulated the problem space size. In the problems that we face in our day-to-day lives, there are factors that influence the problem space. Problem space can be defined as the complete component range that we face in the process of solving a problem. The range encompasses numerous components including: problem definition, identification and test of possible solutions, and choice and implementation of a solution. In addition, it includes numerous small steps in between the key stages. For instance, if a couple has only one car the solution to which car to use will be found much easier and faster than if they were two cars. If it is only one car then they have to use that single car but if they are two then they have to decide between the two. In this case, the problem space is much smaller due to necessity. The problem space will increase with an increase in the number of cars.
In our anagram experiment, we manipulated the letter cases to vary the anagram. In one set of anagrams in used the same case (upper case). However, in another set of anagrams we mixed upper case and lower case letters. Mixing the upper case and lower case letters creates a mental obstacle for the subjects because people are naturally inclined to group same case letters together. The mixed letter case scenario is the same as the analogy of a couple having more than one car. Having more than one car requires more time to arrive a solution. The experiment allows us to gain insights on how people solve problems in the real world using simple tasks.
A similar study was conducted by White, Freund and Csiki (2002) in the University of Arkansas using college students. They revealed that mixed letter groups disrupts the problem solving process. The main purpose of the study was to assess whether use of mixed case letters disrupts the solution process. The level of measurement was the number of anagrams solved in each case. This study also used anagrams with mixed letter case and same letter case. However, unlike the White, Freund and Csiki (2002), we measured the time taken to solve each anagram in both scenarios. The study used a sample size of 30 while we used a sample size of 18. The sample size was informed by financial and time limitations. The study used a two-sample t-test to compare the statistics from the two samples: mixed letter case anagrams and same letter case anagrams. The study used a between group and within group design approach. The study revealed that the difference in number of correctly solved anagrams was marginally significant t (30) = 1.72, p < .01. We also adopted a two sample t-test in answering the research hypothesis and a similar research design.
Similarly, Dooling & Lachman (1971) revealed that increases the size of the title of a passage reduces the comprehension and retention of prose. Although the study is in a different setting it portrays the same message. Increasing the complexity of problem increases the difficulties faced by people in solving that task. Consequently, more time will be taken to solve the problem. The study used a 2*3*2 factorial design. The study used a sample of 120 study participants. The participants were introductory psychology students. The participants were required to read passages and grasp the ideas in the passage. The presence or absence of a thematic title was the experimental manipulation. F-test was used in data analysis. Analysis of words correctly reproduced yielded significant results F (1,108) = 7.18, p<.01 with syntactic constraint F (2,108) = 5.83, p < .01. Presence of a thematic title increased participants’ ability to recall by 18 percent. The research design and objective was different from the current study. However, the both has the same underlying concept that increasing the problem space makes problem solving complex.
It is on this backdrop that this study hypothesis that changes in the problem space changes the time taken to solve an anagram. Therefore, the null and alternate hypothesis are as follows:
Null Hypothesis: The time taken to solve an anagram is equal under same and mixed groups.
H0: µs = µm
Alternate Hypothesis: The time taken to solve an anagram is the not equal under same and mixed groups.
Ha: µs ≠ µm
Results
The researchers agreed by consensus that there would 10 anagrams with some of them having same case letter (only capital letters) or one with mixed case letters (small and capital letters). To investigate the effect of problem space on anagram solving, the time taken by the subjects to solve the anagram was recorded in seconds if it was less than 90 seconds otherwise it was recorded as 90 seconds. The study manipulated the study space into two groups of letters (same and mixed). The mean and standard errors are presented in figure 1. There was a significant difference in the time taken to solve the anagram under the two groups (same and mixed): t (17) = -4.909, p < .05. This means that the difference in means is significantly different.
In other words, problem space has a significant influence on the time taken to solve an anagram. The mean, standard deviation and standard errors of the time taken to solve the problem under mixed and under same case letters is presented in figure 1. The mean time taken under same was 35.56 seconds with a standard deviation of 28.75 while that under mixed was 59.39 with a standard deviation of 22.63. The difference in the mean was 23.83 with a standard error of 4.85. The result suggest that changing the problem space increases the complexity of the problem and subsequently the time taken solve the problem. Mixing lower and upper case letters creates a mental obstacle thus increasing the problem space. Therefore, the subjects took more time solving the anagrams with mixed case letters. Specifically, our results suggest that it people will take more time to solve anagrams with a larger problem space compared to those with a smaller problem space. The findings support the hypothesis that changes in the problem space changes the time taken to solve the problem.
Thus, the study can conclude that problem space has a significant effect on anagram solving. Specifically, the nature of the relationship is positive: an increase in the problem space increases the time taken to solve the problem.
References
Dooling, D. J., & Lachman, R. (1971). Effects of comprehension on retention of prose.
Witte, K. L., Freund, J. S., & Csiki, I. (2002). Case-mixing effects on anagram solution.
The Journal of General Psychology, 129, 117-126.
