Abstract
The study was conducted to establish the number of words students could form from anagrams in a given time span. It entailed grouping students by their problem-solving ability and subjecting them to a timed practice session. The results indicated varying abilities among students in achieving the stated objective. The study linked student results to high and low transition probabilities to draw substantive conclusions.
The research reviewed previous studies and compared their findings based on student performance. The students were required to solve 20 anagrams in 3 minutes, and the results were analyzed using Test methods. The corresponding p-values, S stat, and Pearson correlation values were documented. A comparison of the high transition probability (HTP) and low transition probability (LTP) was computed based on the aforementioned statistical values and parameters.
Introduction
Most words contain letters that can be easily rearranged to form other words. The formation of such appellations is subject to transition probability, which is the likelihood of changing an idiom from one state to another. A total of 22 anagrams were solved in the allocated 5 minutes. Previous studies have shown varying transition probabilities for anagrams. Liu et al. (2022) and Murray et al. (2022) explored the variation in solution time for anagrams with varying frequencies in Thorndike-Lorge counts. The study concluded that the speed of the solution was directly proportional to the frequency counts: that is, low-frequency counts of Thorndike-Lorge resulted in faster solutions.
Valerjev & Dujmović (2020) observed that the anagrams could have high or low transition probability depending on the words. However, Lengyel’s (2019) research reported identical figures for both measurements and a similar number of anagrams. The researchers experimented with the number of anagrams that could be deciphered in 5 minutes. Sinaga et al. (2020) examined the factors affecting the development of words from anagrams and concluded that word order was a significant factor. With reference to the Mayzner and Tresselt (1959) study, we hypothesized that word probability transitions rise along with the number of anagrams. It employed the Saussure approach to compute the probability variation of different words, as discussed later.
Method
Participants
The research included 12 students as participants to assess the number of anagrams solved in 2 minutes. Including the students on the participant list highlighted their sharp problem-solving skills. The study also provided a reliable basis for assessing the significance of the research at the student level. The students leveraged the study’s advantages to gain a deeper understanding of research methods and approaches. Lastly, the inclusion of several students provided varying results, which are ideal for analysis, interpretation, and presentation in the course analysis.
Materials and Setting
The research was conducted in a classroom setting under timed supervision. First, the students were allowed to practice with two anagrams, with each consisting of 5 letters. The pretest and experimental tests consisted of 20 anagrams for detailed analysis. The pretest involved grouping students into categories based on their anagram-solving abilities. There were two broad categories of student groups: high and low, which were selected based on the outcome of flipping a fair coin.
Students were randomly assigned to the high- and low-outcome groups to minimize potential bias. The students were given a solution paper and allowed to use a pen or pencil to write their solutions. The total time allocated for the study was 5 minutes, with 2 minutes spent on the practice problems and the remainder on the test questions. The students were expected to solve 20 anagrams within the stipulated time to assess their skills and speed.
Experimental Design
The research matched the different variables to compare their relationship. The independent variable was the pretest score, while the high and low transition probability scores were treated as dependent variables. The results were generated randomly as the student performance could not be identical.
Procedure
The test was carried out in two phases: the practice and pretest stages. The practice session lasted 2 minutes, and students were required to solve 2 5-word anagrams. The anagrams were “OGNRW” and “TWORE,” and the students were expected to construct words from them using all available letters. The pretest session consisted of 20 anagrams, and students were required to solve them within 3 minutes.
The students were grouped based on their ability to solve the anagrams as stated earlier. They were further grouped into two broad categories: “high transition probability” and “low transition probability.” The broad groups were formed by flipping a coin, with a head indicating “high” and a tail indicating “low.” In this case, the categories were random, so there was no bias.
There were two types of results for both groups, one for “practice” and the other for the “pretest.” To start the test, the instructor shouted “go” so the students would begin the solutions and maximize their time. During the practice session, the students were given two 5-letter anagrams to solve. The time allocated for this stage was 2 minutes, and the results were written down on paper and later populated into an Excel file for analysis.
The students were instructed to stop after the time had elapsed. In the pretest session, each student was supposed to solve 20 five-letter anagrams in 3 minutes. The results were also recorded on paper using a pen or pencil, depending on the student’s preference. The results were only acceptable if recorded within the allocated study time.
Results
The analysis entailed calculating the average scores for both the pretest and transition probabilities. The results were categorized into two broad groups, as shown in Figure 1 above: “high transition score” and “low transition score.” Participants were matched evenly across the broad categories to ensure equitable results. In the “high transition” category, the average anagram score for the pretest was 8.22, while that of the HTP was 7.0.
The corresponding results for the “low transition” category were 8.44 and 6.44, respectively. The standard deviation (SD) for “high pretest” was 3.597839 as indicated in the figure above. The SD value for the HTP was 2.1794459, which is slightly lower than the pretest results. The standard deviation of the mean of random samples (SEM) was 1.19928 and 0.726483 for the pretest and HTP in the “high” category.
In the “low transition probability” scenario, the average anagram score for the pretest was 8.4444, whereas the corresponding value for the conventional LTP score was 6.4444. The SD results were 3.844188 and 3.35824. The SEM results were 1.281396 for the pretest and 1.119413 for the LTP. In both HTP and LTP categories, the square root of the number was 3. Generally, the pretest results provided a reliable basis for analyzing the HTP and LTP results.
Figure 2 illustrates the results of the t-test comparing the pretest and HTP scores. It encompasses one-tailed and two-tailed computations. The person correlation for this observation was 0.1594, while the t-stat value was 0.9406. The corresponding p-values for one-tailed and two-tailed were 0.1872 and 0.3744, respectively.
The value for person correlation for the LTP score was 0.5637, as shown in Figure 3. The t-stat value was 1.7693. The p-values for one-tailed and two-tailed were 0.0574 and 0.1148, respectively.
The analysis laid the basis for the discussion and conclusions presented later in the study. The HTP variance was 4.75, while the LTP variance was 11.28. The Pearson correlation was insignificant, with a magnitude of approximately 10^-17. The t critical values for one-tailed and two-tailed were 1.8595 and 2.3060, respectively. The corresponding P-values were 0.3441 and 0.6881.
Discussion and Conclusions
The Mayzner & Tresselt (1959) study associated the order of letters with the number of solutions made in a given unit of time. The study relied on a theoretical framework designed to account for the effect of letter order on solution time. Since each anagram provoked a varied set of true solutions, it was easier to form words if the movement of letters was minimal. As a result, the corresponding responses were achieved faster.
The study also observed that if letters were moved many times, it would take longer to form the target words, thereby reducing the number of words or solutions conceptualized by the students within the stated study time. Based on the results, it was hypothesized that the probability of word transitions increases with a surge in the number of anagrams.
Our study yielded different results from Mayzner & Tresselt’s (1959) research due to similarities in the HTP and LTP anagrams. Burlacu (2020) investigated the factors influencing the solution of anagrams, focusing on time and letter count. The study resolved that shorter anagrams were easier to solve. It also established that the order of letters affected the rate at which students could form new words from anagrams. The study explained that moving a letter multiple steps interfered with students’ concentration and challenged their problem-solving skills.
The findings of our research differ from those of the aforementioned studies for several reasons. First, the sample size was small, and students spent more time practicing anagrams than on the actual test. This created bias and anxiety, resulting in poor performance. The study presented its limitations, distractions, and experimental design, while emphasizing only the quantity of responses.
There was a significant difference in solution time among the students, affecting the validity of the overall results. The students did not spend the same amount of time solving a particular anagram, and these factors were not taken into account. A further study should thus be conducted to explore factors such as time variation in problem-solving, rather than focusing solely on the number of words generated within a given time frame.
References
Burlacu, A. (2020). Impact of Letter Type and Frequency on a Primed Lexical Decision Task.
Lengyel, Z. (2019). Anagram Based L2 Activation. Indonesian Research Journal in Education| IRJE|, 300-318.
Liu, X., Hu, Z., Deng, X., & Kuhlman, C. J. (2022, December). A Bayesian uncertainty quantification approach for agent-based modeling of networked anagram games. In 2022 Winter Simulation Conference (WSC) (pp. 310-321). IEEE.
Mayzner, M. S., & Tresselt, M. E. (1959). Anagram solution times: a function of letter order and word frequency. Journal of Experimental Psychology, 56(4), 376.
Murray, J., Sutter, A., Lobifaro, A., Cousens, G., & Kouh, M. (2022). Incorporation of prior knowledge and habits while solving anagrams. Journal of Eye Movement Research, 15(5).
Sinaga, H., Herman, H., & Pasaribu, E. (2020). The Effect of Anagram Game on Students’ Vocabulary Achievement At Grade Eight of SMP Negeri 8 Pematangsiantar. Journal of English Educational Study (JEES), 3(1), 51-60.
Valerjev, P., & Dujmović, M. (2020). The Impact of the Length and Solvability of Anagrams on Performance and Metacognitive Judgments. In 21st Psychology Days in Zadar: Book of Selected Proceedings: International Scientific Conference (pp. 217-230). University of Zadar.