Scientific Research in School Volume 3 Issue 1 2021
Scientific research question Can humans generate random sequences and does the methods of writing and speaking act as a variable in the randomness of the sequence generated?
Scientific hypothesis That, humans are more effective at generating a string of random numbers when they are spoken aloud rather than when they write them on a piece of paper.
Methodology Ethics Statement Each participant was informed that their involvement in the study was voluntary, and that the results of their participation would not be traced or impact their relationship with researcher and school. The research was deemed to have minimal impact to participants with approval from the Barker Institute. Preparation A pilot test, of 6 participants who were asked to recite or write 200 digits in an order they considered to be random, was conducted to determine how to best conduct the actual experiment. The results concluded that providing 200 digits did not prove too difficult for the participants, however we do not believe participants would be comfortable giving over 300 digits as they were already struggling by the last 20 digits in the 200. Some participants took longer than other and the entire process for each individual averaged around 10 minutes, with the recording of each set of digits taking 3-4 minutes and the supplementary questions being 1 - 2 minutes. As each of these participants only did one, their results were only used for the pilot study and not used in the 21 described below. Data Collection A sample group of 21 student subjects (min. age: 15, max. age: 18) with no previous knowledge of the experiment were asked to provide a string of 200 from the digits (0,1,2,3,4,5,6,7,8,9) via two different methods (written and spoken); a larger sample size than Persaud (2005) as argued by Figurska et al. (2008). Each participant was asked to write down the digits in a 20x10 grid or asked to speak out loud and have their sequence recorded by the researcher. They were then asked to complete the other activity via the other method; the order of method s was alternated between participants (see Table 4). The participant was then asked supplementary
questions, asking them to comment and reflect on their own performance. This was to ensure data from participants were from an “engaged attempt”. The data was typed and analysed in excel (see Table 3: Results). Data Analysis With the independent variable speaking or writing the numbers, the dependent variable is how random the generated sequence is. This was calculated with the suggested method (Barbasz et al., 2008) of two indexes used in conjunction with one another, with the slight adjustment to the correlation function over 10 steps rather than only 9 to ensure repetition is caught and for ease of interpretation The results were analysed in three ways: 1.
Two t-tests were used to compare speaking and writing on each quantitative metric, providing the simplest answer to the research question. If both metrics return p < 0.05 the result will be considered significant as there is still only a one-in-twenty probability that a false positive would be returned from a non-different sample. However, if only one returns p < 0.05 then a higher threshold will be required (α=0.025), as there is a one-in-ten probability that a false positive would be returned for just one of the two metrics if α=0.05.
2.
The quantitative measures were compared to the Shannon’s Entropy and Correlation Function for a known random sequence (𝜋𝜋𝜋𝜋) and classified categorically as either highly random (if it is closer to the ideal value than 𝜋𝜋𝜋𝜋), random (if it is within twice the distance of 𝜋𝜋𝜋𝜋, nonrandom (within three times the distance of 𝜋𝜋𝜋𝜋), or highly non-random. Histograms were produced indicating the randomness across each of these functions. Results for speaking and writing were then compared with two X2 tests of difference.
3.
Finally, case studies were investigated including closer inspection of the distribution of the frequency of each digit (related to Entropy) and distribution of the Correlation Function to explore what was preventing individuals (if anything) from achieving randomness.
Science Extension Journal • 79
