More Numbers

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I just finished the second phase of the experiment which I began in early June and wrote about again here after finishing the first phase. (Making links to my earlier blog posts is really fun. I have no idea why, but it is.) For the last twenty days, I have been attempting to memorize a string of twenty digits in a minute twice each day, thereby attaining forty data points. For twenty of these, I put my hand on my face while I was trying to remember the numbers, and for the other twenty, I kept my hands away from my face. The point of this experiment was to discover whether or not I think better when my hands are on my face, and I was really hoping that the answer would be yes. It would be very convenient if I could instantly make myself smarter just by putting my hand on my face.

Actually, the real reason for this experiment was to give me a reason to tape stuff like this to my walls. The important thing here is interior design. My room looks very elegant decorated like this.

Unfortunately, just like in the first phase of this experiment, my results were inconclusive. Although there did seem to be trends in the results, the actual calculations revealed that the trends weren’t large enough to actually prove anything. The differences could conceivably have been due to random chance. I think it’s worth noting, though, that this time the results were almost good enough to be statistically significant. The trends probably mean something, even though I don’t have good enough evidence to insist that they definitely do. And what the trends show is that I remember stuff better when my hands are on my face. I definitely intend to make use of this information when I’m taking the GRE in two weeks.

Now I just have to decide what the next phase of this experiment is, because I don’t want to give up this delightfully fun game.

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Statistical Stuff

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Three weeks ago today, I wrote this blog post in which I described an experiment that I was about to start. The first phase of the experiment was to take twenty days, and it has recently been completed. In case you didn’t see the first post about this experiment and don’t feel like reading it now, I will briefly summarize. Over the course of twenty days, I have collected sixty data points measuring how well I was able to memorize a string of twenty digits, acquired from an online random number generator. I collected these data samples three times a day (early morning, late morning, and late afternoon) and memorized the numbers using three different methods. (sitting at a desk without my hands on my face, sitting at a desk with my hands on my face, and pacing in a circle around my room)To reduce the effects of confounding variables, the time of day and the method used did not correspond. I used the online random number generator to determine the order in which I would use the three methods each day.

My scores ranged from two to twenty, but most of them were in between eleven and fifteen, and the later ones seemed to be higher on average. Apparently, my number-memorizing skills are improving. I have just now determined that the average was 13.60 and the standard deviation was 4.25. (I am very curious to know if that’s a ‘good’ score or not, but since nobody else has done an identical experiment, as far as I know, there’s no standard for comparison) For most of the last twenty days, I have been coming to the disappointing conclusion that there is no statistically significant difference between the three different methods, but I was still curious about what I would find when I added up the scores and did the math.

At first, it looked promising. The averages for the three different methods were 12.68, 14.10, and 13.24, which seems to be different enough to actually mean something. Out of curiosity, I also calculated the individual averages for the three different times of day and got 14.95, 14.48, and 11.23 respectively, which verifies my assumption that I tend to kind of be a morning person. But since I already knew that, the data that I was really looking at was the difference between the three memorization methods.  At that point in my statistical analysis, I thought I had actually discovered something interesting.

Unfortunately, the thing with the standard deviation messed that up. 4.25 is a pretty large standard deviation for something with a 20-point scale. The definition of ‘statistically significant’ depends upon where you want to set the margin of error, but 4.25 is a pretty reasonable number to use for that, and it makes the math really easy if margin of error is equal to one standard deviation. That means that the differences in my data are not significant unless they fall outside of the range from 9.35 to 17.85, which they do not.

Now, I suppose I could calculate the within standard deviations rather than using the overall standard deviation, but I’m pretty sure that my results wouldn’t be any different. Each method had approximately the same range, and since I already know they had similar averages, their standard deviations are probably going to be pretty close also, and I’ll have to reach the same anticlimactic conclusion, which is that there wasn’t a significant difference.

In case anyone is still interested in that slight little insignificant difference, I can inform you that the best score came from memorizing the numbers while sitting at the desk with my hands on my face, and the worst score came from memorizing the numbers while sitting at the desk without my hands on my face. I’m not entirely convinced that there isn’t something to my hypothesis that having one’s hands on one’s face somehow improves cognitive ability.

This calls for some further tests.