Need help predicting the future

waitinforatrain

Edit: Excuse the title

Hi all,

I'm trying to replicate the experiment from Dr Sean O'Donnells "Future Memory and Time". He claims to have done a 30 day experiment with guessing cards, and scored himself on a number of variables of prediction (correct suit, correct colour, high or low etc), and that the graph of his scores went consistently up over 30 days. He has some theories on why this works etc etc.

Being the skeptic that I am, I have to verify this for myself. I designed a computer program to do the same thing, and basically I'm trying to minimise the random variation in the scores so that I can see any subtle increase in the scores I get.

There are three variables he used in his experiment, but it's been a few years since I've had a copy of the book so I can't remember what they are at this time.

The current scoring system:
Correct colour: 1 point
High/low correct: 1 point (high is 7 or over, low is 6 or less, aces are low)
Correct suit: 2 points (1/2 the chance of guessing it compared to the other 2 variables)


So here's a benchmark simulation I did:

90
97
86
78
88
84
82
74
71
98
87
66
82
86
88
93
92
90
88
86
83
67
93
72
74
Mean: 83.8
St D: 8.90225

This is 70 guesses per day over 25 days (only the total score is shown).
As you can see there is a large variation in the numbers, and any subtle 'prediction' or 'influence' I might have may be obscured by this.

So, questions:
1. Is there any way to reduce the standard deviation without increasing the guesses or number of days to an unfeasable amount?

2. Is there any way of comparing the standard deviations relative to each other? For example if I doubled the guesses from 70 to 140, the total scores would increase, which would increse the mean and standard deviation. Would it just be a matter of dividing the scores by 2 to compare them?

Thanks

waitinforatrain

Anyone?:)

bnt

First of all, I'm not sure why you're saying that increasing the number of trials would increase the mean or the standard deviation. The Mean and StDev describe the distribution of results: what the average result is (the mean), and how much the results tend to deviate from that mean (StDev). If you're trying to see how well those numbers fit the standard distribution, you might also want to use the Kurtosis function on the data, which tells you how "peaky" the figures are.

The only way that the StDev could come down is if all the trial results were closer to the mean i.e. more consistent, day-to-day, and from the data they're just not that consistent (kurtosis = -0.473, which suggests a fair amount of randomness). 98 is about 1.6 standard deviations above the mean, and 67 is almost 1.9 StDevs below - not much you can do about that without fudging the results.

Increasing the number of trials (days) should not automatically increase or decrease either Mean or StDev, but it will give you more confidence in those figures. Once you have a sufficient number of trials (typically 30 or more), those values can probably be considered good indicators of what is happening. If you increase the number of trials, you should find that the data becomes a better fit to the standard distribution and the kurtosis goes down - as long as these really are independent trials that mean something, that is! I admit I don't understand your scoring system and what you think it's going to tell you, I'm just looking at the statistics you're provided for each day, and they contain a fair degree of randomness - like it or not.

edit: had another read of the OP: if you're trying to analyse the trend of those results over time, then Mean and StDev don't tell you much. I'm using Excel on the data, so I plotted the data and added a trendline. This shows a slight downward slope over time (m=-0.1869) , but the randomness means that the results are a very poor fit to the trend (R² = 0.0244) i.e. no reliable trend to be seen there, IMHO.