dlorde
Philosopher
- Joined
- Apr 20, 2007
- Messages
- 6,864
And you are wrong dlorde, statistically two out of two tests at 50% chance is correct at 75% probability that I am telepathic but who would rely on such a small sample size and say it is valid? 10000 to 1 or 99.99% certainty is the target to reach before the JREF will acknowledge that I am telepathic, not 75% probability that I am based on two 50:50 tests.
You are right that more trials would be needed for an acceptable level of confidence. But I am not wrong about your mistaken interpretation of the results for one and two 50/50 tests. It's a subtle mistake, easy to make.
Remember that the figures (25% or 1-in-4 chance) for correct results in two 50/50 tests refer only to the probability of getting that result by guessing (by random chance). This means that if you guessed, you'd be wrong 75% of the time. It does not mean there is 75% chance that you are telepathic (i.e. it is not a 75% chance you weren't guessing).
Another example - if, before you tossed a coin twice, I called "Heads, heads", and you then threw 2 heads, it doesn't mean there is a 75% chance that I really knew what the outcome would be - it's more likely I just got lucky. By just guessing in many such tests, I'd be right 25% of the time and wrong 75% of the time, and many such tests would be required to say anything meaningful about the probability that it was not due to chance.
These figures are always given in terms of the probability of getting a result by chance. The lower that probability, the more likely the results are not due to chance. The inverse of that figure isn't the probability that the results are not due to chance (i.e. getting a result that you'd only expect by chance one time in a hundred doesn't mean a 99% chance you're telepathic).
The figures in the tables linked by Pixel42 will give you the figures for the number of tests you need to get right in various numbers of trials, for a confidence level of 1:100 (table 1), 1:10,000 (table 2), and 1:1,000,000 (table 3). The confidence level is the probability that you'd get those results by chance alone.
Notice that the tables don't deal with less than 5 trials - even for relatively unlikely events, you need a reasonable number of trials to state a level of confidence about the results.
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