Analysis of the results
...
Unblinding the guesses:
Hokulele: CR=0
Hokulele's actual answer: "The first number that came to my attention is 1, so that is my choice for this test."
Ladewig: CR=-5
Ladewig's actual answer: "I concentrated on the assigned task and an image of a brightly lit piece of paper appeared, the circled number on it was 2."
stanfr: CR=-5
stanfr's actual answer: "I like number 1 cause it's the first thing I thought of."
Kid Eager: CR=-5
Kid Eager's actual answer: "Please note number 4 for moi!"
fagin: CR=-4
fagin did not send me his/her guess.
Femke: CR=0
Femke's actual answer: "I think you wrote 2 in your circle."
gabeygoat: CR=0
gabeygoat's actual answer: "guessed 4 de4f022d0deba6911bedf9a0350256aa"
...
First of all, I would like to thank Agatha for posting quickly all (actual) answers she received, only about one hour after I sent her a message asking her to do so. If you have participated in this test, and you find any discrepancy between the answer you sent to Agatha and the answer (by you) she posted, please say it.
1) Hokulele's masked (with "xx") answer was:
The first number that came to my attention is xx, so that is my choice for this test.
The (full) answer she sent to Agatha was (see above):
The first number that came to my attention is 1, so that is my choice for this test.
These two answers (masked and actual) appear to agree with each other, to be compatible. She provided no MD5 hash, but I decided in
post #127 (
before I knew which answers were correct) that this would be only a minor and acceptable violation (it might even be viewed as an
improvement) of the protocol of this test , and that the corresponding answers should be still considered as valid. I see three reasons for this. First, sending answers to the "referee" (the person you have to refer to, to know the actual answer) Agatha, already provides substantial protection with respect to the risk of guessed numbers being altered after I have revealed the target (and/or credibility ratings); adding an additional layer of protection may not be absolutely indispensable. Secondly, as remarked by Agatha in
post #15 (I responded in
post #17), my initial protocol contained a serious weakness (almost an error actually), because, if answerers provide both their masked (or blinded) answer, and the MD5 hash of their actual answers, I can find out their guessed number (although I probably wouldn't do it) by trying xx = 1, or 2, or 3, or 4, until the corresponding hash is identical with the provided hash (I corrected this "error" in
post #17). I cannot reasonably blame people for not following a flawed protocol (participants in the test could have followed my revised procedure in
post #17, but this is perhaps a little too complicated for many of you, who perhaps don't have time to read (carefully) all posts of the thread). Thirdly, of the seven forum members who gave answers which were found valid in
post #127 above, only one (stanfr) provided a MD5 hash. But stanfr did not reveal the sentence used to produce this hash, so it is not useful.
2) Ladewig's blinded answer was:
I concentrated on the assigned task and an image of a brightly lit piece of paper appeared, the circled number on it was xx.
...
His actual answer:
I concentrated on the assigned task and an image of a brightly lit piece of paper appeared, the circled number on it was 2.
.
OK
3) stanfr's blinded answer:
...
the number i came up with is ##
what's the point? what does my statement have to do with credibility?
As many have pointed out, your protocol is flawed. If I said for example:
I chose ## because that is the number most mentalists will chose.
How is this going to do anything to demonstrate 'telepathy'? All it will test is how versed you are in mentailism.
His actual answer:
I like number 1 cause it's the first thing I thought of.
Here, there is a problem: the text stanfr posted in the thread is different from the text he sent to Agatha. I said, in the opening post:
...
It may also be useful (I recommend it) that you send your (full) answer, in the form of a private message, to either
Agatha, or
Femke...
I recommended participants send their full answers to Agatha or Femke,
not a different answer obviously. I believe sending a different answer to the referee is a serious violation of the protocol of this test, because the credibility rating I gave to the masked answer (with "xx") is not necessarily valid for the "actual" answer in such a case.
4) Kid Eager's blinded response:
The last time I partcipated in this guessing game I was accused of being in a mental institution and therefore my response was invalid.
I'm now in a high-sided elastic banjo with an eskimo parasol, so rest assured that my response is both fluffy and perky.
The number I'm seeing is XX.
His actual response:
Please note number 4 for moi!
Here, I am facing the same problem as with stanfr above: the answer with "xx" provided in the thread is different from the answer sent to (and posted by) Agatha. If Kid Eager had sent to Agatha the message: "Please note number 4 for me!" ("moi" is the French word which means "me" in English), one might argue that this message is simple, normal and serious-sounding, and that sending such a message should not be considered as a (serious) violation of the protocol. But Kid Eager sent an odd combination of English and French, with a possible emphasis on
himself (note incidentally that "moi" is 50% longer than "me").
5) Femke answered:
...
I think you wrote xx in your circle.
...
while her actual, complete answer was:
I think you wrote 2 in your circle.
Here, there is again perfect agreement between the blinded answer and the full answer, so this answer is valid.
6) gabeygoat answered:
I'm gonna guess xx
not sure what im doing
while his actual answer was:
guessed 4 de4f022d0deba6911bedf9a0350256aa
Here again, for the third time in this test, there is a discrepancy between the blinded answer (with "xx") posted in the thread, and the actual answer sent to Agatha.
If I consider only, in my final analysis of the results, the answers by members of this forum who abided by the recommended protocol (note: not providing a MD5 hash is not considered here as a serious violation, for the reasons explained at the beginning of this post), then there are only three valid answers: those by Hokulele, Ladewig and Femke. Hokulele's (numerical) answer (1) is incorrect, while
Ladewig's and Femke's answer are correct (a special thank you to them).
This means the the final rate of correct answers in this test is equal to 2/3 = 66.7%.
This correct answer rate is much higher than the (approximately) 25% expected from chance alone, and seems to support my telepathy hypothesis (the assumption that I have a propensity to communicate my thoughts to others everywhere on the surface of this planet).
The probability of obtaining a hit rate equal to, or larger than 2/3 (if chance alone is responsible for the results, and assuming a probability of 25% of answering correctly), called the
p-value, is equal to: p = 15.6%. This is not statistically significant, because of the smallness of the sample (3 valid answers only). This means that a test like this one would have to be repeated several times, and with favorable outcomes, before a safe conclusion about the existence of telepathy can be drawn.
If I give a credibility rating of CR=-10 to all answerers who sent to Agatha an answer different from the one they posted in the thread (except, of course, for the replacement of the guessed number by "xx"), the average CR for those who answered (numerically) correctly is:
CR = (-5 + 0)/2 = -2.5, while the average CR for those who provided incorrect numerical answers is:
CR= (0 - 10 - 10 -10)/4 = -7.5.
This seems to confirm the finding I reported at the end of my previous test, namely that that (numerically) incorrect answers tend to be less credible.
) The point i was making is that any dimwit can correctly figure that my number was 1 from the fact that my statement highlights "first". Amazingly, Michel still thought Hokulele picked '2' 
