If a student were able to correctly identify 15 of 20 cards in this experiment, we would reject the notion that they were guessing based on the p-values. Why would such a definitive result not increase our confidence that the student has ESP, based on the scientific interpretation of this experiment? Explain your reasoning.
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Step 1 - Consider multiple hypotheses: This person could have gotten 15 of 20 cards right
by luck, by ESP, or by determining the identity in some other way (cheating, inadvertent
mistakes in the execution of the experiment, or something we haven't thought of).
Step 2 - Determine how unlikely it is to guess, by pure luck, 15 or more cards: One
can calculate the probability of correctly guessing 15 of 20 cards, as you say, calculating the p-value.
Note: I won't elaborate here about why scientists usually use this p-value measure (15 or
more) instead of the direct probability (just 15) when analyzing experimental results.
Step 3 - Interpret this probability: Obviously, the probability of matching 15 or more cards
correctly by chance is extremely low. Therefore, we can be very con dent that the person was not guessing; it is beyond reasonable doubt that he or she somehow was getting information
about the cards.
Usually scientists draw the line of \reasonable doubt" around 1 in 20 (0.05), sometimes
as low as 1 in 100 (0.01). But this result is way beyond reasonable doubt. We routinely send people to jail (or even the executioner) on weaker evidence than this.
Warning 1: The tricky concept of proof. People in general apply the word
"proof" to a variety of concepts. It can mean personal certainty, or "shown beyond
reasonable doubt". Scientists, on the other hand, use "proof" to mean absolute certainty, which is different from personal certainty.
Consider a person who is certain that humans are causing global
by luck, by ESP, or by determining the identity in some other way (cheating, inadvertent
mistakes in the execution of the experiment, or something we haven't thought of).
Step 2 - Determine how unlikely it is to guess, by pure luck, 15 or more cards: One
can calculate the probability of correctly guessing 15 of 20 cards, as you say, calculating the p-value.
Note: I won't elaborate here about why scientists usually use this p-value measure (15 or
more) instead of the direct probability (just 15) when analyzing experimental results.
Step 3 - Interpret this probability: Obviously, the probability of matching 15 or more cards
correctly by chance is extremely low. Therefore, we can be very con dent that the person was not guessing; it is beyond reasonable doubt that he or she somehow was getting information
about the cards.
Usually scientists draw the line of \reasonable doubt" around 1 in 20 (0.05), sometimes
as low as 1 in 100 (0.01). But this result is way beyond reasonable doubt. We routinely send people to jail (or even the executioner) on weaker evidence than this.
Warning 1: The tricky concept of proof. People in general apply the word
"proof" to a variety of concepts. It can mean personal certainty, or "shown beyond
reasonable doubt". Scientists, on the other hand, use "proof" to mean absolute certainty, which is different from personal certainty.
Consider a person who is certain that humans are causing global
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