Beyond a Reasonable Doubt

Earlier today I read a chapter in Jeffrey S. Rosenthal's book Struck By Lightning that focused on reliability in terms of conclusions based on statistical data. He mentioned something I haven't heard of before, something called a p-value. P-values are used to differentiate actual conclusions from those resulting from 'just luck' (for example flipping a coin and getting heads three times in a row), and thus show the probability that one would have observed a specific result just by pure luck. The smaller the p-value the more unlikely that the results were purely the result of luck. In the scientific community, a p-value of 5% is considered 'statistically significant' and thus accurate 'beyond a reasonable doubt'. The p-value of flipping a coin and getting heads three times in a row is 12.5%. This value is obtained by taking 50% of 50% of 50% and indicates that one cannot conclude that the coin is compromised because the three heads may be a result of pure chance. To conclude that the coin is rigged, one must flip the coin and get five heads in a row. This would result in a p-value of 5% and one can say that the coin is rigged 'beyond a reasonable doubt'. However some scientists prefer p-values of at least 1% in order to eliminate any error which would require flipping heads seven times in a row. The reliability of conclusions based on statistical results can be determined by calculating the probability that the results occurred by pure chance. One can look for the truth in claims by considering its p-value.

The Paradoxicality