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Mining of Massive Datasets

Here I post some suplementary material to the book.

Bonferroni correction
Statistical inference logic is based on rejecting the null hypotheses if the likelihood of the observed data under the null hypotheses is low. The problem of multiplicity arises from the fact that as we increase the number of hypotheses in a test, we also increase the likelihood of witnessing a rare event, and therefore, the chance to reject the null hypotheses when it's true (type I error). Bonferroni correction is the most naive way to address this issue. The correction is based on the idea that if an experimenter is testing n dependent or independent hypotheses on a set of data, then one way of maintaining the familywise error rate (FWER) is to test each individual hypothesis at a statistical significance level of 1/n times what it would be if only one hypothesis were tested. So, if it is desired that the significance level for the whole family of tests should be (at most) α, then the Bonferroni correction would be to test each of the individual tests at a significance level of α/n. Statistically significant simply means that a given result is unlikely to have occurred by chance assuming the null hypothesis is actually correct (i.e., no difference among groups, no effect of treatment, no relation among variables).

Null hypothesis
refers to a general or default position: that there is no relationship between two measured phenomena
Given the test scores of two random samples of men and women, does one group differ from the other? A possible null hypothesis is that the mean male score is the same as the mean female score:
H0: μ1 = μ2