The proper procedure would have been to form in advance a hypothesis of what the tails probability is, and then throw the coin various times to see if the hypothesis is rejected or not. If this hypothesis is then tested on the existing data set, it is confirmed, but the confirmation is meaningless. Throwing a coin five times, with a result of 2 heads and 3 tails, might lead one to hypothesize that the coin favors tails by 3/5 to 2/5. See testing hypotheses suggested by the data. If the hypothesis is not tested on a different data set from the same statistical population, it is impossible to assess the likelihood that chance alone would produce such patterns. This is critical because every data set contains some patterns due entirely to chance. (The last step is called testing against the null hypothesis.)Ī key point in proper statistical analysis is to test a hypothesis with evidence (data) that was not used in constructing the hypothesis. The conventional frequentist statistical hypothesis testing procedure is to formulate a research hypothesis, such as "people in higher social classes live longer", then collect relevant data, followed by carrying out a statistical significance test to see how likely such results would be found if chance alone were at work. One form is when subgroups are compared without alerting the reader to the total number of subgroup comparisons examined.
If they are not cautious, researchers using data mining techniques can be easily misled by these results.ĭata dredging is an example of disregarding the multiple comparisons problem. When enough hypotheses are tested, it is virtually certain that some will be reported to be statistically significant (even though this is misleading), since almost every data set with any degree of randomness is likely to contain (for example) some spurious correlations. When large numbers of tests are performed, some produce false results of this type hence 5% of randomly chosen hypotheses might be (erroneously) reported to be statistically significant at the 5% significance level, 1% might be (erroneously) reported to be statistically significant at the 1% significance level, and so on, by chance alone. This level of risk is called the significance. The process of data dredging involves testing multiple hypotheses using a single data set by exhaustively searching-perhaps for combinations of variables that might show a correlation, and perhaps for groups of cases or observations that show differences in their mean or in their breakdown by some other variable.Ĭonventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and necessarily accept some risk of mistaken conclusions of a certain type (mistaken rejections of the null hypothesis). This is done by performing many statistical tests on the data and only reporting those that come back with significant results.
Misuse of data analysis A humorous example of a result produced by data dredging, showing a coincidental correlation between the number of letters in Scripps National Spelling Bee's winning word and the number of people in the United States killed by venomous spiders.ĭata dredging (also known as data snooping or p-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives.
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