Data dredging

Data 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. This is done by performing many statistical tests on the data and only reporting those that come back with significant results. Thus data dredging is also often a misused or misapplied form of data mining.

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.

Conventional 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 level of risk is called the significance. 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. 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. If they are not cautious, researchers using data mining techniques can be easily misled by these results. The term p-hacking (in reference to p-values) was coined in a 2014 paper by the three researchers behind the blog Data Colada, which has been focusing on uncovering such problems in social sciences research.

Data dredging is an example of disregarding the multiple comparisons problem. One form is when subgroups are compared without alerting the reader to the total number of subgroup comparisons examined. When misused it is a questionable research practice that can undermine scientific integrity.

The conventional statistical hypothesis testing procedure using frequentist probability is to formulate a research hypothesis, such as "people in higher social classes live longer", then collect relevant data. Lastly, a statistical significance test is carried out to see how likely the results are by chance alone (also called testing against the null hypothesis).

A key point in proper statistical analysis is to test a hypothesis with evidence (data) that was not used in constructing the hypothesis. This is critical because every data set contains some patterns due entirely to chance. 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.

For example, flipping 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. If this hypothesis is then tested on the existing data set, it is confirmed, but the confirmation is meaningless. 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 three tails and two heads are observed, another hypothesis, that the tails probability is 3/5, could be formed, but it could only be tested by a new set of coin tosses. The statistical significance under the incorrect procedure is completely spurious—significance tests do not protect against data dredging.

Optional stopping is a practice where one collects data until some stopping criteria is reached. While it is a valid procedure, it is easily misused. The problem is that p-value of an optionally stopped statistical test is larger than what it seems. Intuitively, this is because the p-value is supposed to be the sum of all events at least as rare as what is observed. With optional stopping, there are even rarer events that are difficult to account for, i.e. not triggering the optional stopping rule, and collect even more data, before stopping. Neglecting these events leads to a p-value that's too low. In fact, if the null hypothesis is true, then any significance level can be reached if one is allowed to keep collecting data and stop when the desired p-value (calculated as if one has always been planning to collect exactly this much data) is obtained. For a concrete example of testing for a fair coin, see p-value § Optional stopping.