Why the A/B Testing, the Correlation and the Regression are considered methods of Statistical Analysis, while the method of "Association Rules" belong to the Data Mining field ?
Which are the difference between Statistical analysis and Data mining
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The key difference is that statistical analysis reports on different aspects on your data, while data mining mines for a new knowledge about it, discovering some information sometimes not expected in advance.
According to Wikipedia:
Data mining is the process of discovering patterns in large data sets [...]. Data mining is an interdisciplinary subfield of computer science and statistics with an overall goal to extract information [...].
A/B testing is not about patterns, rather about testing in statistical way. Association rules fit into the definition of Data Mining, but it is still subfield of statistics. All in all both methods are from statistics, but different subfields.