Power analysis of different statistical test techniques With reference to this answer which states that chi square test is less powerful compared to other statistical techniques.
Can someone shed some light on power analysis of different techniques like Z test, t test, chi square test, anova test, or other statistical techniques.
Also, why/how is one test powerful compared to other, yet much in use (like chi square)
 A: First, with reference to the previous answer, the chi-squared test of independence isn't universally less powerful than the discrete Kolmogorov-Smirnov (KS) test. It's just that for data that is ordered, KS and similar tests tend to out perform the chi-squared test. For unordered data, the chi-squared test tends to outperform the discrete KS test.
I'm pretty sure that in published literature, the KS and similarly appropriate tests are used more often than the chi-squared test to assess Benford's law. However, some of these tests are not as well known so for casual analysis, it may be that the chi-squared test is used more often.
The literature on comparative power of different tests is huge because the comparative power of different tests usually also depends on the type of deviation from the null. To give you a sense of what this can look like, here's a simple example of a power analysis for different discrete GOF tests, especially see the conclusion. Here, no one test outperformed all the others for the different deviations. This is why it's hard to give universal recommendations and many people are content to stick with the chi-squared test.
