The problem with unadjusted multiple and sequential statistical testing

In research studies, the need for additional samples to obtain sufficient statistical power has often to be balanced with the experimental costs. One approach to this end is to sequentially collect data until you have sufficient measurements, e.g., when the p-value drops below 0.05. I outline that this approach is common, yet that unadjusted sequential sampling leads to severe statistical issues, such as an inflated rate of false positive findings. As a consequence, the results of such studies are untrustworthy. I identify the statistical methods that can be implemented in order to account for sequential sampling.