>By adding 100 more people to your study, have you increased or decreased the likelihood that your results were due to statistical chance? Counter-intuitively,

>By adding 100 more people to your study, have you increased or decreased the likelihood that your results were due to statistical chance? Counter-intuitively, the answer is that you have increased the odds that the result was due to chance. You cannot add or remove people to a study while it is in progress, based on preliminary results in the study, without impacting its statistical validity in important ways. You might have a specific experimental setup and statistical test in mind where this statement is accurate, but in general it is false. For example, imagine that you have a collection of 200 marbles all of which are either red or blue, and you wish to conduct an experiment to estimate whether the total number of blue marbles is greater than or equal to the number of red marbles. If you randomly sample 100 marbles without replacement you can arrive at some estimate of the fraction of each population (the exact methodology doesn't matter for this discussion). Having gained some confidence that your preferred hypothesis was true, you sample another 100 marbles without replacement, at which point you know the exact answer to posed problem (the statistical argument is trivial). It is also worth pointing out that you don't necessarily need to count every marble to arrive at this kind of result (if at some point you have determined that there are at least 101 red marbles you know the exact answer of the proposition). The experiment described above is obvious academic, but it serves as a basic example of adaptive experimental designs that hone in on exact answers by way of pigeonhole principles. There are also statistically flavored extensions of these designs that allow one to assign subjective degrees of belief for different outcomes.