Just how bad is it to peek at your data every few observations and stop collecting data once you have a significant result? Simulate the false positive rate below. You can change the parameters in the sidebar (in the menu if minimised).
This simulated a normal distribution with no effect and ran a 1-sample t-test on the first 10 observations, then collected 5 new observations and peeked again until 50 observations. This procedure was run 100 times and reported the percent of runs that produced a significant result (p < .05) and plotted the N at which the first significant result was found.
There are several papers and blogs discussing this issue: