Many types of research take relatively long periods of time to collect the sample. When involved in this type of research, it is often desirable to analyze the data as they accumulate. There is a danger in doing this. This chapter describes that danger and provides methods that can be used for these accumulating data that avoid the danger. There are two approaches described. The first changes the way P-values are interpreted, making it harder to reject the null hypothesis while the data are gathered. The other involves prediction of what the future observations will show and determination of the probability that the null hypothesis will be rejected at the planned end of the study.