As mentioned, falsification can become rather subtle. Here are some examples that demonstrate this fact.
– After your measure you analyse the data. Overall, the data seem good. However, there are also some weird outliers. As a result, the statistics don’t yield any relevant results. You conclude that there must be something wrong with the instruments, so you decide to remove the outliers from the file without mentioning.
– You are collecting data for several consecutive days. On one of these days, while measuring the data, you do not feel perfectly fine. As a matter of fact, you think that your data might be flawed as a result of the way you feel. At the end of the day, you decide not to take these measurements into account. 
– After having put some hard work into data collection, you find that the relation between two variables was just below the 95% significance level. Nonetheless, you do need this publication. Therefore, you decided to round off 94.55% upwards, now you can just make it.
– After a two day measurement shift, you find that from the data collected on the first day, there is a signification correlation between several of the variables. The data from the second day shows no relations at all. Probably, something went wrong on the second day. Therefore, you decide to remove these data points from the sample.