You missed out the only meaning that is likely to apply to...

You missed out the only meaning that is likely to apply to announcements in a scientific endeavour, which is statistical significance:
3. Statistics. of or relating to observations that are unlikely to occur by chance and that therefore indicate a systematic cause.
http://www.dictionary.com/browse/significant

The determining factors in whether our results are significant our not are:
a) How different the average values are between control and experiment.
b) Sample size
c) Standard deviation of averages.

There are only three possible outcomes... we could make children significantly worse, significantly better, or not make enough difference to be significant.