Effect size is the amount of change that has been observed, in this case the ability to memorize things. Significance is the probability of the result being co

Effect size is the amount of change that has been observed, in this case the ability to memorize things. Significance is the probability of the result being coincidence. So "highly significant" only means "most probably not coincidence". That means you can have a "highly significant" result where the actual result (= effect size) is tiny. In study design, both are related: The higher the number of test persons, the easier it is to archive significance. Therefore, proper design would be to first guesstimate (based on existing literature etc.) the effect size, then define the minimum number of test persons necessary.