I'm looking for examples of studies where the result is highly significant but the effect is so tiny that it is meaningless in a practical sense. These will be shared with undergraduate psychology students to illustrate that statistically significant doesn't always mean important or consequential.
One example might be the effect of birth order on intelligence. Given a large enough sample there highly significant effects (p<.00001). However, these effects are very very small.
For a recent example, see Rohrer, Egloff, and Schmukle (2015): the effect of one birth order position was only one tenth of a standard deviation (1.5 IQ points)
To illustrate this small effect, in our between-family sample of sibships of two, a randomly picked firstborn had a 52% chance of having a higher IQ than a randomly picked secondborn; conversely, a secondborn had a 48% chance of having a higher IQ than a firstborn.
Rohrer, J. M., Egloff, B., & Schmukle, S. C. (2015). Examining the effects of birth order on personality. Proceedings of the National Academy of Sciences, 201506451. http://doi.org/10.1073/pnas.1506451112