I fine example of the unhelpful confusion between statistical and real-world significance appeared in a little New Scientist report this week. The very brief story went as follows:
Girls aged 13 and 14 who use social media frequently tend to be less happy and more anxious than those who use it less. But taking into account sleep, physical activity and cyberbullying, the effect of frequent social media use was found to be insignificant.
A post on the New Scientist blog gives more information, but also seems to buy into the idea that "social media" just isn't the problem - it's sleep loss, lack of exercise and cyberbullying that cause the mental health issues: "Lack of sleep is more of a problem for teen girls than social media".
But that's not what the original article said, or found: Roles of cyberbullying, sleep, and physical activity in mediating the effects of social media use on mental health and wellbeing among young people in England: a secondary analysis of longitudinal data

It's a follow-up to a study that showed an association between frequency of social media use and mental health problems, and attempts to tease out what mediates the linkage. So there's a cluster of cyberbullying, disturbed sleep, reduced physical activity and frequent social media use that correlates with mental health issues. In a particular group of girls, if you look at three of this cluster you don't need the fourth to account statistically for the observed correlation. (In boys, you need the fourth, too.) That doesn't render social media "insignificant", except in a statistical sense - there's undoubtedly a complicated web of relationships within this cluster, as well as with mental health.

Grant Hutchison