> So what does it mean? What was the goal of collecting the data? What would the interpretation have been if the data would show a significant positive effect of Theanine?
I think what the author is saying is that for them to bother with theanine on a permanent basis, it would have to have shown an effect large enough to be apparent just from plotting.
In other words, they mean technical significance as opposed to clinical significance. A small effect can be statistically verifiable without being meaningful in practice.
an effect large enough to be
apparent just from plotting
And how large is that? Without putting a number on it, how do we come to the conclusion that the effect is not large enough? That it didn't show in their sample of data points could have been just random chance.
But before we take the measured effects at face value, I think it's important think about them more. They report significant p values of their success in predicting if the capsule holds Theanine and also for the effect of the capsule when it holds Theanine. Both negative correlations. My first thought reading this is that the Placebo tasted more like Theanine and thinking they took Theanine had a positive effect on the outcome.
I think what the author is saying is that for them to bother with theanine on a permanent basis, it would have to have shown an effect large enough to be apparent just from plotting.
In other words, they mean technical significance as opposed to clinical significance. A small effect can be statistically verifiable without being meaningful in practice.