Any line that starts with "Although not statistically significant" should be automatically deleted.
“Not statistically significant” does not mean the effect does not exist. It means that the study provides weak evidence, but weak evidence ≠ no evidence. It tags things for further study.
This is one of those cases where people get too hung up on P values. You have to look at the bigger picture; look at the entire scientific process.
It may provide evidence of other hypotheses.
So you're right, but you're also wrong, without making yourself more clear.
Poor precision in the use of language around clinical data has been a major problem in all of this, in the press especially, where for the most part they clearly don't give a damn and just have an agenda to spin in most cases. Because of this, scientists publishing ought to try to use language that ensures their work cannot be misinterpreted. The notes in the results section here about non-statistically significant aspects to the data fail that test, since an average reader would likely walk away with a false mental model of what the data is showing.
edit: my comment is wrong, i'm tired and haven't had enough coffee. the criticisms below are valid. i do have a point, but won't jam it in here.
Again, this is incorrect. It provides weak evidence, not no evidence. You talk about precise language here but you are conflating “not statistically significant” with “no evidence”. You can’t just handwave the difference between these two things.
It does provide some evidence: we are more likely to see this result in a world where the hypothesis is true than a world where it is false.
This is a heuristic which helps things stay within our limited reasoning capacity, cuts down on the noise level from all the activity in the scientific community to focus on what's important, and helps with inherently binary organizational decisions (e.g. should this experiment be published in a journal or not? Should we give this medicine to patients or not?)
A better approximation of optimal Bayesian reasoning would be continuous updating of your prior with no cutoff. Even a study with a very weak p-value in the right direction should in theory slightly tweak your priors in favor of the hypothesis. (But you also have to tweak slightly against the hypothesis for studies with very weak p-values in the wrong direction, and compensate for selection effects, e.g. if experiments with underwhelming or wrong-direction p-values are underpublished.)
Even weak p-values below the binary decision threshold contain information. It's just that effectively denoising and acting on that information is more difficult and fraught with pitfalls than binary decisions based on strict thresholds. So science mostly standardizes on the safer approach, although there are some people who try to wring precious drops of information out of experiments that fall below the usual statistical cutoffs (often by so-called meta-analysis that combines results of multiple studies).
But the binary decision “let’s use drug X to treat condition Y”, and the binary decision “let’s investigate the efficacy of drug X on condition Y” each come with radically different tolerances for type I and type II errors.
For example, statistically chocolate doesnt cause acne. Yet I 100% get acne from chocolate.
There is enough variance in people that many things that work anecdotally cannot be proven statistically.
In general, when less data is available, larger p values are considered more interesting, while when more data is available, p must be smaller to be interesting. In particle physics, p < 0.001 means almost nothing. In the particular quoted line, p = 0.07ish which is above the human-defined, conventional threshold of 0.05 but in this case there are almost no other useful data and so the phenomenon is interesting.