The solution is to apply the time-honoured tactic of circumlocution to disguise the non-significant result as something more interesting. The following list is culled from peer-reviewed journal articles in which (a) the authors set themselves the threshold of 0.05 for significance, (b) failed to achieve that threshold value for p and (c) described it in such a way as to make it seem more interesting.
As well as being statistically flawed (results are either significant or not and can’t be qualified), the wording is linguistically interesting, often describing an aspect of the result that just doesn’t exist. For example, “a trend towards significance” expresses non-significance as some sort of motion towards significance, which it isn’t: there is no ‘trend’, in any direction, and nowhere for the trend to be ‘towards’.
What follows is a list of hundreds of phrases authors have used; here are just the O’s:
on the border of significance (p=0.063)
on the borderline of significance (p=0.0699)
on the borderlines of significance (p=0.08)
on the boundaries of significance (p=0.056)
on the boundary of significance (p=0.055)
on the brink of significance (p=0.052)
on the cusp of conventional statistical significance (p=0.054)
on the cusp of significance (p=0.058)
on the edge of significance (p>0.08)
on the limit to significant (p=0.06)
on the margin of significance (p=0.051)
on the threshold of significance (p=0.059)
on the verge of significance (p=0.053)
on the very borderline of significance (0.05<p<0.06)
on the very fringes of significance (p=0.099)
on the very limits of significance (0.1>p>0.05)
only a little short of significance (p>0.05)
only just failed to meet statistical significance (p=0.051)
only just insignificant (p>0.10)
only just missed significance at the 5% level
only marginally fails to be significant at the 95% level (p=0.06)
only marginally nearly insignificant (p=0.059)
only marginally significant (p=0.9)
only slightly less than significant (p=0.08)
only slightly missed the conventional threshold of significance (p=0.062)
only slightly missed the level of significance (p=0.058)
only slightly missed the significance level (p=0·0556)
only slightly non-significant (p=0.0738)
only slightly significant (p=0.08)
https://mchankins.wordpress.com/2013/04/21/still-not-significant-2/
