Concerns have been expressed over standards of statistical interpretation. Results with p<0.05 are often referred to as “significant” which, in plain English, implies important. This leads some people directly into the misconception that this provides proof that associations are clinically relevant. There are calls for statistics educators to respond to these concerns. This article provides novel plain English interpretations that are designed to deepen understanding. Experience teaching post-graduates at Imperial College is discussed. A key issue with focusing on “significance”, is the common inappropriate practice of implying no association exists, simply because p>0.05. Referring to strengths of association in “study participants” gives them gravitas, which may help to avoid this. This contrasts with the common practice of focusing on imprecision, by referring to the “sample” and to “point estimates”. Unlike formal statistical definitions, interpretations developed and presented here are rooted in the application of Statistics. They are based on one set of study participants (not many random samples). Precision of strengths of association are based on using strengths in study participants to estimate strengths of association in the population (from which participants were selected by probability random sampling). Reference to “compatibility with study data, dependent on statistical modelling assumptions”, reminds us of the importance of data quality and modelling assumptions. A straight-forward graph shows the relationship between p-values and test statistics. This figure and associated interpretations were developed to illuminate the continuous nature of p-values. This is designed to discourage focus on whether p<0.05, and encourage interpretation of exact p-values.