Statistical Literacy: Seeing How Statistical Significance Is Contextual

In observational studies, a statistically significant relationship can become statistically insignificant after taking into account the influence of a confounding factor. This is simply a result of the fact that in observational studies, all associations are contextual. Associations can change depending on what you take into account. First, a graph type is introduced that displays the influence of both binary predictor variables on a rate outcome. Secondly the non-interaction condition is introduced to simplify the presentation. Three cases are examined: an association is changed, does not disappear and is not reversed, an association is changed, does not disappear and is reversed, and an association is changed and disappears (is spurious). Third, confidence intervals are used to identify whether an observed difference between two percentages is statistically significant. The influence of a third factor is shown to be able to transform a statistically significant relation into one that is statistically insignificant. Although none of this is new, this approach to statistical significance and the influence of context is readily presented and easily understood. This approach is strongly recommended for those teaching introductory statistics.