An idea has been proposed that the tone of a public health message (for example, a road safety message) needs to match the personality of the audience receiving it. This might also be true of, for example, a message promoting public transport. If the necessity of matching message to audience is a reality, it refers to what is termed crossover interaction in a factorial experiment: one thing is superior to another in condition 1, but is inferior in condition 2. A model for this involves taking the numerical difference between two quantities, and then some nonmonotonic function of the difference. In the present context, that would be measuring the tone of a message and the personality of the audience on the same scale, calculating the difference, with the response being an inverted-U shaped function of the difference. That is, the biggest response occurs for the smallest difference. The present paper attempts to integrate (on the one hand) the words that have been used in specific instances of heterogeneity of effects with (on the other hand) the mathematical symbols and expressions intended to be adaptable to a broad range of applications. Making a mathematical model familiar will facilitate the communication of particular instances of its use. (a) For the covering entry of this conference, please see ITRD abstract no. E216383.
Abstract