Interpret an association in context

Interpreting an association

An association describes a tendency in paired data. State how the response variable tends to change as the explanatory variable changes, and limit the conclusion to the observed cases

1. Start with the roles Name the explanatory variable first and the response variable second \(\displaystyle \text{EV}=x,\quad\text{RV}=y\)
2. Preserve the direction A positive association has the same general movement; a negative association has opposite movement \(\displaystyle \text{positive: }x\uparrow\Rightarrow y\uparrow,\quad\text{negative: }x\uparrow\Rightarrow y\downarrow\)
3. Use tendency wording Use words such as tends to or generally because individual cases can differ \(\displaystyle \text{as }x\text{ increases, }y\text{ tends to increase}\)
4. Do not claim causation An observed association does not show that changing one variable causes the other to change \(\displaystyle \text{association}\not\Rightarrow\text{causation}\)

Worked example

A school survey records five pairs of evening screen time and sleep duration. The data show a negative association. State the interpretation for the observed students

1. \(\displaystyle \text{EV}=\text{evening screen time},\quad\text{RV}=\text{sleep duration}\)Screen time is the explanatory variable and sleep duration is the response variable
2. \(\displaystyle \text{negative association}\Rightarrow\text{RV tends to decrease as EV increases}\)A negative association means the response tends to move down as the explanatory variable moves up
3. \(\displaystyle \text{Among the students surveyed, sleep duration tends to decrease as evening screen time increases}\)The interpretation uses tendency wording for the observed students
4. \(\displaystyle \text{association}\not\Rightarrow\text{causation}\)The survey does not by itself show that screen time causes the change in sleep duration

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