A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table.
$$\begin{array}{l}
\begin{array} { | l | r r r r | }
\hline &{ \text { sleep-disordered breathing } } \
& \text { none } & \text { mild } & \text { moderate } & \text { severe } &\text { total }\
\hline \text { death } & 476 & 320 & 165 & 86&1047 \
\text { no death } & 2953 & 1477 & 562 & 255&5247 \
\hline \text { total } & 3429 & 1797 & 727 & 341 \
\hline

\end{array}
\end{array}$$ We want to know whether the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death. What is the degrees of freedom for the appropriate chi-square test?

Question

A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table.
$$\begin{array}{l}
\begin{array} { | l | r r r r | } 
\hline &{ \text { sleep-disordered breathing } } \
& \text { none } & \text { mild } & \text { moderate } & \text { severe } &\text { total }\
\hline \text { death } & 476 & 320 & 165 & 86&1047 \
\text { no death } & 2953 & 1477 & 562 & 255&5247 \
\hline \text { total } & 3429 & 1797 & 727 & 341 \
\hline

\end{array}
\end{array}$$ We want to know whether the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death. What is the degrees of freedom for the appropriate chi-square test?

Quizplus · Accepted Answer

The degrees of freedom for a chi-square test in a contingency table are calculated as (number of rows - 1) * (number of columns - 1). Here, we have 2 rows (death, no death) and 4 columns (none, mild, moderate, severe), so the degrees of freedom are (2-1)*(4-1) = 1*3 = 3.

A Study Prospectively Examined Whether Sleep-Disordered Breathing Was Associated with an Increased