Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?
$\begin{array}{|l|l|l|}\hline & \text { Males } & \text { Females } \\\hline \text { Fatal } & 275 & 142 \\\hline \text { Non-fatal } & 3024 & 564 \\\hline\end{array}$
-To determine whether there appears to be a statistically significant relationship between sex of the driver and fatality of their accidents we would conduct a ?² analysis. When performing this analysis, which of the values below is closest to the contribution to the ?² statistic from the "non-fatal : female" category?

Question

Consider the following values for numbers of major traffic accidents involving male and female drivers. The accidents are divided into ones involving a fatality and ones that did not. What is the relative risk for male drivers with regard to fatal accidents?

\begin{array}{|l|l|l|}\hline & \text { Males } & \text { Females } \\\hline \text { Fatal } & 275 & 142 \\\hline \text { Non-fatal } & 3024 & 564 \\\hline\end{array}

-To determine whether there appears to be a statistically significant relationship between sex of the driver and fatality of their accidents we would conduct a ?² analysis. When performing this analysis, which of the values below is closest to the contribution to the ?² statistic from the "non-fatal : female" category?

Quizplus · Accepted Answer

The analysis in question is a Chi-square ($\chi^2$) analysis, used to determine if there is a significant relationship between two categorical variables. To calculate the contribution to the $\chi^2$ statistic from the "non-fatal : female" category, we use the formula: $$ \frac{(O - E)^2}{E} $$ where $O$ is the observed frequency and $E$ is the expected frequency. The expected frequency is calculated based on the marginal totals and the overall total. For the "non-fatal : female" category, the observed frequency is 564. The expected frequency can be calculated as: $$ E = \frac{(\text{Total non-fatal}) \times (\text{Total females})}{\text{Grand total}} = \frac{(3024 + 564) \times (142 + 564)}{275 + 142 + 3024 + 564} $$ Plugging in the numbers: $$ E = \frac{3588 \times 706}{4005} \approx 631.22 $$ Then, the contribution to the $\chi^2$ statistic is: $$ \frac{(564 - 631.22)^2}{631.22} \approx 7.42 $$ This calculation shows how much the "non-fatal : female" category contributes to the overall $\chi^2$ statistic, indicating the difference between observed and expected frequencies in this category.

Consider the Following Values for Numbers of Major Traffic Accidents