Question

Binge Drinking The American College Health Association - National College Health Assessment survey \(,{ }^{17}\) introduced on page 60 , was administered at 44 colleges and universities in Fall 2011 with more than 27,000 students participating in the survey. Students in the ACHA-NCHA survey were asked "Within the last two weeks, how many times have you had five or more drinks of alcohol at a sitting?" The results are given in Table 7.31 . Is there a significant difference in drinking habits depending on gender? Show all details of the test. If there is an association, use the observed and expected counts to give an informative conclusion in context. $$ \begin{array}{c|rr|r} \hline & \text { Male } & \text { Female } & \text { Total } \\ \hline 0 & 5,402 & 13,310 & 18,712 \\ 1-2 & 2,147 & 3,678 & 5,825 \\ 3-4 & 912 & 966 & 1,878 \\ 5+ & 495 & 358 & 853 \\ \hline \text { Total } & 8,956 & 18,312 & 27,268 \\ \hline \end{array} $$

Short answer

The answer is determined by comparing the computed Chi-Square test statistic with the critical value. If the test statistic is greater than the critical value, it can be concluded that there is a significant difference in drinking habits by gender.

Step-by-step solution

- Determine the Observed Counts

The observed counts are already given in the table in the exercise. The counts correspond to the number of males and females in each category of drinking habits.

- Calculate the Expected Counts

The expected count for each cell in the table is calculated using the formula: (Row Total * Column Total) / Grand Total. To find the expected value for each cell, multiply the total for each row by the total for each column then divide by the overall total (27,268). The calculated values will be the expected counts for each cell.

- Compute the Chi-Square Test Statistic

The Chi-Square test statistic is computed using the formula: \[\chi^{2} = \sum \frac{(O - E)^{2}}{E}\]where 'O' is the observed count and 'E' is the expected count. The test statistic should then be computed for each cell in the table and then summed to get the overall test statistic.

- Determine the Degrees of Freedom and Find the Critical Value

The degrees of freedom for the Chi-Square distribution are calculated using the formula: (number of rows - 1) * (number of columns - 1), which in this case is (4 - 1) * (2 - 1) = 3. Find the critical value for a Chi-Square distribution with degrees of freedom using a statistical tables.

- Draw Conclusion

Compare the computed Chi-Square test statistic with the critical value. If the computed value is greater than the critical value, reject the null hypothesis and conclude that there is a significant difference in drinking habits by gender. If the observed chi-square statistic is smaller, there is no evidence to suggest there's an association between drinking habits and gender.

Key concepts

Binge Drinking Statistics

Binge drinking, defined as consuming a significant amount of alcohol in a short period, is a concerning behavior with various health and social consequences. Gathering and analyzing statistics on binge drinking, especially within specific populations such as college students, helps public health officials, educators, and policymakers to understand and address the issue.

Surveys like the American College Health Association - National College Health Assessment provide valuable data on such behaviors. By examining the frequency of consumption, trends can be identified, interventions can be planned, and the effectiveness of policies can be assessed over time. These statistics not only reveal overall patterns within the student body but also allow for a deeper analysis of subgroup behaviors, such as by gender or age groups.

Gender Differences in Drinking Habits

Exploring gender differences in drinking habits is elemental to understanding the social dynamics and implications of alcohol consumption. It's commonly researched that males and females may have different patterns of drinking, influenced by biological, psychological, and cultural factors.

Studies, like the ACHA-NCHA survey, usually display variations in the frequency and quantity of alcohol consumed by different genders. For instance, males might be more inclined toward higher frequency and quantity, while females may have varied patterns. It is these nuances that underscore the need for gender-sensitive approaches when designing educational programs and interventions for reducing harmful drinking behaviors.

Statistical Significance

When examining data from surveys on habits like drinking, the concept of statistical significance becomes paramount. It's a measure that helps to determine whether the observed differences in data, such as between male and female drinking habits, are due to random chance or reflect a true underlying pattern.

If we find that data reaches a level of statistical significance, we accept that our results are not the product of happenstance, but instead may represent a meaningful phenomenon. In studies related to health behaviors, finding statistically significant results can lead to more targeted public health strategies and can validate the need for new policies or interventions.

Expected Counts Calculation

The heart of the Chi-Square test is the comparison of observed counts with what we would expect in a world where no association exists between the variables—in this case, gender and drinking behavior. Expected counts are theoretical frequencies that we'd predict if there were no difference or relationship between the groups we're studying.

The Chia-Square test uses the formula \( (Row Total \times Column Total) / Grand Total \) to calculate these expected counts, creating a benchmark against which the actual observed counts are measured. The discrepancies between the observed and expected values, quantified through the Chi-Square statistic, inform us if there's a statistically significant difference between groups or if any observed difference is within the realm of randomness.