# Analysis of two-way tables--drinking behavior and class attendance

This activity offers students direct experience with the 4 steps involved in hypothesis testing for two categorical variables, as presented in a two-way table:

1. State the appropriate null and alternative hypotheses, Ho and Ha.
2. Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic.
3. Find the p-value of the test.
4. Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.[1]

## Contents

### Inference for two categorical variables

Use this activity for in-class collaborative group work.

Estimate for completion time: 45 minutes

Materials needed:

• 4-step hypothesis testing template (shown below) for each group (handout, in .odt file format--OpenOffice.org Writer)
• Analysis software (SPSS, PPSP, SAS, R, Minitab, Excel, Calc)
• Data[2]:
Missed a class Nonbinger Occasional binger Frequent binger
No 4617 2047 1176
Yes 446 915 1959

(: reminder to add handout, in .odt file format )

# Activity

 Analysis of a two-way table In the Harvard School of Public Health 1999 College Alcohol Study, a random sample of students from 119 4-year U.S. colleges were surveyed as to frequency of alcohol consumption and occurrence of typical alcohol related problems. In particular, students who drank alcohol in the past year were asked if they had missed a class due to drinking. Based on reported frequency of alcohol consumption, students were classified by level of binge drinking behavior.[3] Design and implement hypothesis test Form students into groups of 2-4 students. Each group will need access to a laptop with statistical software loaded and a copy of the handout. Have the students complete the handout as a group, which includes the following information. Identify the following: Explanatory variable: Response variable: State the appropriate null and alternative hypotheses and set the significance level. Ho: Ha: Significance level: Indicate what distribution is to be used for the hypothesis test, including degrees of freedom: State what test statistic will be used to summarize the data. Indicate whether a one-tailed or two-tailed test will be used. Enter the data or open a provided dataset into the statistical software. Check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic. Summarize the sample data in a two-way table. Describe how the groups compare using conditional percentages. Confirm that the conditions for use of the chosen test statistic have been met. (Continue even if the conditions are not met, and be ready to discuss noted violations in follow-up.) Calculate and report the test statistic. Find the p-value of the test. p-value: Explain what the p-value means. Create a sketch of the appropriate distribution, label the x axis and shade the region(s) corresponding to the p-value. Based on the p-value, decide whether or not the results are significant and draw your conclusions in context. Indicate whether or not Ho is rejected. Provide a reason for this decision. Draw conclusions based on the results, given the context of the scenario. Use data from the analysis to support your claim. Follow-up discussion Review the results. Were the conditions met? Were the test results significant? What can we conclude about our research question based on the results. Are there limitations to our study? Sample? Generalizing to population? Method? How do you think the very large sample size affected the chi-square statistic?

### Resources

The following resources were used for ideas and organization in the development of this activity:

### References

1. Open Learning Initiative. Statistics. Retrieved from the Open Learning Initiative web site http://oli.web.cmu.edu/openlearning/forstudents/freecourses/statistics.
2. Wechsler, Henry, Lee, Jae Eun, Kuo, Meichun, and Lee, Hang. "College Binge Drinking in the 1990s: A Continuing Problem," Journal of American College Health. 48 (2000), pp. 199-210
3. Wechsler, Henry, Lee, Jae Eun, Kuo, Meichun, and Lee, Hang. "College Binge Drinking in the 1990s: A Continuing Problem," Journal of American College Health. 48 (2000), pp. 199-210