36-303: Variance Calculations for Teams C and E Brian Junker March 24, 2011

Team C (Performance vs Attendance in CMU classes) and Team E (Accuracy of Bus Schedules) both have a sample design that involves clustered sampling within strata. These notes should help you think about variance, SE and confidence interval calculations for your projects. You will also be able to think about sample size calculations.

Teams C and E have sample designs involving one-stage clustered sampling within strata (stratified one-stage clustered sampling).

• For team C, each stratum is a college in the university (HSS, CIT, CS, CFA, etc.) and the clusters within each stratum are departments within each college. The individual responses will be from instructors for “all^{1}” undergrad courses in the department.

• For Team E, each stratum is a 3-hour block of time during the day (morning, lunch, afternoon, evening) and the clusters within each stratum are 1-hour observation periods within a 3-hour block. The individual responses will be observations on each bus visiting the two Forbes & Morewood bus stops.

1Team C is still deciding whether “all” means just core major required courses, or includes all possible undergrad offerings.