Subject: 36-303: Team C & E variance calculations From: Brian Junker Date: Sun, 27 Mar 2011 13:47:18 -0400 To: ssindler@andrew.cmu.edu, eboncek@andrew.cmu.edu, klchang@andrew.cmu.edu, lmosca@andrew.cmu.edu, cjchang@andrew.cmu.edu CC: thiggins@andrew.cmu.edu, mbelenky@andrew.cmu.edu, jsperger@andrew.cmu.edu, tianw@andrew.cmu.edu, chaowang@andrew.cmu.edu Both of your teams (C and E) have sampling designs that involve one-stage clustered sampling within strata stratified one-stage clustered sampling). For Team C each stratum is a college (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" undergrad courses that meet your criteria for entering the study (either all courses required for the major, or all undergrad courses, depending on what your group decides). For Team E each stratum is a 3-hour block (morning, lunch, afternoon, evening) and the clusters within each stratum are 1-hour observation periods sampled over the two weeks of observation that you are doing. The individual responses will be observations on each bus visiting the two Forbes & Morewood bus stops. Both teams should do SE and CI calculations using a slightly modified version of the formulas on the "stratified sampling" handout. The modification is this: instead of using individuals (instructors, buses) as the "units" in the stratified sampling handout, you will use clusters (departments, 1-hour observation blocks) as the "units". The "response" for each unit will be the average over all individuals in that unit (so the response for a department will be the average over all courses in that dept, the response for a 1-hour block will be an average over all the buses in that block). You will need to look up or calculate N_h (the total number of clusters within each stratum: for team C the number of depts within each college; for team E the total possible number of 1-hour obs periods in a 3-hour block [aggregated over your two weeks of observation]), and you will need to know n_h (the number of depts sampled in each college for C, and the number on 1-hr obs periods sampled over the course of your two weeks within each stratum, for team E). Then all the formulas from the stratified sampling handout work perfectly, using your clusters as the units in that handout. Of course if you have any questions, please don't hesitate to consult with each other (within *and* between teams is fine!) or ask me (via email or meetings). all best, -BJ -- Brian Junker (412) 268 - 2718 Department of Statistics brian@stat.cmu.edu 232 Baker Hall FAX: (412) CMU-STAT Carnegie Mellon University or (412) 268-7828 Pittsburgh PA 15213 USA WWW: http://www.stat.cmu.edu/~brian/