In the United States, an airplane flies under either "Visual Flight Rules"
("VFR") or "Instrument Flight Rules" ("IFR").  Typically, VFR means the pilot 
can see at least three miles in all directions, including a clear view of the
ground.  When there is less visibility, e.g., when the airplane is in clouds,
the flight must be under IFR.  In order to fly IFR legally, the pilot must have
an "instrument rating."  To earn an instrument rating, the pilot must: (1) pass 
a comprehensive, standardized, multiple-choice exam; (2) take at least 15 hours
of instrument flight instruction (in an airplane); (3) fly at least 40 hours
under instrument conditions (real or simulated); and (4) meet other requirements
that are not relevant here.  Some of the hours required to meet requirements (2)
and (3) may be performed in an "FAA-approved ground simulator," which is a big,
expensive machine, including a cockpit similar to one in an airplane, that
simulates the instrument readings and the physical motions of being in an
airplane under IFR conditions.  Most flight instructors and students do not have
access to FAA-approved ground simulators.  Most students require substantially
more hours of instrument instruction and flying than the minimums stated in (2)
and (3).

     Several software companies with interest in pilot training have developed
IFR simulators that will run on a fast microcomputer.  Each simulator program 
has a database of airports, navigational aids (special radio stations operated 
by the FAA to facilitate navigation under IFR conditions), and related
information.  The program displays real-time images of airplane instruments on
the computer monitor that provide a fairly realistic simulation of the
instruments in a real airplane being flown under IFR conditions.  Since one
operates the computer on a desktop, there is no simulation of the physical
motions of being in an airplane.

     PC-based simulators have not been approved by the FAA for flight training.
That is, the hours spent operating a PC-based simulator cannot be counted 
towards the flight hours required to earn an instrument rating.  However, many
flight instructors feel that experience with a PC-based flight simulator can
enhance training and help students reduce the actual flight time required to
become a proficient IFR pilot.

     An organization interested in pilot training sponsored a study with the
primary objective of evaluating the impact of PC-based simulators on training 
for an instrument rating.  One  volunteer instructor was recruited at each of 
two or three airports within each class of airport (see Table 1). An 
instructor's instrument training students (up to 9 per instructor) were
randomly assigned to one of three levels of use of a PC-based flight simulator:
None (control group), Low (approximately the same number of hours on the
simulator as in the airplane), and High (approximately twice as many hours on
the simulator as in the airplane).  To achieve balance, randomization was
performed within each group of three successive students; that is, for a 
specific instructor, the first three students were randomly assigned to the 
three treatments, then the next set of three students was randomly assigned, 
and finally the third set of three students (if that many were available) was
assigned.

     Each instructor subjected each of his/her students to a flight test at each
of five evaluation times: at baseline (initiation of training) and after 25%,
50%, 75%, and 100% of the instrument training curriculum.  The flight test was
conducted in accordance with the FAA's Instrument Rating Practical Test
Standards, which require evaluation in the following areas: (1) Air Traffic
Control Clearances and Procedures, (2) Flight by Reference to Instruments, (3)
Navigation Aids, (4) Instrument Approach Procedures, and (5) Emergency
Operations.  (Several other areas are also evaluated in an actual flight test 
but were not included in this study.)  The test in each area requires evaluation
of the student on multiple tasks.  The scores from the various tasks are
averaged, producing one score in the range 0-100 (0 <--> abject failure, 100 
<--> extremely proficient) for each of the evaluation areas listed above. Thus,
each time a student was evaluated, the student received 5 scores, one for each
area.

     Pilots initiate instrument training at various ages and various levels of
experience.  Each pilot's age at baseline was recorded.   Each pilot's as total
hours of pilot time (at baseline) was used as a measure of the pilot's prior
experience level.  

     The objectives of the study were:

  To evaluate the effects of various levels of PC-based simulator training on
   mean flight test scores for each of the 5 areas of evaluation, and
   evaluate how this effect varied with class of airport and/or evaluation time.

  To evaluate the effect of class of airport on mean baseline score and also on
   each post-baseline score.

  To evaluate the variability of scores from airport (instructor) to airport
   (instructor) within class of airport.

  To evaluate the effect of amount of training (represented by evaluation
   times) on scores, and evaluate how this effect varied with class of airport
   and/or level of PC-based simulator training.

  To evaluate the covariance structure and covariance parameters of the
   repeated multiple types of measurements from each student.


     The data are available in PCSIM.SSD (SAS version 6.04 dataset) and 
PCSIM.ASC (ASCII), which contain one observation or record for each evaluation
time for each student; the observation or record contains scores from all five
evaluation areas.  The data are also available in "rolled out" datasets,
PCSIMR.SSD (SAS version 6.04 dataset) and PCSIMR.ASC (ASCII), which contain one
observation or record for each evaluation area score for each evaluation time 
for each student; i.e., there are up to five observations (records) for each
evaluation occasion for each student. The names and descriptions of variables
are shown in Table 2.

     Unfortunately, some data are missing.  However, for the purposes of this
problem you may assume that any missing data are missing completely at random,
for reasons totally unrelated to the process under study.