This exam is open book, open notes; you may use a calculator. Show your work to receive full credit. Use the back if more space is needed. Each question (or part) is worth 10 points.
1) Confound a 
factorial into 2 blocks of 8 using BCD as
the defining contrast. Show which factor/level combinations go
into which block.
2. Describe the experimental design used for each of the following, and give a skeleton ANOVA (sources and df only). Be sure to tell me what are treatments, units, blocks, etc.
a) We wish to study gender bias in paper grading. We have 12 ``lower" level papers, and 12 ``advanced" level papers. There are four paid graders who do not know the students or their names. Each paper is submitted for grading exactly once (ie, no paper is graded by more than one grader). We look at gender by the name put on the paper: either a male first name, a female first name, or just initials. The 12 lower level papers are assigned at random to the combinations of grader and name gender, as are the advanced level papers. The response we measure is the grade given (on a 0-100 scale).
b) Song bird abundance can be measured by sending trained observers to a site who listen for the calls of the birds and make counts. Consider an experiment on the effects of three different forest harvesting techniques on bird abundance. There are six forests, and there will be two harvests in each of the six forests. The harvest techniques were assigned in the following way:
c) Consider an experiment to determine if police arrest policies affect the recurrence of spouse assault. When police arrive at a spouse assault complaint, a randomization is performed and one of three actions is taken: warning (stay away for 8 hours and cool off), short arrest (book and release), or long arrest (keep overnight). The response measured is the number of spouse assault incidents in which the perpetrator is involved in the next six months. Three hundred perpetrators are included in the study.
d) Consider a study on the influence of two factors on the potency of frozen boar semen. The semen can be frozen using one of two different cryo-protectors (factor A) and using one of two temperature regimes (factor B). Potency is measured by counting the number of fertilized eggs produced when the semen is thawed and used. We expect large sow to sow differences in fertility, so we block on sow by using one factor/level combination in each of the two horns of the uterus. Eight sows were used, with the following treatment assignment.
3) Describe an appropriate experimental design for each of the following situations.
a) We wish to study the effect of blood doping (injection of extra red blood cells prior to a race) on the performance of distance runners (time to complete the race). One hundred runners have agreed to participate in our study. Each runner will be doped with either red blood cells or a placebo eight hours prior to the race. A factor that may influence time is cardiovascular efficiency (CVE). We may measure CVE one day after the race.
b) We wish to study the differences in liking among three modified fat margarines. We expect large subject to subject differences in liking ratings, and we expect some differences in liking due to meal (breakfast, lunch, or dinner). There are 12 subjects available. The testing must be done all on one day, but we may use any subject for all three meals that day.
c) We wish to study the effects of soil density, pH, and moisture on seed germination. Each factor has two levels. Pots are prepared with appropriate combinations of the factors and then seeds are added to each pot. Four pots are put in a tray, and the trays are scattered around the greenhouse. We have resources for 24 pots.
d) We wish to study new varieties of corn for disease resistance. We start by taking 4 varieties (A, B, C, D) and cross them (eg. pollen from type A, B, C or D fertilizing flowers from type A, B, C, or D), getting 16 crosses. (This is called a diallel cross experiment, and yes, 4 of the 16 ``crosses'' are actually pure varieties.) The sixteen crosses produce seed, and we now treat the crosses as varieties for our experiment. We plant seed from the 16 crosses and observe the disease resistance of the resulting crops. We have 48 plots available, 16 plots in each of St. Paul, Crookston, and Waseca.
4. (Data from Mason, Gunst, and Hess 1989.) A Latin square experiment was performed to study the effect of traffic light signal sequences. Row blocks are five intersections, column blocks are five time periods. The response is unused red light times in minutes (which I think is the amount of red light time when no one is waiting). Analyze these data based on the following summaries:
