MaMOSCOREDMAMAN 90 14.9 Exercises 853 response variable. A control group is also included to measure the change in reasoning for chil- dren not given any special instruction. A pilot study with only 20 students was to be conducted prior to the complete study to determine potential problems. Demonstrate how to assign 5 of the 20 students to each of the four instructionalonditions- no instruction (control), piano lessons, computer video games, and instructor-so that the assignment is completely random. 14.2 Refer to Exercise 14.1. The researchers decide to use the following model, which relates the response variable y to the four instructional conditions. y = u+ T;+ & for i = 1, 2, 3,4 and j = 1, 2, 3, 4, 5 a. Write an equation relating the mean reasoning score, u;, to the parameters in the above model without any constraints on the model parameters. b. Rewrite the equation relating the mean reasoning score, Mi, to the parameters in the above model after imposing the standard constraints placed on the model parameters. ing the pilot study, the researchers conduct a study involv-Vi - y:) V2 14.9 Exercises 14.2 Completely Randomized Design with a Single Factor Edu. 14.1 Researchers in child development are interested in developing ways to increase the sport temporal reasoning of preschool children. Spatial-temporal reasoning relates to the chils ability to visualize spatial patterns and mentally manipulate them over a time-ordered sequel of spatial transformations. This ability, often referred to as thinking in pictures, is important for generating and conceptualizing solutions to multistep problems and is crucial in early child denied opment. The researchers want to design a study to evaluate which of several methods proposed to accelerate the growth in spatial-temporal reasoning yields the greatest increase in a child's development in this area. There are three methods proposed: taking piano lessons for 3 months playing specially developed computer video games for 3 months, and playing specially designed games in small groups supervised by a trained instructor. The researchers measure the effective. ness of the three programs by assessing the children and assigning each one a reasoning score both before and after participation in the program. The difference in these two scores is the