There has been a major initiative to include the use of laptop computers as a part of the lesson plan in math and science courses in middle schools. There has been some resistance to the inclusion due to costs and the reluctance on the part of some teachers to increase their use of technology-based instruction. A major study was designed in a large midwestern state to study these issues. The school districts in the state were divided into three groups: urban, rural, and mixed urban-rural. Ten school districts were randomly selected within each of these three groups. Five randomly selected schools provided a weeklong workshop on how to include laptops in their daily instruction, and the other five schools were given only a manual that described laptop ­implementation strategies. Six teachers were randomly selected from each of the 30 schools. The teachers’ classroom and lesson plans were then examined to determine the degree to which they had included laptops into their instruction. The researchers were interested in determining the impact on instruction of type of school district and type of training. Also, they wanted to measure the variability among schools of the same type and among teachers from the same schools.
a. Identify each of the factors as fixed or random; justify your answer.
b. State whether the factors are nested or crossed; provide reasons for your answers.
c. Provide an AOV table that includes source of variation, df, and expected mean squares.