Question

question 1 (8 points)
a university statistics department is conducting a series of randomized comparative experiments to compare teaching methods. the response variables include students final exam scores and a measure of their attitude toward statistics. one study compares two teaching methods: hands - on learning through labs and traditional lecture - based instruction. the experimental units are six lecture sections of a basic statistics course, taught by three different instructors, as shown in the table below

a. describe the design of an experiment using blocking to determine which lecture method is most effective. be sure to explain how you will randomly assign the treatments.
b. explain the advantages of a randomized block design over a completely randomized design in this case.

Explanation:

Part a

• Blocking: Since there are three instructors (Hector, Ross, Pieters), we will form three blocks. Each block will consist of the sections taught by a single instructor. For example, Block 1 has sections 1 and 5 (taught by Hector), Block 2 has sections 2 and 3 (taught by Ross), and Block 3 has sections 4 and 6 (taught by Pieters).
• Random Assignment: Within each block, we randomly assign one of the two teaching methods (hands - on learning through labs or traditional lecture - based instruction) to each section. For instance, in Block 1 (Hector's sections), we can flip a coin. If it's heads, section 1 gets hands - on learning and section 5 gets lecture - based instruction; if it's tails, section 1 gets lecture - based instruction and section 5 gets hands - on learning. We do the same random assignment (using a random number generator or a similar randomization device) within Block 2 (Ross's sections) and Block 3 (Pieters's sections).

Part b

• Reducing Variability: In a completely randomized design, differences in instructor teaching styles (a confounding variable) could affect the response variables (final exam scores and attitude). By blocking on instructors, we reduce the variability within each block. Instructors have their own unique teaching characteristics. For example, one instructor may be more engaging in general. By comparing the two teaching methods within the same instructor (block), we can more accurately attribute differences in the response variables to the teaching methods rather than to differences in instructors.
• Increasing Precision: Randomized block design allows for a more precise estimate of the treatment (teaching method) effect. Since we control for the instructor factor (by having both treatments within each instructor's block), the experimental error (variability not due to the treatment) is reduced. This makes it easier to detect a true difference between the two teaching methods if one exists.

Answer:

Part a

Form three blocks based on instructors (Hector, Ross, Pieters). Randomly assign one of the two teaching methods to each section within each block (e.g., using coin - flip or random number generator).

Part b

Randomized block design reduces variability due to instructor differences (a confounding variable) and increases precision in estimating the teaching method effect.