Q 1.99. - Elementary Statistics

Question

Dental Hygiene: Which Toothbrush? In an experiment reported by J. Singer and D. Andrade in the article " Regression Models for the Analysis of Pretest / Posttest Data " ( Biometrics, Vol . 53, pp . 729-735 ), the effect of using either a conventional or experimental ( hugger ) toothbrush was investigated. Twelve female and 12 male preschoolers were selected. Within each gender group, six were randomly assigned to the conventional toothbrush and the remaining six to the experimental toothbrush. After each subject brushed with the assigned toothbrush, a dental plaque index was measured. The higher the dental plaque index, the greater was the amount of plaque on an individual's teeth. 

(a) Is the statistical design described here a completely randomized design or a randomized block design? Explain your answer. 

(b) If the statistical design is a randomized block design, what are the blocks?

Step-by-Step Solution

Answer

Part (a) Randomized block design.

Part (b) Male and female.

Part (a) Step 1. Given information.

The given statement is:

In an experiment reported by J. Singer and D. Andrade in the article " Regression Models for the Analysis of Pretest / Posttest Data, the effect of using either a conventional or experimental ( hugger ) toothbrush was investigated.

Twelve female and 12 male preschoolers were selected. Within each gender group, six were randomly assigned to the conventional toothbrush and the remaining six to the experimental toothbrush. After each subject brushed with the assigned toothbrush, a dental plaque index was measured. 

The higher the dental plaque index, the greater the amount of plaque on an individual's teeth.  

Part (a) Step 2. Identify if the given statistical design is a completely randomized design or a randomized block design.

In the experiment, 12 female preschoolers and 12 male preschoolers were chosen, resulting in two blocks. 

In addition, six children in each group were randomly assigned to a regular toothbrush and six to an experimental toothbrush.

The dental plaque index was assessed after each child brushed with the given toothbrush. 

As a result, the given statistical design is clearly a randomized block design.

Part (b) Step 1. Identify the blocks.

The experimental units (preschoolers) are grouped under two blocks in the offered study.

As a result, there are two blocks involved: male and female.