12.7 - Example 6 - Evaluation of Sunscreens

Example 12-6 Section

Click on the question mark for each question about the experiment to help un-pack clues toward understanding the appropriate design.

Evaluation of Sunscreens

A study was designed to evaluate the effectiveness of two different sunscreens \( \left( s_1 \text{ and } s_2\right) \) for protecting the skin of persons who want to avoid burning or additional tanning while exposed to the sun. A random sample of 40 subject (age 20 to 25) agreed to participate in the study. For each subject a 1-inch square was marked off on their back, under the shoulder but above the small of the back. Twenty subjects were randomly assigned to each of the two types of sunscreen. A reading based on the scolor of the skin in the designated square was made prior to the application of a fixed amount of the assigned sunscreen, and then again after the application and expose to the sun for a 2 hour period. The company was concerned that the measurement of color is extremely variable, and wanted to assess the variability in the readings due to the technician taking the readings. Thus, the company randomly selected ten technicians from their world-wide staff to participate in the study. Four subkects, two having \(s_1\) and two having \(s_2\), were randomly assigned to each technician for evaluation. The data recorded are the differences (post-exposure minus pre-exposure) for the subject in the study A high reponse indicates a greater degree of burning.

  Technician (B)
Sunscreen (A) 1 2 2 4 5 6 7 8 9 10
\(s_1\) 8.2 3.6 10.7 3.9 12.9 5.5 9.1 13.7 8.1 2.5
7.6 3.5 10.3 4.4 12.1 5.9 9.7 13.2 8.7 2.8
\(s_2\) 6.1 4.3 9.6 2.3 12.4 4.8 8.3 12.9 8.0 2.1
6.8 4.7 9.2 2.5 12.8 4.0 8.6 13.6 7.5 2.5

Experimental Design

Treatment Design

 

How many treatments are there?

 

How many levels of each treatment are there?

 

If there is more than 1 treatment, how are they related?

Crossed: each level of treatments occur with all levels of other treatments. (Factorial)

Nested: levels of a treatment are unique to different levels of another treatment.

 

Are treatments fixed or random effects?

 

Are there continuous covariates? (ANOCOVA)

Randomization Design

 

What is the experimental unit?

An experimental unit is defined as that which receives a treatment, (e.g., plant, person, plot of ground, petri dish, etc.).

Is there more than one experimental unit? (Split Plot)

 

How are treatment levels assigned to experimental units?

Completely at random? CRD

Restriction or randomization?

one-dimension: RCBD

two-dimension: Latin Square

 

Are there sample units within experimental units? How many true replications are there?

 

Are there repeated measurements made on experimental units?


Solution

What is the experimental design?

A two factor crossed design with 2 replications in a CRD.

Sunscreen is a fixed effect, technicians are a random effect.