12.6 - Example 5 - Accuracy of Calcium Evaluation

Example 12-5 Section

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

Accuracy of Calcium Evaluation

A consumer product agency wants to evaluate the accuracy of determining the level of calcium in a food supplement. There are a large number of possible testing laboratories and a large number of chemicals assays for calcium. The agency randomly selected three laboratories and three assays for use in the study. Each laboratory will use all three assays in the study. Eighteen samples containing 10 mg of calcium are prepared and each assay-laboratory combination is randomly assigned to two samples. The determinations of calcium content are given below:

Assay Laboratory
1 2 3
1 10.9 10.5 9.7
10.9 9.8 10.0
2 11.3 9.4 8.8
11.7 10.2 9.2
3 11.8 10.0 10.4
11.2 10.7 10.7

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 recieves 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 (random effects) factorial with 2 replications in a CRD