12.5 - Example 4 - Comparing MPG for Gasoline Blends

Example 12-4 Section

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

Comparing MPG for gasoline Blends

A petroleum company was interested in comparing the miles per gallon achieved by four different gasoline blends (A, B, C, and D). Because there can be considerable variability due to differences in driving characteristics and car models, these two extraneous sources of variability were included as "blocking" variables in the study. The researcher selected four different brands of cars and four different drivers. The drivers and brands of cars were assigned to blends in the manner displayed in the table below. The mileage (in mpg) obtained over each test run was recorded as follows:

Driver Car Model
1 2 3 4
1 A(15.5) B(33.8) C(13.7) D(29.2)
2 B(16.3) C(26.4) D(19.1) A(22.5
3 C(10.5) D(31.5) A(17.5 B(30.1)
4 D(14.0) A(34.5 B(19.7) C(21.6)

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?

Crossed1: each level of treatments occur with all levels of other treatments. (Factorial)

Nested2 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?
This experiment is A single factor (one-way) experiment with 4 replications in a Latin Square design