Question

13.8 Properties of cemented soils. Refer to the Bulletin of Engineering Geology and the Environment (Vol. 69, 2010) study of cemented sandy soils, Exercise 1.9 (p. 7). The re searchers applied one of three different sampling methods (rotary core, metal tube, or plastic tube) to randomly se- lected soil specimens, then measured the effective stress level (Newtons per meters-squared) of each specimen. Suppose that each method was applied to 10 soil specimens-a total of 30 measurements in all. Consider an analysis to compare the mean effective stress levels of the three sampling methods. 728 Chapter 13 Principles of Experimental Design a. What are the experimental units for this study? b. What type of design is employed? Identify the features (e.g., treatments, blocks) of the design. c. What is the dependent (response) variable of interest? d. Write the model for this design.

Answer 1

a. The experimental units for this study are soil specimens. These specimens are selected randomly.

b. In this experiment a completely randomized design is employed since the treatments are randomly allotted to different units of the experiment without grouping(blocking) of homogeneous soil specimens. The three treatments in this experiment are rotatory core, metal tube,or plastic tube. There are no blocks in this experimental design.

c. The dependent(response) variable of interest is the effective stress level of each specimen(measured in Newtons per meters-squared.)

d. The model for this design is as follows.

$Y_{ij} = \mu \;+\;\tau_i\;+\;e_{ij}$ , i= 1,2,3; j = 1,2,3,...,10.

where,

$Y_{ij}$ is the response for ith treatment and jth replicate

$\mu$ is the general mean effect

$\tau_{i}$ is the i^th treatment effect

e_ij is the error term corresponding to i, j ^th observation.