Statistics: Designs and Treatments

Boiling point of Salt Water Experiment

Ex.3: For experiment 2, Complete steps (a)-(c) of the checklist.

Experiment 2: Does the boiling point of water differ with different concentrations of salt?

CheckList

(a) Define the objectives of the experiment

The purpose of this experiment is to determine the boiling point of water with different levels of concentration of salt.

(b) Identify all sources of variation

(i) Treatment factors and their levels

The treatment factor in this experiment is salt water of different concentrations. It can be chose to have three levels: low, medium, and high concentrations relative to the same amount of water. The levels are coded 1 for low, 2 for medium, and 3 for high.

(ii) Experimental units.

The experimental units will be the identical beakers and heaters that will be assigned to each level of salt water. The salt from the same package will be divided into three amounts represent three different levels - low, regular, and high, and the weight of each amount will be weighted on a digital laboratory scale and should be corresponding to the required assigned amount for each level. The experiment should be done at the same place and the same time. Salt should be completely dissolved in water before heating, so salt water is also an experimental unit.

(iii) Blocking factors, noise factors, and covariates.

The blocking factors will be the types of salt, as each type of salt might be different in their composition, e.g. Producing area, treatments to the salt before packaging...etc. Different composition of salt will have different solubility and thus result in a different boiling point. Apart from these differences in the composition of the salts, the amount of salt might not be as precise as the required amount, due to measurement errors. This also applies on the measurement of the amount of water for each level of salt, as well as the temperature of water.

(c) Choose a rule by which to assign the experimental units to the levels of the treatment factors.

A rule for this assignment could be the block design. We first divide the salts into different types (e.g. regular, iodized, and sea), as it's a major blocking factor that would affect the result of the experiment. Then we will assign them to the three treatment factor levels. An equal number of observations will be made on each of the three treatment factor levels. Therefore, r cubes of each level of salt water will be prepared. These cubes will be randomly matched to the types of salt using a random number table.

Colors of Exam Paper Experiment

Ex.7: For experiment 8, write down all the possible sources of variation. In your opinion, should this experiment be run as a completely randomized design, a block design, or a design with more than one blocking factor? Justify your answer.

Experiment 8: compare the effects of different colors of exam paper on students' performance in an examination.

Possible sources of variation for this experiment are:

-The course for which the examination is about, for example, a mathematical exam or an essay type exam.

-The type of the examination, like a multiple choice exam, or a short answer exam.

-The selection of the group of students for the experiment, e.g. the students' mood on the day of examination, the personality of each student, the eyesight of each student...etc.

-The examination place and the condition, e.g. the temperature of the room; lighting; lengths of exam; day vs. night exam...etc.

Since there are many sources of variation observed in this experiment, so it should be run as a design with more than one blocking factor. E.g. divide students (experimental units) into groups (blocks) with similar background, personality, and levels of education, and then further divide the students corresponding to different types of examinations. We could also continue to divide the students