For each of the following explain when the experimental desi

For each of the following, explain when the experimental design is appropriate and give an example situation.

(a) Completely randomized design

(b) Randomized complete block design

(c) Completely randomized design with a factorial experiment

(d) Repeated measures designs

Solution

(a) One Factor Completely Randomized Design:

This is the simplest design and the easiest to carry out. The design contains only one factor, and can handle unequal numbers of observations per level.

An Example: In an attempt to study fat absorption in doughnuts, 24 doughnuts were prepared (six doughnuts from each of four kinds of fats). The dependent variable is grams of fat absorbed, and the factor variable is the type of fat. The factor contains four levels (four types of fat were tested). The researcher accidentally dropped one of the doughnuts from the second type of fat, so the second type of fat contains five observations instead of six.

The analysis of variance table follows:

(b)Randomized Complete Block Design:

This design is easy to carry out. It is essentially a one-way analysis of variance with replications (blocks). This design always contains exactly one observation per cell. Units assigned to the same block are as similar as possible in responsiveness, thus increasing the precision of treatment comparisons by eliminating block-to-block variation. Blocks can represent time, location or experimental material. Examples of blocks include repeated testing over time, litter-mates, and groups of experimental plots as similar as possible in terms of fertility, drainage, and liability to attack by insects.

Note:     Factor A is always the experimental treatment

              Factor B is always the replication or block

An Example: A researcher wants to study the effects four seed treatments and a control group (a total of five treatment levels) on the germination of soybean seeds. The factor variable is the type of treatment (1 to 5). Five germination beds were prepared for each level of treatment and 100 seeds factors were planted in each bed. Thus, the replications are the five beds. The dependent variable is the number of plants in each bed which failed to germinate. There are two factors: treatment and replication.

The analysis of variance table follows:

(C)Two-Factor Factorial in Completely Randomized Design:

  When compared to a one-factor-at-a-time approach, factorial designs are superior because they enable interactions between different factors to be explored. Instead of performing two experiments (one for each factor), the researcher can perform one experiment to determine the effects of each factor and their interaction. Unbalanced designs are acceptable.

An Example: Sixty baby male rats were randomly assigned to one of six feeding treatments. The dependent variable is the weight gain of the rats. The feeding treatments were a combination of two factors, source and level of protein. Three of the rats died before the experiment was completed. The six feeding treatments were a combination of two factors:

    Factor A (3 levels): Source of protein: Beef, Cereal, Pork

    Factor B (2 levels): Level of protein: High, Low

The analysis of variance table follows:

(d) Repeated measure designs:

In this type of design, each subject functions as an experimental block. A block is a categorical variable that explains variation in the response variable that is not caused by the factors that you really want to know about. You use blocks in designed experiments to minimize bias and variance of the error because of these nuisance factors.

In repeated measures designs, the subjects are their own controls because the model assesses how a subject responds to all of the treatments. By including the subject block in the analysis, you can control for factors that cause variability between subjects. The result is that only the variability within subjects is included in the error term, which usually results in a smaller error term and a more powerful analysis.

Example:

An experiment was conducted to determine how several factors affect subject accuracy in adjusting dials. Three subjects perform tests conducted at one of two noise levels. At each of three time periods, the subjects monitored three different dials and make adjustments as needed. The response is an accuracy score. The noise, time, and dial factors are crossed, fixed factors. Subject is a random factor, nested within noise. Noise is a between-subjects factor, time and dial are within-subjects factors.