Randomized Complete Block Design
Chapter 2. Randomized Complete Block Design
2.1 Randomized Complete Block Design
2.1.1 Examples
When examining the effect of a factor, it is often helpful to remove the effect of excess variation through the use of blocking. A blocking variable is one that may affect the variation of the response, but is unrelated to the primary hypothesis of interest. The desired result is to have homogeneous experimental units within each block so that when the blocking effect is removed (through modeling), all individuals can be considered homogeneous before receiving the treatments. The term randomized complete block design usually refers to a design where there is a single fixed factor of interest and a single random blocking effect. The number of experimental units in each block is such that within each block each of the treatments can be randomly assigned the same number of times. Some examples of a randomized complete block designs follow.
Examples of Randomized Complete Block Design
Snakebite Venom
To compare the immune response of mice to the venom of four poisonous snakes, venom is taken from adult male coral, copperhead, sidewinder, and pit viper snakes. One mouse from each of seven litters are randomly assigned to the four snakes. Each receives minute amounts of the venom of the corresponding snake by injection. The increase in antibody activity as measured from a blood sample is the response. The four treatments that constitute the fixed factor are the four snakes of interest. The seven litters represent all litters and thus make up a random effect. Litter is a blocking effect since it is not of primary interest to determine the variation in antibody activity between litters, but instead to remove the added variation that comes with differing litters.
Recyclable Scrap Metal
Before beginning a full-scale operation to promote recycling of metals in a large county, a recycling agency conducts a study to compare recycling opportunities in the six largest
2.1 Randomized Complete Block Design
2.1.1 Examples
When examining the effect of a factor, it is often helpful to remove the effect of excess variation through the use of blocking. A blocking variable is one that may affect the variation of the response, but is unrelated to the primary hypothesis of interest. The desired result is to have homogeneous experimental units within each block so that when the blocking effect is removed (through modeling), all individuals can be considered homogeneous before receiving the treatments. The term randomized complete block design usually refers to a design where there is a single fixed factor of interest and a single random blocking effect. The number of experimental units in each block is such that within each block each of the treatments can be randomly assigned the same number of times. Some examples of a randomized complete block designs follow.
Examples of Randomized Complete Block Design
Snakebite Venom
To compare the immune response of mice to the venom of four poisonous snakes, venom is taken from adult male coral, copperhead, sidewinder, and pit viper snakes. One mouse from each of seven litters are randomly assigned to the four snakes. Each receives minute amounts of the venom of the corresponding snake by injection. The increase in antibody activity as measured from a blood sample is the response. The four treatments that constitute the fixed factor are the four snakes of interest. The seven litters represent all litters and thus make up a random effect. Litter is a blocking effect since it is not of primary interest to determine the variation in antibody activity between litters, but instead to remove the added variation that comes with differing litters.
Recyclable Scrap Metal
Before beginning a full-scale operation to promote recycling of metals in a large county, a recycling agency conducts a study to compare recycling opportunities in the six largest