Anova
Chapter 15: Introduction to the Design of Experimental and Observational Studies
The Models in Analysis of Variance(ANOVA) and in Regression are different. In regression model, all the response and predictors are continuous (quantitative) variables. However, in ANOVA model, the response is continuous but the predictors are categorical (qualitative) variables. There are some concepts here. 1. Factor and factor level. A factor is a predictor (explanatory or independent) variable. A factor level is a particular form of the factor. Mostly, the level can not be compared. 2. Single-factor and multi-factor studies. Single factor study means there is only one factor in the study. Thus, the model only includes one response and one predictor. Multi-factor means there are more than one factor in the study. An important case in the multi-factor study is two-way ANOVA model. 3. Experimental and Observational studies. An experimental study means the level of all the factors can be totally controlled. An observational study means the level of the factors can not be controlled. If some of them can be controlled and some of them can not, them people treat it as an experimental studies and called the controlled factor signal factor and uncontrolled factor noise factor. 4. If a continuous variable is treated as a categorical variable, then it is also called a factor variable. 5. Treatment and block. The factor can be called either treatment or block variable. Both of them are treated as nominal variables. The interesting variable is called treatment and the uninteresting variables are called blocks. 6. Experimental design. If the factors levels can be controlled, then people try to make all the factors orthogonal to each other.
Chapter 16: One-Way (Single-factor) ANOVA Model
One Way ANOVA model has one response and one predictor. The response is continuous variable but the predictor is nominal variable. Mean Cells Model Assume that factor A has I levels and in each level there
The Models in Analysis of Variance(ANOVA) and in Regression are different. In regression model, all the response and predictors are continuous (quantitative) variables. However, in ANOVA model, the response is continuous but the predictors are categorical (qualitative) variables. There are some concepts here. 1. Factor and factor level. A factor is a predictor (explanatory or independent) variable. A factor level is a particular form of the factor. Mostly, the level can not be compared. 2. Single-factor and multi-factor studies. Single factor study means there is only one factor in the study. Thus, the model only includes one response and one predictor. Multi-factor means there are more than one factor in the study. An important case in the multi-factor study is two-way ANOVA model. 3. Experimental and Observational studies. An experimental study means the level of all the factors can be totally controlled. An observational study means the level of the factors can not be controlled. If some of them can be controlled and some of them can not, them people treat it as an experimental studies and called the controlled factor signal factor and uncontrolled factor noise factor. 4. If a continuous variable is treated as a categorical variable, then it is also called a factor variable. 5. Treatment and block. The factor can be called either treatment or block variable. Both of them are treated as nominal variables. The interesting variable is called treatment and the uninteresting variables are called blocks. 6. Experimental design. If the factors levels can be controlled, then people try to make all the factors orthogonal to each other.
Chapter 16: One-Way (Single-factor) ANOVA Model
One Way ANOVA model has one response and one predictor. The response is continuous variable but the predictor is nominal variable. Mean Cells Model Assume that factor A has I levels and in each level there