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STA 106 Discussion
Types of Factors (Studies) • Experimental factors: Levels of the factor are assigned at random to the experimental units. Cause-and-effect relationships between the experimental factors and the outcome or response variable can be established in an experimental study. • Observational factors: Levels of the factor are characteristic of the experimental units and is not under the control of the investigators. A cause-and-effect relationship between the observational factors and the outcome or response variable is difficult to establish in an observational study. • Mixed Study: a study includes both observational factors and experimental factors. 2 Design of Experimental study The basic principles of experimental design are • Replication: deals with variation/uncertainty, allows for generalization. • Randomization: deals with confounding factors, allows for cause-effect statements. • Blocking (stratification): reduces known but irrelavant sources of variation, improves statistical effi- ciency Some experimental designs: • Complete randomized design (CRD): treatments (combinations of the factor levels of the different factors) are randomly assigned to the experimental units. • Randomized complete block design (RCBD): treatment combinations are assigned randomly to the experimental units within a block. • Balanced incomplete block design (BIBD): every treatment appears with every other treatment in the same block the same number of times, but every block does not receive the full suit of treatments. 3 Design of Observational Study • Cross sectional studies : measurements are taken from one or more populations or sub- populations at a single time point or time interval. • Logitudinal Study: measurements are taken from one or more groups over a period of time. – Cohort study (prospective study): one or more groups are formed in a nonrandommanner according to some hypothesized causal factors, and then these groups are observed over time with respect to the outcome of interest. Example: A group of smokers and a group of non-smokers were followed since their early 30s, and their health indices were recorded over years until their late 60s.(What is going to happen ?) 1 – Case control study (retrospective study): groups are defined on the basis of an observed outcome, and the differences among the groups at an earlier time point are identified as potential causal effects. Example : study of lung cancer (case/observed outcome) and smoking (control group) based on data collected on lung cancer patients. 4 Exercise The problems below come from Applied linear Statistics Models, by Kutner, Chapter 15. 4.1 Problem 15.10 In a study to investigate the effect of color of paper (blue, green, orange) on response rates for questionnaires distributed by the “windshield method” in supermarket parking lots, four supermarket parking lots were chosen in a metropolitan area and 10 questionnaires of each color were assigned at random to cars in the parking lots (10× 3 questionaires per lot, 120 total questionaires). (a) Is this study experimental, observational, of mixed? Why? (b) Identify all factors, factor levels, and factor-level combinations. (c) What type of study design is being implemented here? (d) What is the basic unit of study? 4.2 Problem 15.11 A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and the time required in physical therapy until successful rehabilitation. Data on the number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) were collected. (a) Is this study experimental, observational or mixed? Why? (b) Identify all factors, factor levels, and factor-level combinations. (c) What type of study design is being implemented here? (d) What is the basic unit of study? 4.3 Solution: 15.10: (a) Mixed. Color of paper is experimental factor, and parking lot is an observational factor. (b) Factor 1: color of paper, three levels (blue, green, orange). Factor 2: supermarket parking lot, four levels. (c) Randomized complete block design. (d) Car. 15.11: (a) Observational. (b) Fitness status, three levels (below average, average, above average). (c) Cross-sectional study. (d) Person. 2