EXST7015 : Statistical Techniques II Geaghan ANOVA Design Identification Page 5 James P. Geaghan - Copyright 2011 Experimental Design Identification To correctly design an experiment, or to analyze a designed experiment, you must be able to look at a design situation and correctly assess the salient aspects of the design. I will ask you to identify the design, the treatment variable, dependent variable, degrees of freedom error, experimental unit, sampling unit (if any), and if the treatment is fixed or random. To begin with, determine what the investigators are trying to do and what they plan to measure. What is the Objective of the study? Specifically, what hypotheses are to be tested? What is the variable of interest? What unit is the treatment applied to? What, exactly, is the unit measured? Suppose an investigator wants to compare the oxygen levels in seven predefined "habitats" in the Louisiana marsh. He will randomly select and sample 4 sites in each habitat. One oxygen measurement is made at each site. What variable is being measured? This variable will produce a series of measurements or quantities? Oxygen levels (usually in ppm) What are the treatments? What is the investigator interested in comparing or testing for differences? Habitats (t=7) Are there any blocks (i.e. sources of variation that should be recognized, but which are not important to the investigator). For example, did he replicate the experiment in several different rivers or several locations along the coast? Are the 4 “replicates” just multiple observations or are they taken in 4 separate places? Apparently no blocks. What are the experimental units for the experiment? What unit was the treatment applied to or what was sampled for each treatment (habitat)? A site (s=4) Are there separate sampling units at each site, or is only one measurement taken in each experimental unit? In this case it is a water sample on which oxygen is measured. Since there is only a single sample at each site we can consider each sample to represent the site. Also the sites If there were multiple samples taken at each site these would be the sampling units. These in turn can be split into sub-sampling units. Apparently this was not done. Is that all? There are other issues, not all of which we have covered. Are the treatments fixed or random? Is the design balanced? Are there any particular hypothesis tests of interest (contrasts)? Are the treatment levels quantitative? Any other special post ANOVA applications? The topic of “Design” will be discussed in the second half of the course. For the moment our objective is only to learn to identify the components of an experiment. Therefore, I will put a design description on the Internet and during each class period I expect you to have looked at it and to be prepared to answer the following questions.EXST7015 : Statistical Techniques II Geaghan ANOVA Design Identification Page 6 James P. Geaghan - Copyright 2011 Questions: 1) What is the treatment arrangement for this experiment? (a) single factor (b) factorial (c) nested 2) What is the experimental design for this experiment? (a) CRD (b) RBD (c) LSD (e) Split-plot (d) Repeated Measures 3) Does it seem more likely that the treatments are fixed or random? (a) fixed (b) random 4) What is the experimental unit for this experiment? (a) pens (b) diets (c) live weight (d) egg yolk weight (e) individual chickens 5) What is the sampling unit for this experiment? (a) pens (b) diets (c) live weight (d) egg yolk weight (e) individual chickens 6) What is the dependent variable for this experiment? (a) pens (b) diets (c) live weight (d) egg yolk weight (e) individual chickens 7) What is the treatment variable for this experiment? (a) pens (b) diets (c) live weight (d) egg yolk weight (e) individual chickens 8) If the design is RBD, what are the blocks? (a) pens (b) diets (c) live weight (d) egg yolk weight (e) individual chickens (f) NA 9 & 10) How many degrees of freedom are available for testing the treatment (combinations)? Enter the correct value here: numerator = ___________ , denominator = ___________ For the little experiment discussed the source table is: Source d.f. Treatment 6 Error 21 Total 27 A final note on the Daily Designs. These will start early in the semester with the simpler designs and progress to more complicated designs. Our only objective with these designs is that you learn to identify the important aspects and components of the designs. During the second half of the course we will discuss the designs in detail. We will see why these components exist, how they are analyzed and how they are interpreted. At the start of each class I will role a dice. If a value of 6 is obtained we will have a quiz. If any other value is rolled I will simply give you the answers to the quiz. If a value other than 6 is rolled, then that number is not to be counted again until after a 6 has occurred. For example, if I roll a 3 then any values of 3 on subsequent days would not count until a 6 occurred. Once a 6 is rolled all numbers are back in contention.EXST7015 : Statistical Techniques II Geaghan ANOVA Design Identification Page 7 James P. Geaghan - Copyright 2011 Identifying designs The simplest type of design is the Completely Randomized Design (CRD) This will consist of: 1) a treatment (at least one, possibly more), and 2) an error term (at least one, possibly more) Example 1: A researcher is studying the size of tomatoes from plants grown under three watering regimes, (A) daily watering, (B) watering at 2–day intervals and (C) watering at 3–day intervals. Eighteen plants are planted in large pots and 6 are randomly selected for each watering regime. Plant productivity is measured as the total weight of the first 10 tomatoes (in cm) produced by each plant or pot (these are synonymous for this study since there is only one plant per pot). B ABCBAA BCABCC ABCCA Diagnosis: What are the treatments and experimental units? The objective is to compare the total weight of tomatoes. The variable of interest (dependent variable) is the total weight of the tomatoes. The treatment is the variable whose levels are to be compared. In this case the treatment has 3