Introduction to Experimental DesignTerminologyTerminology (continued)Slide 4Example 1A Cartoon Representation of the ExperimentExample 1 (continued)Slide 8Slide 9Slide 10Slide 11Example 2Example 2 (continued)Slide 14Slide 15Slide 16Three Fundamental Experimental Design Concepts Attributed to R.A. FisherExample 3Example 3 (continued)Slide 20Slide 21Slide 22Slide 23The Importance of RandomizationSlide 25Slide 26Generating Random Assignments in RSlide 28Slide 29Slide 30Slide 31Some General Microarray Experimental Design AdviceBiological Replication Should be MaximizedExample 4: Two-Treatment CRDAssign 8 Plants to Each Treatment Completely at RandomRandomly Pair Plants Receiving Different TreatmentsRandomly Assign Pairs to Slides Balancing the Two Dye ConfigurationsConfoundingAnother Example of Problematic ConfoundingSlide 40Slide 41An Example of Useful ConfoundingAn Example of Useful Confounding (continued)Slide 44Pooling Tissues or RNA SamplesDesigns A and C measure pools rather than individual samples.1Introduction to Experimental Design1/26/2009Copyright © 2009 Dan Nettleton2TerminologyExperiment – An investigation in which the investigator applies some treatments to experimental units and then observes the effect of the treatments on the experimental units by measuring one or more response variables.3Terminology (continued)Treatment – a condition or set of conditions applied to experimental units in an experiment.Experimental Unit - the physical entity to which a treatment is randomly assigned and independently applied.4Terminology (continued)Response Variable – a characteristic of an experimental unit that is measured after treatment and analyzed to assess the effects of treatments on experimental units.Observational Unit - the unit on which a response variable is measured. There is often a one-to-one correspondence between experimental units and observational units, but that is not always true.5Example 1•An experiment was conducted to study the effects of three soil moisture levels on gene expression in maize seedlings.•A total of 36 seedlings were grown in 12 pots with 3 seedlings in each pot.•The 3 soil moisture levels (low, medium, and high) were randomly assigned to the 12 pots with 4 pots for each soil moisture level.•After three weeks, RNA was extracted from the above-ground tissues of each seedling.•Each of the 36 RNA samples was hybridized to a microarray slide to measure gene expression.6A Cartoon Representation of the ExperimentLL L LMMMMHH H H7Example 1 (continued)1. Name the treatments in this experiment.2. Name the experimental units in this experiment.3. Name the observational units in this experiment.4. Name the response variable or variables in this experiment.8Example 1 (continued)1. Each of the three moisture levels represents a treatment.2. The moisture levels were randomly assigned to the pots, so the pots are the experimental units. A pot consisting of 3 seedlings is one experimental unit.3. Gene expression was measured for each seedling, so the seedlings are the observational units. 4. Each probe on the microarray slide provides one response variable. Thus, we will have several thousand response variables in this example.9Terminology (continued)Response Variable – a characteristic of an experimental unit that is measured after treatment and analyzed to assess the effects of treatments on experimental units.Explanatory Variable – a variable that can potentially be used to explain variation in a response variable.10Terminology (continued)Factor – an explanatory variable that can take any one of two or more values.Levels – the different values of a factor.Treatment Factor – a factor whose levels are chosen and controlled by the researcher to understand how one or more response variables change in response to varying levels of the factor.11Terminology (continued)Treatment Design – the collection of treatments used in an experiment.Full Factorial Treatment Design – treatment design in which the treatments consist of all possible combinations involving one level from each of the treatment factors.12Example 2•An experiment was conducted to gauge the effects of a drug and feed consumption on gene expression in rats. •A total of 40 rats were housed in individual cages.•Half of the 40 rats were randomly assigned to a calorie-restricted diet where daily feed rations contained approximately 50% of the calories normally consumed by rats of the type used in the experiment. The other 20 rats were provided with access to feeders that were always kept full so that their calorie intake was completely unrestricted.13Example 2 (continued)•Within each diet group, four doses of an experimental drug (0, 10, 20, and 30 mg/kg body weight) were randomly assigned to rats with 5 rats per dose within each diet group.•At the conclusion of the study, gene expression was measured for each rat using microarrays.14Example 2 (continued)1. Name the treatment factors used in this experiment.2. Name the levels of each factor.3. Name the treatments used in this experiment.4. Was a full factorial treatment design used?5. Name the experimental units used in this experiment.6. Name the observational units used in this experiment.15Example 2 (continued)1. The treatment factors are diet and drug.2. The levels of the factor diet are restricted and unrestric t ed. The levels of the factor drug are 0, 10, 20, and 30 mg/kg body weight 3. Each combination of diet and drug is one treatment. (R0, R10, R20, R30, U0, U10, U20, U30)4. A full-factorial treatment design was used because all possible combinations of diet and drug were considered.5. Each rat is an experimental unit and also an observational unit.16Terminology (continued)Completely Randomized Design (CRD) – experimental design in which, for given number of experiment units per treatment, all possible assignments of treatments to experimental units are equally likely. Block – a group of experimental units that, prior to treatment, are expected to be more like one another (with respect to one or more response variables) than experimental units in general.Randomized Complete Block Design (RCBD) – experimental design in which separate and completely randomized treatment assignments are made for each of multiple blocks in such a way that all treatments have at least one experimental unit in each block.17Three Fundamental Experimental Design Concepts Attributed to R.A. FisherRandomization –