Single factorMultiple factorIES 612/STA 4-573/STA 4-576Spring 2005Week 8 – IES612-week08-lecture.docDesign Issues (Ch 14 text)“Design of experiment” = “process of establishing a framework through which the comparison oftreatments or groups can be made in terms of recorded response” (OL 14, p. 829)Note: balance between the control of condition and depiction of reality must be maintained – “ecological validity” – when can you use the lab vs. when must you work in the field?Study types:1. Observational – factors not manipulated, sampling from populations where factors (trts) already present and want to compare populations with respect to some response (e.g. samples, polls, surveys, epi. studies)2. Experimental – randomly assign subjects to treatment conditions and observe the response of interestExamples* Community study where elderly receive care using either a consumer-directed system or a traditional case manager system.* Perch growth in the presence of gobi and/or zebra mussels* Species presence as a function of stream characteristics* Web weight as a function of temperature and species of spider* Contaminant level in effluent as a function of temperature and pressureResearch Plan ingredients (OL 14, p. 831)1. Objectives2. Study Factors3. Extraneous Factors14. Response5. Randomization method6. Protocol for recording responses7. Replications needed8. Resources Principles to consider when designing an experiment1. Randomization – create groups as similar as possible prior to an experiment2. Control – comparison group (concurrently conducted with the study)3. Replication – how many experimental units? Sensitivity to detect important differences.How might you do a RANDOMIZATION?Suppose we wanted to randomly assign 12 experimental units (here pieces of meat) to one of fourpackaging conditions with 3 units assigned to each condition.Step 1: Assign a unique number (label) to each experimental unit – say “1” to “12” (=nT)Step 2: Randomly permute the labels.Step 3: Assign the units corresponding to the first n1=3 permuted labels to group 1, the next n2=3permuted labels to group 2, etc.Let’s make this concrete …ods rtf;proc plan;title "generate randomization/allocation scheme for 12 steaks"; factors meat=12; run;ods rtf close;Factor Select Levels Ordermeat12 12 Random2meat11 9 12 1 7 8 3 6 4 5 10 2So, Condition 1 = Steaks 11, 9, 12; Condition 2 = Steaks 1, 7, 8Condition 3 = Steaks 3, 6, 4; Condition 4 = Steaks 5, 10, 2meat11 9 12 1 7 8 3 6 4 5 10 21 2 3 4Packaging ConditionAs an aside, you can also use this to generate a random sample (which is essentially the first “n” of “N” permuted labels).NOTE: At the start of processing, random number seed=581671001.ods rtf;proc plan;title "generate random sample of 10 from 40 in sampling frame"; factors n=10 of 40;ods rtf close;The SAS log noted that NOTE: At the start of processing, random number seed=581671001.(in case you wanted to replicate this stream of random numbers).n29 18 11 37 2 5 19 39 26 33* you can use random number tables or other devices to do a randomization.Why have control groups? Does control group = untreated group? Guaranteed treatment for the common cold – I call it “chicken soup” – You will be cured after 3 days or your money back! Justification for guarantee? I did a study where I gave soup to 25 people with colds and they all felt better when I asked them 3 days later. Reaction?Lots of types of control groups:1. Untreated2. Placebo33. Sham (often in surgery or neuroanatomy studies)4. Standard treatment (may not be ethical to have an untreated group)5. Vehicle (sometimes you have to give a treatment in some medium)6. Historical (can be problematic)What does “blinding” mean in an experiment?Single-blind study (subject doesn’t know treatment)Double-blind study (subject & physician/experimenter don’t know treatment)Triple-blind study (subject, experimenter & analyst don’t know treatment)[code is broken after completion of the study]Treatment StructureFactor = manipulation/population of interest (analogous to independent variable in regression)Level = unique value of factorTreatment = (single factor study) level of factorTreatment = (multiple factor study) unique combination of factor levelsSingle factorFactor = packaging conditionLevels = vacuum, mixed, CO2, plasticPackaging Condition (Factor)vacuum mixed CO2 plastic1 2 3 4TreatmentMultiple factorFactor A = gobi (levels = present/absent)Factor B = Zebra mussel (levels = present/absent)B (Zebra mussel present) B (Zebra mussel absent)A (gobi present) 1 2A (gobi absent) 3 44Experimental Units (EU) and Measurement Unit (MU)Experimental Units (EU) = entity to which treatment is randomly assigned or is randomly sampled from one of the “treatment” population [OL 14, p. 833]Measurement Unit (MU) = entity on which a measurement is takenExample: Meat packaging study: EU = MU = piece of meatExample: Teratology study: EU=dam/litter; MU=pupNOTE: Sometimes, MU called “pseudoreplicate” if MU doesn’t equal the EU (in ecology literature)Experimental Error = variation among EUs assigned to the same treatment and observed under the “same” experimental conditionsSources of Experimental Error?1. natural differences in EUs2. variation in devices that record the MUs3. variation in the treatment conditions4. effects of extraneous factorsControlling Experimental Error? OL 14.41. Procedures for conducting study standardized (“local control” of Kuehl) – train data collectors/lab technicians, standard protocol for recording data and conducting experiment, etc.2. Choice of EU/MU (e.g. same age/size class, same level of disability, etc.) – randomly select from population and then randomly assign treatments, select EUs that are similar (although if too similar that generalizability may be questioned) – e.g. transgenic rodents (knockout mice)3. Measurement procedure4. Blocking (a “design” control – before conducting study) – EUs placed in groups 55. Covariates (an “analysis” control – possible after study conducted)Blocking Designs* A blocking design imposes a CONSTRAINT on the randomization of experimental units to treatments* EUs are placed in groups (BLOCK) that are similar with respect to some important characteristic that may affect the response. * EUs are randomly assigned to treatments WITHIN each group/block* Some criteria for determining