Statistics 312 4 Experimental Design 1 Terminology Interest lies in examining the mean response or dependent variable from one or more populations Responses are obtained from people animals things transactions etc which are the experimental units or subjects Examples of experimental units include autos parcels of land machines and engineering majors The variables whose effects on the response are of interest are the factors of the experiment e g brand of gas gas octane the values these factors take on are referred to as the levels of the factors e g Texaco Shell Chevron Arco 87 89 and 92 Gasoline brand is a qualitative factor octane is a quantitative factor Exs 1 2 3 1A 2A 3A Auto mileage based on brand of gasoline Yield of crop from five different seed varieties Reaction time to warning lights of three different colors Auto mileage based on brand and octane of gasoline Yield of crop from five different seed varieties four types of fertilizers and two different irrigation methods Reaction time to warning lights of three colors in eight configurations in a control panel The first set of examples involves a single factor while the second set of examples represents multi factor or factorial situations A treatment is the combination of levels of the factors applied to a specific eu With a single factor a treatment is identical to the level of the factor involved e g Shell or Exxon while with multi factors factorial a treatment is a combination of one level from each factor e g Shell is a level of the factor brand 87 is a level of the factor octane Shell 87 is a treatment Statistics 312 4 Experimental Design 2 Observational studies In an observational study an investigator uses a sample from one or more groups to draw conclusions about these groups or the differences between these groups It is important to recognize that while associations between groups or variables may be obtained through an observational study no conclusions can be reached about the reasons for these differences due to the possible presence of confounding variables A confounding variable is related to both group membership and the response variable being measured A variable is confounded if its effects on the response variable cannot be separated from the effects of the explanatory variable Designed experiments In a designed experiment an investigator manipulates one or more factors and measures the effect on a response variable With random allocation to the experimental groups the effects of any confounding groups should be spread equally among the groups So randomization helps prevent effects from unanticipated variables This allows a conclusion of a cause and effect relationship between the manipulated factor s and the response variable The cause is hidden but the result is known Ovid Laddie s smile was thin Not to sound superior but you re committing what s called a post hoc fallacy Just because one event follows another doesn t mean there s a cause and effect relationship Sue Grafton O Is For Outlaw You can see a lot by observing Yogi Berra And now remains that we find out the cause of the effect Hamlet Act II Scene II To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination he may not be able to say what the experiment died of Ronald A Fisher Blocking is often used in an experiment if there is some nuisance factor that can be anticipated as having an effect on the response The subjects of the experiment are first separated into blocks which are as alike as possible in the anticipated factor homogenous The variation in outcome due to different randomizations can be made smaller on average This increases the likelihood that true differences between the two groups can be accurately detected Blocking reduces variation by distributing anticipated factors that might affect the response equally to the treatment groups BASIC PRINCIPLES OF EXPERIMENTAL DESIGN Statistics 312 4 Experimental Design 3 1 Replication A repetition of the complete experiment Provides an estimate of experimental error The greater the number of replications the greater the precision smaller variance of the estimates of factor effects based on sample mean s Replication repeated measure 2 Randomization Random assignment of treatments to the experimental material experimental units and random order of individuals runs of the experimental trials Helps guarantee validity of the assumption of independence of the errors or individual observations Helps remove extraneous effects that could influence response by averaging out these extraneous effects 3 Blocking Taking heterogeneous experimental units and dividing the experimental units into more homogeneous subgroups Reduces experimental error and variability due to nuisance factors Completely Randomized Design CRD Treatments are assigned to eu s randomly The corresponding observational study would involve taking independent random samples from groups having the same treatment Randomized Block Design RBD Similar eu s are grouped into blocks and treatments are assigned to eu s randomly within each block Read pp 469 472 Do problems on next two pages of these class notes Statistics 312 4 Experimental Design 4 Problems 1 A physical education instructor wants to compare the percentage of body fat for joggers cyclists and swimmers a What is the response b What is the factor c What are its levels d What are the treatments e This could be based on an observational study or on a designed experiment When would it be an observational study and when would it be a designed experiment f For a designed experiment can you suggest any blocking Explain 2 The following passage is from A two step intervention to increase mammography among women aged 65 and older American Journal of Public Health Oct 1997 Janz Nancy K Schottenfeld David Older women are less likely to obtain screening mammograms although such screening could reduce breast cancer mortality by at least 30 In national surveys the two most common reasons offered by older women for not having a mammogram were that they did not know they needed a mammogram and that their physician had not recommended one Four hundred and sixty women were randomized to a control or a two step intervention group 223 in the intervention group and 237 in the control group The two step intervention consisted of 1 a personal letter from the primary care physician with a coupon incentive and 2 for women who did not