Design Supplemental Design вЂў Completely randomized вЂў Randomized block design вЂ“ Latin-Squares вЂ“ Greco-Latin Squares вЂў Repeated measures вЂ“ Pre & post-test designs вЂў Mixed designs (Between subjects factors and repeated measures) вЂ“ Split-plot вЂў Random effects models Completely randomized вЂў The typical situation with only between-subjects factors (IVs) вЂў Participants are randomly assigned to treatment groups вЂў DonвЂ™t trust yourself to do this, peeps is bad at randomizing вЂў Example in R вЂ“ x=c(1,2,3,4) вЂ“ y=c(.25,.25,.25,.25) пѓџ groups 1-4 пѓџ long run probability of occurrence вЂ“ sample(x, 80, replace=TRUE, prob = y) Randomized block design вЂў Suppose an effect is present that may influence results, but for which you may not be interested in вЂ“ Nuisance variable вЂў We can extend the randomization process to control for a variety of factors вЂў Randomized Block Design вЂ“ An extension of the completely randomized design in which a single extraneous variable that might affect test unitsвЂ™ response to the treatment has been identified and the effects of this variable are isolated by blocking out its effects. вЂў Examples: вЂ“ Researchers collecting the data вЂў Probably a relationship between who is collecting and outcome вЂ“ Experimenter/participant expectations вЂ“ Age вЂў Create blocks of similarly aged individuals Randomized block design вЂў In such a situation we want to randomly assign to treatment groups within each blocking level вЂў Example: Treatment A вЂ“ Experimenter 1: condition 1 condition 2 condition 3 вЂ“ Experimenter 2: condition 1 condition 2 condition 3 вЂ“ Experimenter 3: condition 1 condition 2 condition 3 Randomized Block Design Independent Variables Blocking variable Control: no music Mornings and afternoons Evening hours Experimental treatment slow music Experimental treatment: fast music Randomized block design вЂў Partitioning the sums of squares вЂў F-statistic is now MSb/t/MSresidual вЂў This will be a more powerful test, although less so as SSresdiual approaches SSw/in вЂ“ i.e. less effect due to blocking variable SStotal SSb/t SSw/in SSresidual SSblocks Randomized block design вЂў Conditions: вЂ“ Correlation between blocking variable and DV вЂ“ Treatment and blocking levels > 2 вЂ“ Random assignment within each blocking unit вЂў Goal is to see homogeneous groups w/in each blocking level and treatment levels will look similarly with respect to one another вЂў Methods of implementation вЂ“ Subject matching (age example) вЂ“ Repeated measures (everyone gets all conditions, subjects serve as their own block) вЂ“ Other matched pair random assignment (e.g. twins, husbandwife) вЂў Latin-squares and Graeco-Latin squares extend the blocking to 2 and 3 nuisance variables respectively вЂ“ Consult Winer or Kirk texts Latin Square Design вЂў A balanced, two-way classification scheme that attempts to control or block out the effect of two or more extraneous factors by restricting randomization with respect to the row and column effects вЂ“ Randomly assign treatment levels according to levels of the nuisance variable such that each level of the treatment variable is assigned to the levels of the nuisance variables вЂў Can help with sequence effects with RM variables вЂў This special sort of balancing means that the systematic variation between rows, or similarity between columns, does not affect the comparison of treatments. Latin Square вЂў Example controlling for previous therapy experience and therapist (A is the treatment, e.g. type of therapy) Therapist Previous therapy (none, yes but no drugs, yes w/ drugs) 1 2 3 1 A1 A2 A3 2 A2 A3 A1 3 A3 A1 A2 Example: 3 groups receive Therapy A1 Group1- therapist1, no previous Group2- therapist2, drugs Group3- therapist3, no drugs вЂў LS design has limited utility in behavioral sciences вЂ“ Not too many cases with factors all with the same number of levels вЂ“ Kirk has suggested that with less than 5 levels itвЂ™s not very practical due to few degrees of freedom for error term (except for when several levels of treatment are assigned to each cell e.g. in a mixed design situation) вЂў Nevertheless, we see we have various ways to control for a number of effects that might be present in our data but not of interest to the study Repeated measures design вЂў Subjects participate in multiple levels of a factor вЂў Simplest is the paired t-test situation, however вЂ�repeated measures designвЂ™ often implies 3 or more applications of some treatment вЂў Example: pre and post-test Mixed design вЂў Between subjects factors with repeated measures вЂў Simple but common example is controltreatment, pre-post вЂў Subjects are randomly assigned to control or treatment groups and tested twice Pre Control Treatment Post Mixed design вЂў This example may appear a straightforward method for dealing with data вЂў However we could analyze it in two additional ways вЂў ANCOVA вЂ“ Test for differences at time 2 controlling (adjusting) for differences seen at time 1 вЂў A simple t-test on the gain scores from pre to post вЂ“ Same result as mixed but w/ different (simpler) output вЂў One method may speak more to the exact nature of your research question (e.g. only interested in time 2 or the rate of improvement from time 1 to 2) Mixed design вЂў Consider also the possibility of an effect in posttest scores (or effect of treatment) due solely to exposure to the pretest вЂ“ E.g. with no prior training GRE scores would naturally be assumed to increase the second time around more often than not вЂў Solomon four-group design вЂў Split-plot factorial controls for a nuisance variable in mixed designs вЂў WeвЂ™ll take a more in depth look at repeated measures and mixed designs later Random effects models вЂў In most ANOVA design we are dealing with fixed effects вЂў Random effects вЂ“ If the levels included in our analysis represent a random sample of all the possible levels, we have a random-effects ANOVA. вЂў With fixed effects the same levels of the effect would be used again if the experiment was repeated. вЂў With random effects different levels of the effect would be used. вЂў The conclusion of the random-effect ANOVA applies to all the levels (not only those studied). Random effects models вЂў вЂў вЂў вЂў Questions to ask: Were the individual levels of the factor selected due to a particular interest, or were they chosen completely at random? Will the conclusions be specific to the chosen levels, or will they be applied to a larger population? If the experiment were repeated, would the same levels be studied again, or would new levels be drawn from the larger population of possible levels? Random effects models вЂў Some examples: вЂў Persuasiveness of commercials вЂў Effect of worker on machine output вЂў Vehicle emissions impact on the environment Random effects models вЂў Determination of fixed vs. random effects affects the nature of the tests involved, how the Fstatistic will be calculated (sometimes), and the conclusions to be drawn вЂў Some designs will incorporate both fixed and random effects вЂ“ Mixed effects designs вЂў DonвЂ™t confuse with previous mixed design factorial discussed previously

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