Notes-Anova-to-Final - ONE-WAY ANOVA One-way ANOVA => deals...

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ONE-WAY ANOVAOne-way ANOVA => deals with averages =>Fisher’s F.It looks like a test of variability but its not. ANOVA serves to test differences between 2 or more means while maintaining alpha at 0.05.it has the same assumptions as an independent t-testit partitions variability into that due to difference between(signal) groups vs that due to difference within(noise) groupsthe ratio of between and within group variance is evaluated against an F distributionpost-hoc tests are employed to find differences between means while maintaining alpha at0.05SPSS provides 18 post-hoc procedures, some more conservative, some more liberalLinear contrast analysis will produce effects for certain cases where F test will notOmnibus tests often fail to tell us what we want to knowUnplanned comparisons are post-hoc tests (e.g. Tukey)conducted after an omnibus testRobert A Belson: planned comparisons involve weighting of data by sets of contrastsRosenthal: planned comparisons guarantee more POWER! But demand the researcher plan aheadRules: ogroups coded with positive weights will be compared against groups coded with negative weightsosum of weights for a comparison should be zerooif a group is not involved in a comparison, assign it a weight of zerothe task of assigning a set of weights to a contrast is calleddummy codingwhen the products of a set of contrasts sum to 0, then the contrasts are orthogonal or independentStd Error = SQRT[MSe * (sum of cj /nj)]oEx. For weights 1, 1, -2 SQRT [9.633 x (12/5+12/5+(-2)2/5]SPSS provides a variety of contrasts including trend analysisMULTIPLE ANOVAMultiple ANOVAs are used to study the effects of treatments on multiple outcome variablesAny relationships among the outcome variables are ignored when conducting multiple ANOVAsResearchers are concerned about inflating the experiment-wise or family-wiseerror rateby conducting multiple ANOVAsoFamilywise error rate -> alpha = 1 – (1-alphapc)nThus MANOVA is wrong!MANOVA is a multivariate (multiple dependent variable) technique and its complicated
oIt does not control Type I error ratesoThe research questions asked by MANOVA and ANOVA are differentoMANOVA creates “Steve”, some best combination of the DV to maximize the difference between groupsIf we are not interested in the relationship between the DVs, we should NOT do MANOVAAnd we should NOT follow MANOVA with ANOVAAlternatives:Discriminant Function AnalysisLogistic Regression**Huberty and Morris (1989): multivariable analysisANCOVA seeks to control for nuisance variables that influence the dependent variableANCOVA works properly only when you have randomlyassigned participants to the levels of the IVTo be fair, ANCOVA may work well to control for pre-treatment differencesFACTORIAL ANOVAFactorial ANOVA permits testing of two or more main effects….oAnd the interaction between variablesA test of Moderationis the equivalent to testing an interaction in Factorial ANOVA

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