Experiments with Multiple IVs What is a factorial design What is the term factor synonymous with Understand factorial design shorthand 2X2 2X3X4 etc A factorial design gives us the power we need to devise an investigation of several factors multiple IVs in a single experiment Simplest possible is 2x2 More like the real world because it is rare that only one factor affects a behavior Factors are designated by letters Levels are designated by subscript numbers So 2 IVs A and B and 2 levels of each 1 and 2 3 IVs one had 2 levels one had 3 levels one had 4 levels 2X3X4 A1 and A2 B1 B2 B3 C1 C2 C3 C4 Compare and contrast main effect and interactions Be able to identify both on a graph of data or in a description of results Main effect refers to the sole effect of one IV in a factorial design do the means differ between groups If the same no main effect Is there a significant difference between means Interaction Joint simultaneous effect on the DV of more than one IV Do the lines cross Does the effect of one IV depend on the level of the other IV If lines are parallel then no interaction Understand your options for assigning participants to groups What are the limitations of each type of assignment What does a mixed factorial design allow us to do 1 or more IV with independent groups and 1 or more IV with correlated groups This is referred to called mixed assignment Factorial designs in which both IVs involve random assignment may be called between subjects factorial designs or completely randomized designs Non random assignment are called completely within groups or within subjects designs Would help assure the equality of participant groups before conducting the experiment Natural pairs and matched pairs face difficulty in within subject design Repeated measures within groups every treatment combination Sometimes difficult and impossible to use repeated measures on multiple ivs smaller designs are more feasible Starting w a 2 group design could you imagine how to expand that study to a 2 X 2 design What about a 3 X 2 design What about a 2 X 2 X 2 design What are the control issues and the practical considerations we must remember when deciding how to assign participants to groups Independent groups need good sized n at least 10 subjects per group to control for outliers and therefore ensure group equality prior to the IV Correlated groups helps ensure groups equality by matching group participants on something natural or a chosen variable or by testing the same participants multiple times Theoretically we can add as many levels of an IV as we want in a factorial design just as theoretically we can add as many IVs as we want to But what do we need to consider when deciding how many levels of each IV to use How many groups are added when you add another level of your IV What is ex post facto research you should know this by now Ex post facto research using a measured rather than manipulated IV A research approach in which the experimenter cannot directly manipulate the IV but can only classify categorize or measure the IV because it is predetermined in the participants Extreme caution in drawing conclusions from such studies bc no control group Given a description of an experiment could you identify the potential main effects and the potential interactions Hey you were given an example of an experiment salesclerk response time depending on clerk sex customer sex and customer hearing status Imagine some specific main effects and interactions that could occur Simplest factorial design with three IV s 2x2x2 experimet 8 groups You should be able to read a description of an experiment and identify the number of IVs the number of levels of each IV and the type of design based on how participants were assigned to groups You should also be able to figure out the best way to assign participants to groups given a particular experimental question Factorial ANOVA more than 1 IV Two Way ANOVA for 2 IVs Three way ANOVA for 3 IVs Random Assignment labels o Independent groups o Completely randomized o Completely between subjects o Completely between groups o Totally between subjects o Totally between groups Matching or Repeated measures o Randomized block o Completely within subjects o Completely within groups o Totally within subjects o Totally within groups Between and within assignment o Mixed factorial A 2 way mixed ANOVA is an ANOVA on an experiment w 2 IV s in which participants were assigned to levels of 1 IV randomly and to levels of the other IV using some sort of correlated groups this description does not tell us how many levels of each IV o Split plot factorial In a computer printout of an ANOVA independent samples correlated samples or mixed you should be able to identify the means for each group and the f ratio and p value for any main effects and any potential interactions Treatment variability variability in DV scores due to the IV between groups Error variability variability in DV scores due to factors other than the IV In a computer printout of a mixed samples ANOVA you should understand the difference b t the between subjects effects and within subjects effects Understand that when an interaction occurs the main effects are moot Understand why A significant interaction renders the main effects moot because those main effects are qualified by the interaction and are not straightforward Crossing lines in conjunction with the low probability of chance for the interaction term denote a significant interaction Given the name of a factorial design or of an ANOVA could you begin to discern how many IVs how many groups and or how participants were assigned to groups Understand interactions Be able to identify them on a graph How does the equation for a factorial ANOVA differ from an ANOVA for multiple groups but 1 IV What does this difference reflect hint different sources of variability When two variables interact their joint effect may not be obvious or predictable from examining their separate effects A significant interaction means that the effects of the various IV s are not straightforward and simple ignore IV main effects when we find a significant interaction Sometimes interactions are hard to interpret particularly when we have more than two IVs or many levels of an IV ANOVA correlated groups fromed by matching or repeated measures not natural sets The two way ANOVA for mixed samples requires that we have two IV s with independent groups for one IV and correlated groups for the
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