Research Methods Test 4 Notes 04 19 2012 Chapter 12 Factorial Designs Factorial Design Factors IV At least 2 IVs in order to have a factorial design More practical and most common are 2 or 3 levels 2 X 2 doubling of our basic 2 level design one IV design from Chapter 10 11 How many numbers 2 X 2 X 3 3 IV S Count the number of numbers Value of numbers 2 levels X 2 levels X 3 levels 2 X 2 4 treatment conditions 2 X 3 6 treatment conditions multiply to get number of treatment If you don t use a factorial design and separate into smaller studies you will lose time efficiency and the interaction Make sure the IV s go together Self esteem and eye color doesn t go with test performance Consider control issues repeated measures gives us greater confidence that there is equality in our groups when we don t have 10 Ss per group Keep it simple stupid KISS don t make your design more complicated that it needs to be More Ss required the more experimental conditions you have the more chances things can go wrong Data interpretation becomes nearly impossible with 4 5 6 IV s most people use 2 or 3 Adding levels into factorial design increases groups in multiplicative fashion 2 X 2 X 2 8 conditions 3 X 2 X 2 12 conditions Ex post facto only way to study race personality sex etc Assigning participants to groups Random assignment IV s involve random assignment Between subjects factorial designs or completely randomized designs Completely within groups or within subjects designs Correlated assignment in order to assure the equality of participant groups Involve a combination of random and correlated assignment with at least one IV using each type of assignment to groups The use of repeated measures is probably more likely than other types of correlated Mixed assignment assignments Main effects of interactions Main effects Interaction Looking at result of each IV separately on the DV Exists when one IV depends on particular level of another IV Crossing lines or lines that converge typically suggest an interaction parallel lines always equals no interaction Factorial ANOVA With factorial designs the sources of treatment variability increase Instead of having one IV as the sole source of treatment variability factorial designs have multiple IV s and their interactions sources of treatment variability The actual distribution of the variance among the factors would depend of course on which effects were significant For a two IV factorial design we use the following equations See page 285 Understanding Interactions When two variables interact their joint effect my not be obvious or predictable from A significant interaction means that the effects of the various IV s are not For this reason we virtually ignore our IV main effects when we find a significant Sometimes interactions are difficult to interpret particularly when we have more than examining their separate effects straightforward and simple interaction two IV s or many levels of an IV Two way ANOVA for independent samples The two way ANOVA for independent samples requires that we have two IV s clothing style and customer sex with independent groups To create this design we would use four different randomly assigned groups of salesclerks Source table o In the body of the source table we want to examine only the effects of the two IV s clothing and customer sex and their interaction o The remaining source w cell or within is the error term and is used to test the IV effects the error term Different statistical program will use a variety of different names for o The effect of sex shows an F ratio of 3 70 with a probability of 07 This IV shows marginal significance o The probability of clothes falls below 01 in the table o The interaction between clothing and customer sex produced an F ratio of 6 65 and a p 02 therefore denoting significance o With a significant interaction we ignore the main effects o Interpret interaction by drawing a graph o When we examine the figure the point that seems to differ most represents the clerks response times to male customers in sloppy clothes If you attempt to interpret the main effects in a straightforward fashion when you have a significant interaction you end up trying to make a gray situation into a black and white picture Two way ANOVA for Correlated Samples correlated groups for both IV s The two way ANOVA for correlated samples requires that we have two IV s with Most often these correlated groups would be formed by matching or by using repeated measures In our example of the clothing customer sex experiment repeated measures on both IV s would be appropriate o We would merely get one sample of salesclerks and have them wait on customers of both sexes wearing each style of clothing Computer results o The clothing effect is significant at the 001 level and the sex effect is significant at the 014 level Because all the participant characteristics are less likely to have an effect because they are clones of one another o However both main effects are qualified by the significant clothing by sex interaction p 0001 Two way ANOVA for Mixed Samples 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 second IV One possible way to create this design in our clothing customer sex experiment would be to use a different randomly assigned group of salesclerks for each customer o Clerks waiting on each sex however would assist customers attired in both types of clothing o 16 clerks will wait on males dressed in both sloppy and casual o 16 clerks will wait on females dressed in both sloppy and casual Source table o The source table appears at the bottom of table 12 4 in your text o As you can see from the heading the btw subjects effects IG and the wth subjects effects RG are divided in the source table o The division is necessary because the btw subjects effects and the wth subjects effects use different error terms o The interaction appears in the wth subjects portion of the table because it involves repeated measures across one of the variables involved Chapter 13 Alternative research designs Single case experimental designs One participant experimental design also known as N 1 designs Includes controls and manipulations just as in a typical experiment Precautions are taken to insure internal validity Case study approach An intense observation of a single individual with complete record of observations often used in clinical settings
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