Experimental Designs Week 4 Solution

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Experimental DesignsWeek 4 SolutionExperimental Designs2. Explain the difference between multiple independent variables and multiple levels of independentvariables. Which is better?Answer:The general purpose of multivariate analysis of variance (MANOVA) is to determinewhether multiple levels of independent variables on their own or in combination withone another have an effect on the dependent variables. MANOVA requires that thedependent variables meet parametric requirements.MANOVA is used under the same circumstances as ANOVA but whenthere are multiple dependent variables as well as independent variables within the modelwhich the researcher wishes to test. MANOVA is also considered a valid alternative tothe repeated measures ANOVA when sphericity is violated.Like an ANOVA, MANOVA examines the degree of variance within theindependent variables and determines whether it is smaller than the degree of variancebetween the independent variables. If the within subjects variance is smaller than the betw-een subjects variance it means the independent variable has had a significant effect on thedependent variables. There are two main differences between MANOVAs and ANOVAs.The first is that MANOVAs are able to take into account multiple independent and multipledependent variables within the same model, permitting greater complexity. Secondly,ratherthan using the F value as the indicator of significance a number of multivariate measures.MANOVAs the independent variables relevant to each main effect are weighted to givethem priority in the calculations performed. In interactions the independent variables areequally weighted to determine whether or not they have an additive effect in terms of thecombined variance they account for in the dependent variable/s.The main effects of the independent variables and of the interactions are examined withall else held constant. The effect of each of the independent variables is tested separately.Any multiple interactions are tested separately from one another and from any significantmain effects. Assuming there are equal sample sizes both in the main effects and the inter-actions, each test performed will be independent of the next or previous calculation (exce-pt for the error term which is calculated across the independent variables).

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3. What is blocking and howdoes it reduce “noise”? What is a disadvantage of blocking?Sol:The Randomized Block Design is research design's equivalent to stratifiedrandom sampling. Like stratified sampling, randomized block designs areconstructed to reduce noise or variance in the data (see Classifying the Exper-imental Designs). How do they do it? They require that the researcher dividethe sample into relatively homogeneous subgroups or blocks (analogous to"strata" in stratified sampling). Then, the experimental design you want to impl-ement is implemented within each block or homogeneous subgroup. The keyidea is that the variability within each block is less than the variability of theentire sample. Thus each estimate of the treatment effect within a block is moreefficient than estimates across the entire sample. And, when we pool these moreefficient estimates across blocks, we should get an overall more efficient estimatethan we would without blocking.How Blocking Reduces NoiseSo how does blocking work to reduce noise in the data? To see how it works,you have to begin by thinking about the non-blocked study. The figure showsthe pretest-posttest distribution for a hypothetical pre-post randomized experi-mental design. We use the 'X' symbol to indicate a program group case and the'O' symbol for a comparison group member. You can see that for any specificpretest value, the program group tends to outscore the comparison group byabout 10 points on the posttest. That is, there is about a 10-point posttest meandifference.

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Now, let's consider an example where we divide the sample into three relativelyhomogeneous blocks. To see what happens graphically, we'll use the pretest mea-sure to block. This will assure that the groups are very homogeneous. Let's look atwhat is happening within the third block. Notice that the mean difference is still thesame as it was for the entire sample about 10 points within each block. But alsonotice that the variability of the posttest is much less than it was for the entire sample. Remember that the treatment effect estimate is a signal-to-noise ratio. The signalin this case is the mean difference. The noise is the variability. The two figures showthat we haven't changed the signal in moving to blocking there is still about a 10-pointposttest difference. But, we have changed the noise -- the variability on the posttest ismuch smaller within each block that it is for the entire sample. So, the treatment effectwill have less noise for the same signal.

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