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# Lecture 12 The Importance of Variance

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Lecture 12 The Importance of Variance Lecture Outline Variance by Design Variance by Manipulation Variance for Outcomes Variance for Parameter Estimation Variance for Hypothesis Testing Before discussing variance it is important for us all to appreciate what variance means Recall that variance simply means the average deviation from the measure of central tendency If there is no meaningful central tendency e g a uniform distribution or no recognizable distribution then variance is not terribly informative Variance therefore is related to both the measure of central tendency and the probability distribution We also know now how to calculate variance Variance is simply defined by the sum of the squared deviations divided by the degrees of freedom In most cases we refer to the variance as 2 or s2 but more often than not it masquerades as a familiar term called Mean Squares MS In any case the concept of variance is central to all of research and I intend to go through each level to emphasize where it is important and why it is important What I outline may be best summarized by Kerlinger s 1973 principle of MAXMINCON MAXimize variable attributable to the effect MINimize error variance and CONtrol for extraneous variance Variance by Design 20 mins The first place to look at variance is in the design What I refer to with the term design is the approach used to maximize the opportunity of finding the effect you wish to study I like to think of design as the methods we use to maximize our change in uncertainty The following methods are relevant to design Sampling The first part of research design where variance is important is sampling Most of our statistics assume that our samples are random samples from the population Why do they assume this property For one we make that assumption so that our parameter estimates fall within the range of probable values but more importantly so that we get proper estimates of variance for our sample What makes them proper The distribution

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