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lec8_jls - BE.104 Spring Biostatistics: Detecting...

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BE.104 Spring Biostatistics: Detecting Differences and Correlations J. L. Sherley Outline 1) Review Concepts 2) Detecting differences and quantifying confidence 3) Detecting relationships and quantifying confidence Variance = σ 2 What do changes in variance tell us? (Review in-class exercises) <graphs> Multiple "populations" present Skewed data; non-normal data An important distinction about the application of normal statistics that is often confused: The sampled POPULATION should be normally distributed- why? Question: If a sample distribution is not normal can we apply parametric statistical methods? Yes, if they are a sample from an “ideal population” that is normally distributed. It is the properties of the ideal population that matter , not the distribution of the sample, per se. Caveat? <graph> Parametric statistical methods address the uncertainty of sampling. Now we focus on the structure of the sample because we know it gives us some information about the structure of the ideal population. So, we must base our decision about using normal statistics on the sample when we have no a priori information about the structure of the ideal population with N members. 1
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Now to detecting differences What we want to ask is: Are two means more different than we would expect based on “error” & statistical variation alone? Consider there is only one ideal population, and we may be looking at sampling variation or statistical variation and error. <picture> So, we define the possible range of differences in the means that could occur by chance/error with some level of confidence. <graph> If this difference is not explained by error & statistical variation (i.e., variance) we then can consider other factors: E.g., A change in a physiological mechanism Which might lead us to: Parallel testing (i.e., a bigger study) Orthogonal testing (i.e. different kind of study; intervention experiment) “More on this later” “Detecting Differences Between Estimated Pop. Means” Our question can be phrased this way regarding the ideal population thinking: <picture with graph> 2
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Two sample distributions, with numerical different sample means, drawn from ideal populations A and B. Hypothesis: A and B are distinct populations with distinct population means, µ . The null hypothesis: the observed numerical difference occurs due to variance, and the
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This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.

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lec8_jls - BE.104 Spring Biostatistics: Detecting...

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