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Exam II Marks

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Chapter 20.1 Correlation

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Correlation is used when we wish to know whether two randomly distributed variables are associated with each other Example – Total length Y1 of aphid stem mothers and mean thorax length Y2 of their parthenogenetic offspring.

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No causal ordering

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Contrast to regression

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Formal model Regression randomly distributed response variable ~ fixed explanatory variable Correlation two random response variables No causal ordering, thus no explanatory variable

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Compute t

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State H A /H o pair Crunch the numbers

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More number crunching > cor.test(dat$th.length,dat$tot.length) Pearson's product-moment correlation data: dat$th.length and dat$tot.length t = 3.0867, df = 13, p-value = 0.008666 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.2070464 0.8720726 sample estimates: cor 0.6503335

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Conclusions r = 0.650, n = 15, p = 0.0086 Thorax length of offspring is positively related to stem mother total length. The relation of offspring thorax length to size of aphid stem mothers is monotonic but not necessarily linear.

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