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Lec12 - Body size males twice as big as females Musculature...

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• Body size : males twice as big as females • Musculature • Grey color of the back • Head crest
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Evolution of sexual dimorphism • Intrasexual selection : Physical advantage of more dimorphic males during agonistic encounters ? • Intersexual selection Female preference for most dimorphic males ?
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25 m 50 m 100 m
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Measurement error • 2 sources : - accuracy of the telemeter (+/- 1 m) - position of the target animal Accuracy of the telemeter Position of the animal 2.5 % 1.96 σ = 5 cm for body size
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When can use the Student’s t method to construct confidence intervals? 1. Conditions of the study design: (a) It must be reasonable to regard the data as random samples from a large population (b) The observations in the two samples must be independent of each other 2. Conditions of the form of the population distribution: (a) If the sample sizes are small , the population distributions must be approximately normal (b) If the sample sizes are large , then the population distributions need not be approximately normal or conduct a t test no bias no hierarchical structure no pairing or dependency between the samples prior knowledge histograms and normal probability plots depends on the degree of non-normality in many cases moderate sample sizes are okay ( n 1 = n 2 = 20)
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The smaller the confidence interval, the more likely it DOES NOT include 0. What if we use Student’s t inappropriately? 1. The t test may be invalid in the sense that the actual risk of Type I error is larger than the nominal significance level α . That is, the P -value yielded by the t test procedure may be inappropriately small. 2. The t test may be valid but less powerful than a more appropriate test. If the conditions do not hold, then the t test may be inappropriate in two ways: hierarchical structure non-independent samples non-normal with long straggly tails Inappropriate use of confidence intervals leads to analogous problems. If the design includes hierarchical structures, your confidence interval may be: 1. Too big 2. Too small ?
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original log transformed What to do if the conditions are not met: 1. Wilcoxon-Mann-Whitney test 2. Transform the data Example of transforming the data : Skin samples from 10 patients with breast implants and 6 (control) patients without implants. As a measure of tissue
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