Lecture15 - Lecture 15 Categorical Data Analysis...

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Unformatted text preview: Lecture 15: Categorical Data Analysis I (Introduction & 1-way GOF Tests) Sources of Information Triola: Chapter 10 otulsky: Chapters 26-29 Sokal & Rohlf: Chapter 17 Dytham: p. 60-64, 147-154 OUTLINE : 1. Intro to categorical data 2. Concept of goodness-of fit 3. One-way classifications • binomial experiments • multinomial experiments Introduction to Categorical Data ecall from Lecture 2 ( Data in Biology ) that: ategorical data = Qualitative data that can be separated into different categories that are distinguished by some non- numeric characteristic. = data at the nominal or ordinal level of measurement ategorical data record counts of items or events, i.e. phenomena that can be named and enumerated. Categorical data are very common in the biosciences. Examples : • The frequency of males and females in a sample; • The frequency of dead and alive Daphnia at the end of a toxicological bioassay; • The frequency of patients that die after a risky operation. • The frequency of parasitized and unparasitized insects in a sample; • The frequency of colour morphs in a fish species; • The frequency of genotypes in samples from a population of corn plants. ote that data can be binomial (i.e., nominal data with 2 categories) or multinomial (>2 categories). Goodness-of-Fit Testing Common Q : do the observed frequencies of a nominal variable (in a sample) agree or disagree with the pattern expected under a biological hypothesis? Examples: Is there a balanced sex ratio in this species of mayflies? If a 1:1 ratio was expected, then a departure from that ratio could reflect an interesting biological phenomenon such as meiotic-drive distorter genes on the Y chromosome, or differential sex-related ortality. (= extrinsic hypothesis ; d.f. = k-1) Or, does the observed frequency of a nominal variable agree with that expected under a statistical model – uniform, binomial, Poisson, etc.? (= intrinsic hypothesis ; d.f. = k-2) In all these cases, the question remains same: do the observed data atch that expected under some hypothesized distribution? Do they fit the expected picture? e examine this by goodness-of-fit (shortened to GOF) measures: There are 3 main approaches : • chi-square ( χ 2 ) test - traditional approach (most widely used) • log-likelihood ratio - newer, but becoming more common (also called G-test; in SPSS = “likelihood ratio”) • exact¡tests¡- used in certain cases (e.g., small sample size) GOF tests = a general method to test a claim that the observed frequencies in the different categories fit ( or deviate from ) a particular ( hypothesized ) distribution. H : the observed frequency distribution fits (or conforms to) a claimed distribution (for the statistical population)....
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Lecture15 - Lecture 15 Categorical Data Analysis...

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