STA6166 F07-21 Comparing More than 2 Populations

STA6166 F07-21 - Topic 21 ANOVA(I 21-1 Topic 21 Inferences For More Than 2 Populations EXAMPLES 1 Suppose we want to compare species diversity of

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Topic 21 - ANOVA (I) 21-1 Topic 21 - Inferences For More Than 2 Populations EXAMPLES : 1) Suppose we want to compare species diversity of microfauna in three different habitats: desert, caves, and arctic tundra. a. Hypotheses and inferences are related to determining whether there are differences in mean diversity among the three habitats and if so, determining how they differ 2) Suppose we want to compare the average growth rate in oysters maintained in four different temperatures. a. Hypotheses might be that average growth rate differs among the four temperatures studied (we could go further and make hypotheses regarding whether the means increase or decrease but then we are moving into the regression setting rather than the ANOVA setting) Defn : A Factor is the variable that separates the groups of interest into distinct populations.
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Topic 21 - ANOVA (I) 21-2 Defn : A Treatment is one level of the Factor under study. If more than one factor is of interest, then a treatment is a combination of levels of the factors. Defn: The treatments are considered to be Populations , each with its own mean and variance. EXAMPLE Oyster experiment. Factor: Treatments (levels of Factor): Populations under Study: Completely Randomized Designs (CRD) Defn : A Completely Randomized Design is an experimental design in which the experimental units are either randomly selected from each of the populations or are randomly assigned to one of the populations. This means that each population and sample is considered independent of all of the other samples and populations.
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Topic 21 - ANOVA (I) 21-3 Recall Defn : An Observational Study is one in which we cannot control the treatment performed on the experimental units. Recall Defn: A Planned Experiment is one in which the treatment is randomly assigned to each experimental unit. For example, suppose we are interested in the effect of three types of submerged aquatic vegetation species on water clarity. Two approaches: 1) find locations with only one of the three species and measure water clarity at those locations. 2) construct “ponds” and fill each with one of the three cover species. Leave alone for a while and then measure water clarity. Is one method better than the other? why?
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Topic 21 - ANOVA (I) 21-4 Assumptions of the CRD: 1) Sampling : a. For observational studies, independent random samples are taken from each of the populations of interest. b. For planned experiments, the treatments are randomly assigned to the randomly chosen experimental units. Here, the populations refer to conceptual ones in which there is one population for each of the treatments in the experiment. c. Samples from each population are independent . EXAMPLE oysters: independent sampling here would mean that oysters were randomly selected for the experiment (no clumps of oysters were taken and then separated, oysters were taken from different locations, oysters were not selected by size, etc) and further that, if the experiment was planned, the oysters were randomly assigned to treatment levels.
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This note was uploaded on 07/22/2011 for the course STA 4702 taught by Professor Staff during the Spring '08 term at University of Florida.

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STA6166 F07-21 - Topic 21 ANOVA(I 21-1 Topic 21 Inferences For More Than 2 Populations EXAMPLES 1 Suppose we want to compare species diversity of

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