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Unformatted text preview: Review of Statistics 101 We review some important themes from the course 1. Introduction Statistics Set of methods for collecting/analyzing data (the art and science of learning from data). Provides methods for Design Planning/Implementing a study Description Graphical and numerical methods for summarizing the data Inference Methods for making predictions about a population (total set of subjects of interest), based on a sample 2. Sampling and Measurement Variable a characteristic that can vary in value among subjects in a sample or a population. Types of variables Categorical Quantitative Categorical variables can be ordinal (ordered categories) or nominal (unordered categories) Quantitative variables can be continuous or discrete Classifications affect the analysis; e.g., for categorical variables we make inferences about proportions and for quantitative variables we make inferences about means (and use t instead of normal dist.) Randomization the mechanism for achieving reliable data by reducing potential bias Simple random sample: In a sample survey, each possible sample of size n has same chance of being selected. Randomization in a survey used to get a good crosssection of the population. With such probability sampling methods, standard errors are valid for telling us how close sample statistics tend to be to population parameters. (Otherwise, the sampling error is unpredictable.) Experimental vs. observational studies Sample surveys are examples of observational studies (merely observe subjects without any experimental manipulation) Experimental studies : Researcher assigns subjects to experimental conditions. Subjects should be assigned at random to the conditions ( treatments ) Randomization balances treatment groups with respect to lurking variables that could affect response (e.g., demographic characteristics, SES), makes it easier to assess cause and effect 3. Descriptive Statistics Numerical descriptions of center (mean and median), variability (standard deviation typical distance from mean ), position ( quartiles, percentiles ) Bivariate description uses regression/correlation (quantitative variable), contingency table analysis such as chisquared test (categorical variables), analyzing difference between means (quantitative response and categorical explanatory) Graphics include histogram, box plot, scatterplot Mean drawn toward longer tail for skewed distributions, relative to median. Properties of the standard deviation s : s increases with the amount of variation around the mean s depends on the units of the data (e.g. measure euro vs $) Like mean, affected by outliers Empirical rule : If distribution approx. bellshaped, about 68% of data within 1 std. dev. of mean about 95% of data within 2 std. dev. of mean all or nearly all data within 3 std. dev. of mean Sample statistics / Population parameters...
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This note was uploaded on 07/12/2011 for the course STA 3030 taught by Professor Agresti during the Spring '11 term at University of Florida.
 Spring '11
 Agresti
 Statistics

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