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Stat 312, Spring Semester, 2002 Topics for the Final Exam Probability background Properties of probabilities and conditional probabilities Random variables Specifying probability distributions (discrete and continuous) Probability density functions Probability mass functions Cumulative distribution function Computation of expectations variances and covariances Central limit theorem Graphical summaries Scatter plots Histograms Box plots Q-Q plots Summary statistics Mean Median Sample variance and standard deviation Quantiles Interquartile range (IQR) Extremes (maximum, minimum) Correlation coefficient Models and parameter estimates Uses of models Organize data Make predictions Optimize designs Basis for theoretical understanding Models for independent observations: Probability distributions Normal Lognormal Exponential Gamma Uniform (discrete and continuous) Binomial Geometric Poisson Estimation of parameters for probability distributions Estimation of the mean, variance and standard deviation Method of moments Maximum likelihood Unbiased estimator Standard error Confidence intervals Models of functional relationships: Regression Response Explanatory variables Tests of significance Quality of the model (R2, adjusted R2, Akaike) Hypothesis testing Basic concepts Null and alternative hypotheses Test statistics p-value Significance level Critical value and rejection region Power, power curve Standard test statistics t statistic (one and two sample) Obtain critical values from normal or t table Generalized likelihood ratio statistic and chi-square approximation Chi square statistic Hypotheses on proportions Test of independence/homogeneity Obtain critical values from chi-square table Analysis of variance (ANOVA) Forms of models Null and alternative hypotheses Main effects and interactions Sources of variation Things to think about Scientific settings appropriate for a test Calculation of p-values and critical values and the conditions under which methods of calculation are valid What “rejection” means scientifically
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