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# Statistical Methods STAT 571

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This 3 page Class Notes was uploaded by Kamren McLaughlin on Monday October 26, 2015. The Class Notes belongs to STAT 571 at University of Tennessee - Knoxville taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/229896/stat-571-university-of-tennessee-knoxville in Statistics at University of Tennessee - Knoxville.

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Date Created: 10/26/15

Stat 571 Statistical Methods List of Topics This course follows the textbook Statistics and Data Analysis From Elementary to Intermediate by Ajit Tamhane and Dorothy Dunlop The chapters covered are l to 13 Chapter 2 on probability is only brie y covered The IMF software package is integrated with the course material The course transparencies and other course information are available in the course home page at httpwebutkeduNleonstat57l Topic Target Number of Days 1 Introduction Statistical Terminology Descriptive statistics or exploratory data analysis inferential statistics population sample variable parameter statistic random sample sampling variability probability versus statistics 1 2 Review of Probability Approaches to probability classical frequentist subjective axiomatic axiomatic approach frequency tables conditional probability Bayes theorem random variables distribution function density function expected value variance and standard deviation quantiles and percentiles covariance and correlation Chebyshev s inequality weak law of large numbers discrete distributions Bernoulli Binomial Poisson continuous distributions Uniform Exponential Gamma normal distribution 3 Collecting Data Historical data types of studies comparative descriptive or noncomparative observational experimental confounding lurking variables control group treatment or intervention control group pretest only design pretestposttest design placebo effect single blind study double blind study concurrent control group historical control group sample surveys prospective studies retrospective studies acceptance sampling censuses target population sampled population sampling and nonsampling errors bias representative sample cohort studies case control studies judgment sampling quota sampling simple random samples sampling rate sampling frame strati ed random sampling multistage cluster sampling probabilityproportionaltosize sampling systematic sampling link systematic sample treatment factors nuisance or noise factors treatment group replicate versus repeat measurements systematic error random error measurement error blocking regression analysis covariates randomization completely randomized design randomized block design iterative nature of experiments 4 Summarizing and Exploring Data Variable types categorical qualitative nominal ordinal numerical continuous discrete interval ratio summarizing categorical data frequency table bar chart Pareto chart pie chart summarizing numerical data mean median skewness outliers measures of dispersion quantiles range variance standard deviation interquartile range coef cient of variation standardized z scores histogram stem and leaf diagram box and whiskers plot fences normal plots departures from normality normalizing transformations runs chart summarizing bivariate categorical data twoway table mosaic plot Simpson s paradox adjusted standardized rates summarizing bivariate numerical data scatter plot simple correlation coef cient sample covariance correlation versus causation straight line regression regression towards the mean regression fallacy summarizing time series data data quot 39 f quot 39 39 5 Sampling Distributions of Statistics Estimates sampling error frequentist approach to statistics sampling distribution of the sample mean Central Limit Theorem Law of Large Numbers normal approximation to the Binomial sampling distribution of the sample variance ChiSquare distribution Student s tdistribution F distribution 6 Basic Concepts of Inference Estimation hypothesis testing point estimation con dence interval estimation estimator estimate bias and variance of estimator mean square error precision and standard error con dence level and limits frequentist interpretation of con dence intervals null and altemative hypothesis type I and II error probabilities of type I and II error acceptance sampling simple and composite hypothesis P value onesided and twosided tests use and misuse of hypothesis tests in practice multiple comparisons 7 Inference for Single Samples Inference for the mean large samples con dence intervals for the mean test for the mean sample size determination for the z interval power calculation for onesided and twosided ztest power function curves sample size determination for the onesided and twosided ztest inference for the mean small samples t distribution con dence intervals based on the t distribution inference on variance con dence intervals for the variance and standard deviation hypothesis test on variance and standard deviation prediction intervals tolerance intervals 8 Inference for Two Samples Independent sample design matched pair design pros and cons of each design side by side box plots comparing means of two populations large sample con dence interval for the difference of two means large sample test of hypothesis for the difference of two means inference for small samples confidence intervals and tests of hypothesis unequal variance case confidence intervals and hypothesis tests sample size determination assuming equal variances confidence intervals and test of hypothesis for matched pair design statistical justification of matched pair design sample size determination for matched pair design comparing variance of two populations 9 Inference for Proportions and Count Data Large sample confidence interval for proportion sample size determination for a confidence interval for proportion large sample hypothesis test on proportion comparing two proportions in the independent sample design confidence interval and test of hypothesis inference for two way count data total sample size fixed row total fixed chi square statistic 10 Simple Linear Regression and Correlation Dependent and independent variables probability model for simple linear regression least squares t goodness of fit of the LS line sums of squares geometry of sums of squares coefficient of determination estimation of error variance statistical inference for slope and intercept tests of hypothesis and confidence intervals analysis of variance prediction of future observation confidence and prediction intervals calibration inverse regression regression diagnostics residual plots mathematics of residuals checking for linearity quadratic model checking for constant variance checking for normality of errors checking for independence of errors checking for outliers standardized studentized residuals checking for in uential observations hat matrix leverage plots data transformations variance stabilizing transformations correlation analysis bivariate normal density function statistical inference on the correlation coefficient correlation between test instruments

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