### Statistics for Researchers

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#### Course Description

Scientific Method, Probability & Statistics Very short history of statistics Why can be confident about the conclusions Probability and decision making Preparation for research (deciding what and how) The big picture: research is a part of a process with inputs and outputs Gathering data Questioners and measurement What to measure Observational Studies Design of Experiments Analysis of Data and Graphical Methods Research Skills and Techniques Research Management Describing Bivariate Data Introduction to Bivariate Data Values of the Pearson Correlation Guessing Correlations Simulation Properties of Pearson's r Computing Pearson's r Restriction of Range Demo Variance Sum Law II Exercises Probability Introduction Basic Concepts Conditional Probability Demo Gamblers Fallacy Simulation Birthday Demonstration Binomial Distribution Binomial Demonstration Base Rates Bayes' Theorem Demonstration Monty Hall Problem Demonstration Exercises Normal Distributions Introduction History Areas of Normal Distributions Varieties of Normal Distribution Demo Standard Normal Normal Approximation to the Binomial Normal Approximation Demo Exercises Sampling Distributions Introduction Basic Demo Sample Size Demo Central Limit Theorem Demo Sampling Distribution of the Mean Sampling Distribution of Difference Between Means Sampling Distribution of Pearson's r Sampling Distribution of a Proportion Exercises Estimation Introduction Degrees of Freedom Characteristics of Estimators Bias and Variability Simulation Confidence Intervals Introduction Confidence Interval for the Mean t distribution Confidence Interval Simulation Confidence Interval for the Difference Between Means Confidence Interval for Pearson's Correlation Confidence Interval for a Proportion Exercises Logic of Hypothesis Testing Introduction Significance Testing Type I and Type II Errors One- and Two-Tailed Tests Interpreting Significant Results Interpreting Non-Significant Results Steps in Hypothesis Testing Signficance Testing and Confidence Intervals Misconceptions Exercises Testing Means Single Mean t Distribution Demo Difference between Two Means (Independent Groups) Robustnes Simulation All Pairwise Comparisons Among Means Specific Comparisons Difference between Two Means (Correlated Pairs) Correlated t Simulation Specific Comparisons (Correlated Observations) Pairwise Comparisons (Correlated Observations) Exercises Power Introduction Example Calculations Power Demo 1 Power Demo 2 Factors Affecting Power Exercises Prediction Introduction to Simple Linear Regression Linear Fit Demo Partitioning Sums of Squares Standard Error of the Estimate Prediction Line Demo Inferential Statistics for b and r Exercises ANOVA Introduction ANOVA Designs One-Factor ANOVA (Between-Subjects) One-Way Demo Multi-Factor ANOVA (Between-Subjects) Unequal Sample Sizes Tests Supplementing ANOVA Within-Subjects ANOVA Power of Within-Subjects Designs Demo Exercises Chi Square Chi Square Distribution One-Way Tables Testing Distributions Demo Contingency Tables 2 x 2 Table Simulation Exercises Case Studies Analysis of selected case studies

Scientific Method, Probability & Statistics Very short history of statistics Why can be confident about the conclusions Probability and decision making Preparation for research (deciding what and how) The big picture: research is a part of a process with inputs and outputs Gathering data Questioners and measurement What to measure Observational Studies Design of Experiments Analysis of Data and...