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Performing Modern Statistical Analysis with R

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Introduction

About the Course Getting Started Motivation for Statistical Analysis The R Programming Language and its Packages

Description

The Pollination Data Summarizing the Data Describing the Data Comparing Groups The Reproducibility Crisis and R Scripts Quiz: Description Summary

Estimation

Estimation with the Pollination Data Standard Deviations and Standard Errors The Normal Distribution and the Central Limit Theorem Quiz: Estimation Summary

Linear Models

Introduction to Linear Model Analysis

Standard Error of the Difference

Confidence Intervals and Darwin’s Question

Releveling to Calculate Mean and Standard Error

Normality and Equal Variance

Challenge: Summary Statistics and Plotting in R

Solution: Summary Statistics and Plotting in R

Quiz: Linear Models

Regression

Introduction to Linear Regression The Janka Hardness Data Correlation and Linear Regression in R Assumptions in Linear Regression Quiz: Regression Summary

Prediction

Prediction Using Regression Confidence Intervals and Prediction Intervals Challenge: Coefficients, Confidence Intervals, and X-matrix in R Solution: Coefficients, Confidence Intervals, and X-matrix in R Quiz: Prediction Summary

Testing

Significance Testing with the t-Test Critical and Observed Values Table of Coefficients Challenge: Critical Value of t in R Solution: Critical Value of t in R Quiz: Testing Summary

Intervals

Comparisons Using Estimates and Intervals Descriptive Statistics Confidence Intervals for Standard Errors Confidence Intervals for Difference in Means Relating the Different Types of Intervals and Error Bars Point Estimates and Confidence Intervals Challenge: Least Significant Difference and Mean in R Solution: Least Significant Difference and Mean in R Quiz: Intervals Summary

Analysis of Variance

ANOVA Tables Analysis of Variance Table Hypothesis Testing Two-way ANOVA Quiz: Analysis of Variance Summary

Factorial Designs

Factorial Designs Comparing Groups Two-Way ANOVA Test with No Interaction Additive Treatment Effects Interactions: Factorial ANOVA The Factorial ANOVA Table Quiz: Factorial Designs Summary

Analysis of Covariance

ANCOVA and the Agricultural Pollution Data ANCOVA with Water Stress and Low-level Ozone ANCOVA and The Table of Coefficients Interactions in ANCOVA and General Linear Models Quiz: Analysis of Covariance Summary

Linear Model Complexities

Analysis of Variance for Balanced Designs Analysis of Variance with Unbalanced Designs ANOVA Tables Versus Coefficients Marginality of Main Effects and Interactions Main Effects of Water Stress and Sulphur Dioxide Challenge: Fitting The Linear Regression Model Solution: Fitting the Linear Regression Model Quiz: Linear Model Complexities Summary

Generalized Linear Models

GLMs and the Trouble with Transformations Transformation with Log Data The Box-Cox Power Transformation Generalized Linear Models in R GLM with Gaussian Variance Quiz: Generalized Linear Models Summary

GLMs for Count Data

Introduction of GLMs for Count Data Quasi-maximum Likelihood Quiz: GLMs for Count Data Summary

Binomial GLMs

The Beetle Mortality Experiment GLM for Binomial Counts Alternative Link Functions Quiz: Binomial GLMs Summary

GLMs for Binary Data

Binary Data and The Wells Dataset Binary GLM for the Wells Dataset Centering Quiz: GLMs for Binary Data Summary

Conclusion

Revisiting the Challenger Dataset with GLMs GLM Analysis of the Challenger Binary Data Recommendations What's Next?Copyright Information

Appendix

Installation The Reproducibility Crisis and R Scripts

Normality and Equal Variance

Let's learn about normality and equal variance by using plots.

We'll cover the following

Normality
Equal variance

Normality

Approximate normality can be judged using a quantile-quantile plot (Q-Q plot). This type of plot graphs the quantiles of the distribution of the residuals versus the quantiles of a random sample of normally distributed numbers. This is, so the residuals fall around a straight line when they match the model.

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