Learning objectives

Students should be able to do each of the following by the end of this course:

What is statistics? overview of the course

• Describe the central goals and fundamental concepts of statistics.
• Describe the difference between experimental and observational research with regard to what can be inferred about causality
• Explain how randomization provides the ability to make inferences about causation.

Working with data

• Distinguish between different types of variables (quantitative/qualitative, discrete/continuous)
• Describe the concept of measurement error
• Distinguish between the concepts of reliability and validity and apply each concept to a particular dataset

R Lab: Basics

• Interact with an RMarkdown notebook in RStudio
• Describe the difference between a variable and a function
• Create a vector, matrix, or data frame and access its elements
• Load data from an R package and view the data

Summarizing data

• Compute absolute, relative, and cumulative frequency distributions for a given dataset
• Generate a graphical representation of frequency distributions
• Describe the difference between a normal and a long-tailed distribution, and describe the situations that give rise to each

Visualizing data

• Describe the principles that distinguish between good and bad graphs, and use them to identify good versus bad graphs.

R Lab: Data visualization

• Plot summary graphs using ggplot

Fitting models (central tendency)

• Describe the basic equation for statistical models (outcome=model + error)
• Describe different measures of central tendency, how they are computed, and which are appropriate under what circumstance.

Fitting models (central tendency) and z-scores

• Describe different measures of dispersion, how they are computed, and how to determine which is most appropriate in any given circumstance. Describe and compute z-scores.

Probability

• Describe the sample space for a selected random experiment.
• Compute relative frequency and empirical probability for a given set of events
• Compute probabilities of single events, complementary events, and the unions and intersections of collections of events.
• Describe the law of large numbers.
• Describe the difference between a probability and a conditional probability
• Describe the concept of statistical independence
• Use Bayes’ theorem to compute the inverse conditional probability.

Sampling

• Distinguish between a population and a sample, and between population parameters and statistics
• Describe the concepts of sampling error and sampling distribution
• Describe how the Central Limit Theorem determines the nature of the sampling distribution of the mean

Resampling

• Describe the concept of a Monte Carlo simulation.
• Describe the meaning of randomness in statistics
• Obtain random numbers from the uniform and normal distributions
• Describe the concept of the bootstrap

Hypothesis testing

• Identify the components of a hypothesis test, including the parameter of interest, the null and alternative hypotheses, and the test statistic.
• Describe the proper interpretations of a p-value as well as common misinterpretations
• Distinguish between the two types of error in hypothesis testing, and the factors that determine them.
• Describe how resampling can be used to compute a p-value.
• Describe the main criticisms of null hypothesis statistical testing

Quantifying effects and designing studies

• Describe the proper interpretation of a confidence interval, and compute a confidence interval for the mean of a given dataset.
• Define the concept of effect size, and compute the effect size for a given test.
• Define the concept of statistical power, and compute statistical power for a given statistical test.

Modeling categorical relationships

• Describe the concept of a contingency table for categorical data.
• Describe the concept of the chi-squared test for association and compute it for a given contingency table.

Modeling continuous relationships

• Describe the concept of the correlation coefficient and its interpretation and compute it for a bivariate dataset
• Describe the potential causal influences that can give rise to a correlation.

The general linear model

• Describe the concept of linear regression and apply it to a bivariate dataset
• Describe the concept of the general linear model and provide examples of its application

Comparing means

• Determine whether a one-sample t-test or two-sample t-test is appropriate for a given hypothesis.
• Compute a one-sample and two-sample t-test on relevant datasets, and compute the effect size and confidence intervals associated with each of these tests.

Statistical Inference R lab

• Demonstrate the ability to apply statistical models to real data in R

Statistical modeling: Practical examples

• Describe how to determine what kind of model to apply to a dataset

Doing reproducible research

• Describe the concept of P-hacking and its effects on scientific practice
• Describe the concept of positive predictive value and its relation to statstical power