Lectures

Lecture 1

Fundamentals of statistical testing

In our first lecture, we will go over some of the basic statistical concepts, adding to our knowledge of distributions and sampling. We will discuss the essential properties of the normal distribution and how we can use them to make inferences from samples to populations. Finally, we will talk about a core principle of statistical testing, the Central Limit Theorem.

Lecture 2

Best guesses and uncertainty

In this lecture we build on the understanding of the sampling distribution of the mean and the standard error and talk more about the uncertainty that is inherent in estimation. We talk about how interval estimates can be used to quantify this uncertainty around point estimates. In particular, we focus on the confidence interval and talk about how it is constructed using the t distribution and how to interpret it.

Lecture 3

From research questions to statistics

After two weeks of abstract concepts, we are now ready to finally talk about how we can use statistics to test hypotheses. In this lecture, we will introduce the framework of Null Hypothesis Significance Testing and explain how it is used to make decisions about the world we live in. We will talk about climbing, alternative realities, and parallel universes

Lecture 4

Correlation

With the foundations of statistical testing under our belt, we encounter our first example of a statistical test: correlation. We discuss the meaning of the correlation coefficient r and what correlation does (and does not!) tell us about the relationships between variables.

Lecture 5

t-tests

We explore how to compare means in different groups and conditions using the ubiquitous t-test. We look at two different types of t-tests, focusing on the independent samples test, which will be a central element of the upcoming TAP assessment.

Lecture 6

Chi-square

Here we encounter the next new tool in our statistical arsenal, the chi-square (χ²) test and its associated distribution. We look at two different types of chi-square tests, focusing on the test of association.

Lecture 7

Linear Model 1: A New Equation

In this lecture we begin our adventures with the linear model, a foundational concept in statistical analysis. We begin with statistical models and the equation of a line, exploring how that equation, representing the linear model, can be used to make predictions

Lecture 8

The Linear Model 2: R² Strikes Back

In this lecture we build our knowledge of the linear model with one predictor. This time we look at how we can evaluate our model, covering significance, confidence intervals, and R²

Lecture 9

The Linear Model 3: Return of the y_i

In this lecture we learn how to extend the linear model that we have been talking about for the previous two weeks to add multiple predictor variables and build more sophisticated models of the world. We will also see what effects linear transformations of variables in the model have on the model coefficients.

Lecture 10

The Linear Model 4: F Awakens

We start the final lecture of the mini-series dedicated to the linear model by talking about adding binary categorical variables to larger models. Then, we discuss an important issue with R² and how it can be mitigated. Finally, we talk about comparing linear model using the F-test

Lecture 11

End of the line

Thus ends our journey of discovery but mourn not for its end is but a beginning of a bigger adventure. The next term awaits you with aRms wide open!