# Table of Contents

- Page ID
- 7199

We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness.

## 1: Introduction

This chapter provides an overview of statistics as a field of study and presents terminology that will be used throughout the course.## 2: Describing Data using Distributions and Graphs

Before we can understand our analyses, we must first understand our data. The first step in doing this is using tables, charts, graphs, plots, and other visual tools to see what our data look like.## 3: Measures of Central Tendency and Spread

Now that we have visualized our data to understand its shape, we can begin with numerical analyses. The descriptive statistics presented in this chapter serve to describe the distribution of our data objectively and mathematically – out first step into statistical analysis! The topics here will serve as the basis for everything we do in the rest of the course.## 4: Z-scores and the Standard Normal Distribution

We now understand how to describe and present our data visually and numerically. These simple tools, and the principles behind them, will help you interpret information presented to you and understand the basics of a variable. Moving forward, we now turn our attention to how scores within a distribution are related to one another, how to precisely describe a score’s location within the distribution, and how to compare scores from different distributions.## 5: Probability

Probability can seem like a daunting topic for many students. In a mathematical statistics course this might be true, as the meaning and purpose of probability gets obscured and overwhelmed by equations and theory. In this chapter we will focus only on the principles and ideas necessary to lay the groundwork for future inferential statistics. We accomplish this by quickly tying the concepts of probability to what we already know about normal distributions and z-scores.## 6: Sampling Distributions

We have come to the final chapter in this unit. We will now take the logic, ideas, and techniques we have developed and put them together to see how we can take a sample of data and use it to make inferences about what's truly happening in the broader population. This is the final piece of the puzzle that we need to understand in order to have the groundwork necessary for formal hypothesis testing. Though some of the concepts in this chapter seem strange, they are all simple extensions of what w## 7: Introduction to Hypothesis Testing

This chapter lays out the basic logic and process of hypothesis testing. We will perform z-tests, which use the z-score formula from chapter 6 and data from a sample mean to make an inference about a population.## 8: Introduction to t-tests

Last chapter we made a big leap from basic descriptive statistics into full hypothesis testing and inferential statistics. For the rest of the unit, we will be learning new tests, each of which is just a small adjustment on the test before it. In this chapter, we will learn about the first of three t-tests, and we will learn a new method of testing the null hypothesis: confidence intervals.## 9: Repeated Measures

So far, we have dealt with data measured on a single variable at a single point in time, allowing us to gain an understanding of the logic and process behind statistics and hypothesis testing. Now, we will look at a slightly different type of data that has new information we couldn’t get at before: change. Specifically, we will look at how the value of a variable, within people, changes across two time points. This is a very powerful thing to do, and, as we will see shortly, it involves only a v## 10: Independent Samples

We have seen how to compare a single mean against a given value and how to utilize difference scores to look for meaningful, consistent change via a single mean difference. Now, we will learn how to compare two separate means from groups that do not overlap to see if there is a difference between them. The process of testing hypotheses about two means is exactly the same as it is for testing hypotheses about a single mean, and the logical structure of the formulae is the same as well.## 11: Analysis of Variance

Analysis of variance, often abbreviated to ANOVA for short, serves the same purpose as the \(t\)-tests we learned in unit 2: it tests for differences in group means. ANOVA is more flexible in that it can handle any number of groups, unlike \(t\)-tests which are limited to two groups (independent samples) or two time points (dependent samples). Thus, the purpose and interpretation of ANOVA will be the same as it was for \(t\)-tests, as will the hypothesis testing procedure. However, ANOVA will, a## 12: Correlations

All of our analyses thus far have focused on comparing the value of a continuous variable across different groups via mean differences. We will now turn away from means and look instead at how to assess the relation between two continuous variables in the form of correlations. As we will see, the logic behind correlations is the same as it was group means, but we will now have the ability to assess an entirely new data structure.## 13: Linear Regression

In chapter 11, we learned about ANOVA, which involves a new way a looking at how our data are structured and the inferences we can draw from that. In chapter 12, we learned about correlations, which analyze two continuous variables at the same time to see if they systematically relate in a linear fashion. In this chapter, we will combine these two techniques in an analysis called simple linear regression, or regression for short. Regression uses the technique of variance partitioning from ANOVA## 14: Chi-square

We come at last to our final topic: chi-square (χ2). This test is a special form of analysis called a non-parametric test, so the structure of it will look a little bit different from what we have done so far. However, the logic of hypothesis testing remains unchanged. The purpose of chi-square is to understand the frequency distribution of a single categorical variable or find a relation between two categorical variables, which is a frequently very useful way to look at our data.