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|Lesson 1||Introduction to Statistical Research Methods|
|Lesson 2||Visualizing Data|
|Lesson 3||Central Tendency|
|Lesson 6||Normal Distribution|
|Lesson 7||Sampling Distributions|
|Lesson 9||Hypothesis Testing|
|Lesson 10||t-Tests for Dependent Samples|
|Lesson 11||t-Tests for Independent Samples|
|Lesson 12||Intro to One-Way ANOVA|
|Lesson 13||One-Way ANOVA: Test significance of differences|
|Lesson 15||Linear Regression|
|Lesson 16||Chi-Squared Tests|
What is statistics? Only one of the most awesome types of math EVER! Statistics helps us make sense of the world around us by providing methods to describe and analyze data. Data comes in many forms:
|Type of data||Description||Examples|
|Discrete||Data for which there are only whole number values||Number of people, Number of countries you’ve visited, price in cents|
|Continuous||Data for which any value in-between whole numbers is possible||Height, distance, length of time|
|Nominal||Data listing names of something||Type of relative (mom, aunt, uncle, cousin, grandfather), type of car|
|Ordinal||Data that describes the rank/order||Year in school (1st grade, 2nd grade), choice on rating scale (e.g., 1-5), months|
|Interval||Numerical, ordinal data with evenly-spaced intervals||Degrees in Fahrenheit|
|Ratio||Interval data where 0 has a clear meaning||Time|
This book focuses on describing and analyzing continuous data, but in Lesson 16 we get into categorical data.
The examples of each type of data above are variables. The actual data values collected for each variable vary; for example, if we recorded the temperature every evening at 8:00 pm (where the variable is “degrees in Fahrenheit”), we would record many different values.
Always analyze data with a critical eye. You should know how a survey or experiment was conducted, who is in the sample, and how the variables are measured. This textbook will help you develop a sense for numbers so that you can tell if something fishy is going on.
For one thing, it’s crucial that you always know exactly how variables are measured. If the variable is height, are you measuring in inches? Centimeters? It’s relatively easy to determine a unit of measurement for height, but what about the variable happiness? Happiness, love, ambition, etc. are examples of constructs, variables that can’t be easily defined or measured.
Quiz: Which are constructs?
For constructs, we have to determine an operational definition; in other words, a precise way of measuring them. For example, maybe we could measure happiness by the number of times people smile or laugh each day. Throughout this book, you’ll use operational definitions to analyze variables and the relationships between them. You’ll also learn how to draw conclusions about an entire population (e.g., all residents of the United States) based on actual population data or a sample of that population (e.g., 5000 randomly selected residents of the United States). Samples must be representative of a population in order to draw inferences about the population; for this to happen, the sample should be chosen randomly (see video), meaning that each member of the population has an equal chance of being chosen to be in the sample.
So let’s dive in! How do we describe a group of numbers? With numbers! Usually we can choose one or several numbers to describe a large group of numbers (we’ll go in detail on this in Lessons 3 and 4). Parameters are numbers that describe a population while sample statistics are numbers that describe samples. Coming up, you’ll use R to generate random samples from a population. In Lesson 3 you’ll see that sample statistics from random samples better approximate population parameters.
We’ll have a lot of R tutorials throughout this book. R is a free, open-source statistical program that is great for doing statistical analysis. You can download R at www.r-project.org. In our first tutorial, you’ll use R to choose a random sample of size n (where n could be 1, 2, 3, …) from a population of size k.
|R Tutorial: Choosing a random sample of size n from a population of size k
Input your data into R. You have two options: