IntroductionStats I

To Do Today• Introductions• Blog: swstats.blogspot.com• Go Over Syllabus• Go Over Textbooks

• Register for EP• Take Intro Survey• Course Intro• Start On Sampling Theory

What this class isn’t• Learning a bunch of discrete formulas

• Learning a bunch of “tests” and figuring out when to use them

• Practicing computation

What Statistics IS• Inferential Statistics is a general method for using data that we

observe to make inferences about a population that is unobservable

• Different “tests” are specific incarnations of this general method

The Approach We Are Going to Take

1. Learn the conceptual framework (and connect this to other concepts we already know)

2. Understand how the method instantiates the concept

3. Perform the method (in SPSS usually)

4. Learn to communicate these results (and tie them into our conceptual framework)

Goals of the Class• Get a reasonable grasp of univariate statistical techniques and

how they are used in research

• Become SPSS pros!

• Learn to communicate statistical results in a research setting (in this case, using APA)

Ready to Begin?

Distributions and Sampling• What (exactly?) is a distribution?

• A frequency distribution is the observed number of data points in a group of categories

But…there is a problem• We have some theoretical information about a die that

overrules the empirical information we have from tossing the die a couple of times

• We, in a way, know what the distribution “should” be (if our theory were correct).

• So how do we model this difference between what “should” be and what we observe?

Probability Distribution Functions (PDF)• A PDF is a mathematical function that describes the

probability of any outcome in a random process.• It is a theoretical idea that attempts to describe empirical

phenomenon• Discrete and continuous

Normal PDF

• PDF’s describe the probability of a bunch of mutually exclusive outcomes. So:• The sum (or integral) of all outcomes must add to 1

So…Why Posit these Imaginary Constructs? • As we saw before, even for the simple case of the dice, there is

some expected variation in any observed frequency distribution from what we would see on average.

Sampling• Any finite sample we take is going to differ from the ideal PDF.

• Almost all of statistics is asking questions in this (kind of crazy) way:

• IF the ideal PDF looks like this:

• Is it likely that I would observe this:

Populations• Inferential Statistics is always making inferences about

populations. • Did two samples come from the same population• Did this sample come from a population that looks like ______• These two variables move together in my sample, is the same

true of the population?

• These inferences are not based on guesses or fuzzy algorithms, but they are derived deterministically from looking at every possible sample from a given population (using elegant mathematical tricks).

The Catch• We are never making inferences the way we would like to:i.e. given this sample, what is the population

• Instead we always have to say, if the population looked like this:

• Could one expect to see a sample like this: