Introduction to Set Theory
James H. Steiger
Sets
Definition. A Set is any well defined collection of
objects.
Definition. The elements of a set are the objects in a
set.
Notation. Usually we denote sets with upper-case
letters, elements with lower-case le
Subscript and Summation
Notation
James H. Steiger
Single Subscript Notation
Most of the calculations we perform in
statistics are repetitive operations on lists of
numbers. For example, we compute the
sum of a set of numbers, or the sum of the
squares of
Introduction
Threats to Internal Validity
Threats to External Validity
Some Basic Threats to Experimental Validity
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James H. Steiger
Some Basic Threats to Experimental Va
Levels of Measurement
James H. Steiger
Measurement
Measurement is the process of assigning
numbers to quantities. The process is so
familiar that perhaps we often overlook its
fundamental characteristics.
Properties of a Quantity
Quantities that we can me
Stories Shape Can Tell
James H. Steiger
Distributional Shape
In earlier lectures, we defined and used a
very useful, but somewhat idiosyncratic
definition of the shape of a list of
numbers.
More commonplace notions involve
evaluating shape by plotting val
Measures of Central Tendency
James H. Steiger
Overview
Optimality properties for measures of
central tendency Two notions of
closeness
Properties of the Median
Properties of the Mean
Optimality Properties
Imagine you were a statistician, confronted
with a
Measures of Variability
James H. Steiger
Overview
Discuss Common Measures of Variability
Range
Semi-Interquartile Range
Variance
Standard Deviation
Derive Computational Formulas for the
Standard Deviation and Variance
Measures of Variability
Several me
Discrete vs. Continuous Variables
Levels of Measurement
A Frequency Distribution Table
The Grouped Frequency Distribution Table
The Frequency Histogram
The Pie Chart
Quantiles
Frequency Distribution Displays
James H. Steiger
Department of Psychology and H
Two Uses for R
Simple Listwise Transformations
Using Functions within Expressions
Dening and Building a Function Library
The Maximum Possible Z -Score
Expected Value of the Maximum
Answering Theoretical Questions with R
James H. Steiger
Department of Psyc
Introduction
The Number Line Diagram
Listwise Operations
Re-Expressing the Information in a List
Eect of Listwise Operations
Exploiting the Vulnerability Box
Properties of Z -Scores
Linear Transformation Rules Revisited
Summary
Whats in a List of Numbers?
Introduction
Dichotomous Decision-Making Under Uncertainty
Statistical Hypothesis Testing
The Z-Statistic
One-Tailed Hypothesis Tests
A Flow Chart for the 1-Sample Test
Statistical Power
A Simplied Approach to Power Calculation
Hypothesis Testing
James H.
Introduction
The Sum of Two Dice Throws
The Sample Mean of Two Dice Throws
Sampling Distributions
Facts about Sampling Distributions
Sampling Distributions
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James H. Stei
Introduction
Set Theory
Probabilistic Experiments and Events
Axioms and Basic Theorems of Probability
Basic Rules for Computing Probability
Joint Events, Conditional Probability, and Independence
Sequences and the Multiplicative Rules
The Keep It Alive St
What is(are) Statistics?
The Role of Statistics in Science
Fundamental Goals of Science
Statistics and the Goals of Science
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
PSY 2101
James H. Steiger
Statistics and the
Approaches to Knowledge
Approaches to Knowledge
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
PSY 2101
James H. Steiger
Approaches to Knowledge
Approaches to Knowledge
Psychology 2101 Introduction
1
Approaches to Kn