17. Chi Square
A. Chi Square Distribution
B. One-Way Tables
C. Contingency Tables
D. Exercises
Chi Square is a distribution that has proven to be particularly useful in statistics.
The rst section describes the basics of this distribution. The following t
13. Power
A. Introduction
B. Example Calculations
C. Factors Affecting Power
D. Exercises
434
Introduction to Power
by David M. Lane
Prerequisites
Chapter 11: Signicance Testing
Chapter 11: Type I and Type II Errors
Chapter 11: Misconceptions
Learning
12. Testing Means
A.
B.
C.
D.
E.
F.
G.
H.
Single Mean
Difference between Two Means (Independent Groups)
All Pairwise Comparisons Among Means
Specic Comparisons
Difference between Two Means (Correlated Pairs)
Specic Comparisons (Correlated Observations)
Pa
9. Sampling Distributions
Prerequisites
none
A.
B.
C.
D.
E.
F.
Introduction
Sampling Distribution of the Mean
Sampling Distribution of Difference Between Means
Sampling Distribution of Pearson's r
Sampling Distribution of a Proportion
Exercises
The conce
11. Logic of Hypothesis Testing
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Introduction
Signicance Testing
Type I and Type II Errors
One- and Two-Tailed Tests
Interpreting Signicant Results
Interpreting Non-Signicant Results
Steps in Hypothesis Testing
Signicance Test
6.4
Factoring - Trinomials where a
1
Objective: Factor trinomials using the ac method when the coecient
of x2 is not one.
When factoring trinomials we used the ac method to split the middle term and
then factor by grouping. The ac method gets its name fro
2.1
Graphs - Points and Lines
Often, to get an idea of the behavior of an equation we will make a picture that
represents the solutions to the equations. A graph is simplify a picture of the
solutions to an equation. Before we spend much time on making a
2.5
Graphing - Parallel and Perpendicular Lines
Objective: Identify the equation of a line given a parallel or perpendicular line.
There is an interesting connection between the slope of lines that are parallel and
the slope of lines that are perpendicula
2.2
Graphing - Slope
Objective: Find the slope of a line given a graph or two points.
As we graph lines, we will want to be able to identify dierent properties of the
lines we graph. One of the most important properties of a line is its slope. Slope
is a
6.1
Factoring - Greatest Common Factor
Objective: Find the greatest common factor of a polynomial and factor
it out of the expression.
The opposite of multiplying polynomials together is factoring polynomials. There
are many benits of a polynomial being f
6.3
Factoring - Trinomials where a = 1
Objective: Factor trinomials where the coecient of x2 is one.
Factoring with three terms, or trinomials, is the most important type of factoring
to be able to master. As factoring is multiplication backwards we will
2.3
Graphing - Slope-Intercept Form
Objective: Give the equation of a line with a known slope and y-intercept.
When graphing a line we found one method we could use is to make a table of
values. However, if we can identify some properties of the line, we
3.1
Inequalities - Graphing and Solving
When we have an equation such as x = 4 we have a specic value for our variable.
With inequalities we will give a range of values for our variable. To do this we
will not use equals, but one of the following symbols:
8.8
Radicals - Complex Numbers
Objective: Add, subtract, multiply, rationalize, and simplify expressions using complex numbers.
World View Note: When mathematics was rst used, the primary purpose was
for counting. Thus they did not originally use negative
6.2
Factoring - Grouping
Objective: Factor polynomials with four terms using grouping.
The rst thing we will always do when factoring is try to factor out a GCF. This
GCF is often a monomial like in the problem 5x y + 10xz the GCF is the monomial 5x, so w
8.1
Radicals - Square Roots
Objective: Simplify expressions with square roots.
Square roots are the most common type of radical used. A square root unsquares a number. For example, because 52 = 25 we say the square root of 25 is 5.
The square root of 25 i
8.2
Radicals - Higher Roots
Objective: Simplify radicals with an index greater than two.
While square roots are the most common type of radical we work with, we can
take higher roots of numbers as well: cube roots, fourth roots, fth roots, etc. Following
2.4
Graphing - Point-Slope Form
Objective: Give the equation of a line with a known slope and point.
The slope-intercept form has the advantage of being simple to remember and use,
however, it has one major disadvantage: we must know the y-intercept in or
10.6
Functions - Logarithms
The inverse of an exponential function is a new function known as a logarithm.
Lograithms are studied in detail in advanced algebra, here we will take an introductory look at how logarithms works. When working with radicals we
10.6
Functions - Compound Interest
Objective: Calculate nal account balances using the formulas for compound and continuous interest.
An application of exponential functions is compound interest. When money is
invested in an account (or given out on loan)
9.11
Quadratics - Graphs of Quadratics
Objective: Graph quadratic equations using the vertex, x-intercepts,
and y-intercept.
Just as we drew pictures of the solutions for lines or linear equations, we can draw
a picture of solution to quadratics as well.
9.7
Quadratics - Rectangles
Objective: Solve applications of quadratic equations using rectangles.
An application of solving quadratic equations comes from the formula for the area
of a rectangle. The area of a rectangle can be calculated by multiplying t
10.1
Functions - Function Notation
Objective: Identy functions and use correct notation to evaluate functions at numerical and variable values.
There are many dierent types of equations that we can work with in algebra. An
equation gives the relationship
9.2
Quadratics - Solving with Exponents
Another type of equation we can solve is one with exponents. As you might
expect we can clear exponents by using roots. This is done with very few unexpected results with the exponent is odd. We solve these problems
9.4
Quadratics - Quadratic Formula
Objective: Solve quadratic equations by using the quadratic formula.
The general from of a quadratic is ax2 + bx + c = 0. We will now solve this formula for x by completing the square
Example 1.
ax2 + bc + c = 0
cc
2
ax
9.3
Quadratics - Complete the Square
Objective: Solve quadratic equations by completing the square.
When solving quadratic equations in the past we have used factoring to solve for
our variable. This is exactly what is done in the next example.
Example 1.
8. Advanced Graphs
A. Q-Q Plots
B. Contour Plots
C. 3D Plots
264
Quantile-Quantile (q-q) Plots
by David Scott
Prerequisites
Chapter 1: Distributions
Chapter 1: Percentiles
Chapter 2: Histograms
Chapter 4: Introduction to Bivariate Data
Chapter 7: Int
16. Transformations
A. Log
B. Tukey's Ladder of Powers
C. Box-Cox Transformations
D. Exercises
The focus of statistics courses is the exposition of appropriate methodology to
analyze data to answer the question at hand. Sometimes the data are given to you
15. Analysis of Variance
A. Introduction
B. ANOVA Designs
C. One-Factor ANOVA (Between-Subjects)
D. Multi-Factor ANOVA (Between-Subjects)
E. Unequal Sample Sizes
F. Tests Supplementing ANOVA
G. Within-Subjects ANOVA
499
Introduction
by David M. Lane
Prere
18. Distribution-Free Tests
by David M. Lane
A. Benets of Distribution-Free Tests
B. Randomization Tests
1. Two Means
2. Two or More Means
3. Randomization Tests: Association (Pearson's r)
4. Contingency Tables (Fisher's Exact Test)
C. Rank Randomization