Download Math 108 Introduction to Statistics

Math 108 Introduction to Statistics
Fall 2016
Instructor:
Dr. Jeff Graham
Office:
Fisher 312
Office Hours: MW 3 - 4, TTH 10 – 11, or by appointment
Email:
[email protected]
Phone:
372-4467
Text:
Tokunaga
Fundamentals of Statistics for the Social and Behavioral Sciences by Howard
Grading
There will be two exams and a comprehensive final exam. Each exam will be worth 15% of your grade
and the final will be worth 20%. There will also be roughly weekly quizzes which will total to 25% of your
grade. There will be several projects, maybe 3-5, that will use the computer program SPSS or something
similar. These assignments will make up the other 25% of your grade. I will start with a ten point
grading scale, the 90 - 100 A, 80 - 89 B, 70 - 79 C, 60 - 69 D, and 59 on down is an F. These levels are
guaranteed not to go up. Your final grade may vary from this scale, but only to your advantage. For
example, you may end up with an 89 average and receive an A, A-, B+, or a B depending on your
individual performance and the overall class performance. For example, your grade might move up if
your final exam score is much higher than your average grade for the course. In general, I will try to give
you the grade that I think best reflects your performance in the class, but it will never be lower than
your average grade would indicate.
How to get a good grade in this class
Most classes I will assign homework and mostly I will not pick it up. You might be tempted to not do it,
but if you want to get a good grade in this class, you should do the homework. All the grades you earn
in the class will be based on your completing the home work. The quizzes will be based on the
homework, each of the exams is based on the quizzes, and the final is based on the exams. It all builds
from the homework, so you should do it.
Most classes, I leave time available for talking about the homework. If no one has questions I assume
there are no problems and I will cover more material.
General Policies
The university policies on attendance and cheating as described in the student handbook will be
followed. A quick summary: Come to class and don’t cheat.
Learning Goals
These sound a little intimidating, but they boil down to learning some math and how to use it.
1. Abstract a problem into a symbolic or mathematical model or framework.
Statistics is a mathematical framework for collecting, organizing, and interpreting data. There
are three main topics in our introductory statistics class; descriptive statistics, probability, and
inferential statistics. A statistical study involves identifying a question, designing a method of
collecting meaningful data, analyzing, and drawing sound conclusions from this analysis. A
typical statistics class would spend at least some time on each of these steps.
2. Interpret such a model in terms of a real world construct.
Statistics texts are very big on this topic. Every text has numerous examples drawn from the
natural and social sciences, engineering, medicine and many other fields of study. Students in a
statistic class will learn to take the information from the problem, perform appropriate
calculations, draw conclusions from the calculations and interpret the results in the original
context.
3. Reason from precisely stated principles using deductive methods and draw valid
conclusions.
Probability theory starts with axioms, and so this section of the course involves reasoning from
those axioms. For example, given information about a population, we ask students to determine
the probability a random sample will turn out a certain way. Hypothesis testing and related
topics (Type I, II errors and the like) are also examples of deductive reasoning. A highly simplified
version of the typical hypothesis test is as follows: given a hypothesis to test, calculate a test
statistic from a data sample, and based on the value of this test statistic the student decides
whether or not to reject the hypothesis. This glosses over the reasoning needed to choose the
appropriate test statistic, but it is a prime example of deductive reasoning in this course.
4. Recognize, manipulate and reason from or about abstract patterns.
Mathematics is the science of patterns and so every course we teach is really all about
recognizing, manipulating, and reasoning from patterns. In statistics, descriptive statistics and
regression are all about identifying patterns. For example, the main goal of descriptive statistics
is to attempt to identify information about the distribution of a set of data. Is it skewed? Is it
symmetric? Are there outliers? Does it look normally distributed? Linear regression tries to
determine the strength of a linear relationship between two variables. For both of these topics,
one generally starts with a plot of the data to help identify any obvious features.
A Rough Outline of the Course
1.
2.
3.
4.
5.
Descriptive Statistics (Chapters 1 - 5)
Hypothesis Testing (Chapters 6 – 10)
ANOVA (Chapters 11 – 12)
Regression (Chapter 13), plus some supplemental material on multiple regression
Categorical Data and Chi Square (Chapter 14)