|
Week 1
 Basic
Probability
Get Knowledge
through Web Lectures
Make notes (Print
these files. Then take notes on the print-out while reading the Web
Lectures)
Do
homework (Required)
Practice
(Recommended)
As you can see there are four activities available to you for learning
about basic probability. The Day to Day section of the Tutorial has
detailed instructions for working through each of these activities.
Interface
of Science and Statistics
Get
Knowledge through Web Lectures
Make notes
Do homework (None Required)
Practice (Not Available)
There is no homework for this topic. But it is a very important topic
that gives meaning to how statistics fits with scientific thinking.
These ideas will be parts of several required web homeworks as well
as several recommended practice homeworks. These ideas will be tested
on both midterm and final exams.
Week 2
Normal
Distribution
Get
Knowledge by reading Web Lectures
Make notes
Do
homework (Normal Tool is necessary to do the web homework)
Use Normal Tool
Practice (Recommended)
Use of the Normal Tool is necessary to do the required web homework
as well as the recommended practice homework. Instructions for using
the Normal Tools are integrated into the Normal Distribution lecture
(click on Get Knowledge).
Interact
& Integrate
Use
Sample from Normal Tool
Practice (Recommended)
Using the Sample from Normal Tool is really part of the Normal Distribution
topic, but it requires some thoughtful integration of ideas. The Sample
from Normal Tool allows you to take random samples from a normal probability
distribution. Every sample is different, so every student gets different
data and consequently different answers. So there is no "correct"
answer. Do not look for an answer key; there is none. What is important
is to understand the concept.
You can get to practice problems two ways. First, when you click on
"Use Sample from Normal Tool" and the tool opens up, scroll
down the page and you will see three problems. The same three problems
are available by clicking on "Practice."
We highly recommend collaborating with other students as you learn
about sampling and samples. Use e-mail, the Discussion Forum, or Live
Chat with Drawing Board.
It is very important to give your self EXPERIENCE with sampling, since
the process of sampling is crucial to understanding many statistical
concepts that we will cover. It's not particularly hard to understand,
all you need to do is have some experience with sampling. Come back
and play with the Sample from Normal Tool later in the class to reinforce
these ideas when we are using them.
Binomial
Distribution
Get
Knowledge
Make notes
Do homework (Binomial tool necessary to do web homework)
Use Binomial Tool
Normal Tool (Normal Tool is used
for a few problems in Binomial HW)
Practice (Recommended)
The Normal Tool is also used for a few problems in the Binomial Homework
by way of review.
Note (If you have trouble manipulating windows). To do
Binomial Homework, we recommend the following procedure. First
click on "Do Homework" on the list above to open the Web Homework.
Select Binomial Distribution from the web homework menu. Second,
click on "Use Binomial Tool," above. Two pages open--the tool
itself (pale yellow) and a web page (brown, with the StatCenter symbol).
Use the Binomial Tool to do all the Web Homework problems asking about
the binomial distribution. Third, when you get to homework problems
that ask you about the Normal Distribution, click "Back" on
the (brown) binomial web page. Ducks in a Row will appear in its place.
Fourth, click on "Normal Tool" in the above list. Again
two pages open--the normal tool itself and a (brown) web page. Use the
Normal Tool to complete the web homework. Submit the homework. Click
"Back" to see Ducks in Row again. (On small screens you may
have to minimize windows during the above procedure to see the homework
and tools clearly.)
We will use the Binomial distribution as a foundation for important
ideas later; so it is important to start learning about it. Do the homework;
it will guide toward making important conclusions, But, since the Binomial
Tool is interactive, you can play around with it, making your own discoveries
and getting your own sense of the Binomial distribution. When playing
change N and p. Change between probability inside and probability outside.
Just follow your curiosity long enough to be familiar with how the Binomial
works.
Week 3
Central
Tendency
Get Knowledge
Make notes
Do
homework
Practice (Recommended)
StatTool (optional)
StatTool Tutorial
Up to this point we have been developing a lot of theory. Now you'll
start learning some statistics. We'll come back and use the theory after
a while, when you've had time to digest it.
We are also introducing a new feature: StatTool. We highly recommend
your using StatTool, even though we are not grading you for it's use.
(But when you check your homework, you will notice that using StatTool
will give you either 1 or 2 points so that you and the instructor can
keep track of StatTool use.)
StatTool is a simple statistical analysis program that let's analyze
data using most of the statistics you will learn in this course. Most
scientific data analysis is done by computers, so it's good to learn
how to use a data analysis program. You will need to be familiar with
StatTool later in the course when you do research in Virtual Lab. The
data from your Virtual Lab experiments are automatically sent to StatTool
so that you can analyze them.
StatTool is explained briefly in the Practice Homework for Central
Tendency. It will calculate the correct answers for the Central Tendency
Practice Homework problems that require calculation.
Variability
Get Knowledge
Make notes
Do
variability homework
Do standard scores
homework
Practice (Recommended)
StatTool (optional)
Central Tendency (the Mean, the Median, and the Mode) are pretty straightforward.
Things get a little more complicate as learn about how to measure and
describe how "spread out" a group of numbers are.
Interact
& Integrate
Double
Sample and Detect Difference Lecture
Make Notes for Detect Difference & Double
Sample
Use double sample
tool
The Double Sample Tool allows you to set up two Normal Distributions,
one red and one green. You can make them as close together or as far
apart by changing each of their mu's. You can make them as compact or
spread out as you want by changing their sigma's. Then you can sample
from both of them simultaneously. You get descriptive statistics for
each sample. If you pay attention to the data in the two samples you
gain invaluable experience about how differences in data sets indicate
differences in populations.
The Detect Difference & Double Sample lecture is one of the most
important lectures in this course as far as gaining a deep understanding
of the meaning of the statistics. Please read it carefully and make
good notes. Understanding this material will make later parts of
the course much easier.
When you click on "Use double sample tool" a menu comes up.
Just click on "Double Sample" to use the tool.
Below tool's menu are two problems (scroll down). Problem 1 gives you
a structured experience with the Double Sample Tool. But it is important
to play around and interact with the tool, making your own conclusions.
Come back to this tool when we are learning about a t-test for independent
means later; this tool will give you insight into that statistic
Get
Experience for later theory
Play
Detect Difference
Detect Difference Tutorial
Detect Difference simulates the basic puzzle faced by scientists when
they do a two group study. Suppose a scientist has two groups of volunteer
participants. S/he gives one group a placebo and the other group a newly
developed chemical that might lower blood pressure. No one knows if
it lowers blood pressure or not; that's why the scientist is doing research--to
find out. At the end of the study s/he has two samples of numbers, one
sample from each group.
S/he looks at the numbers. If the new chemical is ineffective (as most
are) then what s/he is looking at is two samples drawn from the same
population. If the new chemical is effective at lowering blood pressure
then the two samples are drawn from two different populations. (That
is, if the chemical works, then the group which received the chemical
is a sample from a population of people with low blood pressure--and
the placebo group is a sample from a population with high blood pressure.)
S/he looks at the two sets of numbers. S/he has to decide whether these
two samples lead to the conclusion that there are two populations (the
chemical is effective) or that there is only one population (the chemical
is ineffective).
This game puts you into that scientific puzzle. You have the data.
Do you conclude there is one population or two populations? That's the
essence of a deep and common scientific puzzle.
If you play around you will notice that there buttons with little labels
like "t=", "M", "SD", and "SEM".
These are statistics that you've not learned about. But if you press
the buttons you get the statistics even if you don't know what they
mean. You can press the buttons or not. If you do you may notice they
are useful to you are not. Probably the mean (M) will be useful. Either
way (whether the stats make sense or not) it's ok. You're just gaining
experience with a scientific thinking puzzle.
Of course, how well you do is recorded and counts toward your course
grade.
Week 4
Correlation
Get Knowledge
Make notes
Do
correlation concepts homework
Do correlation calculations homework
Practice (Recommended)
StatTool (optional)
In Central Tendency and Variability we focused on a single variable.
With correlation we begin to think about how two variables relate to
each other.
Regression
(begin)
Get Knowledge
Make notes
Do
linear functions homework
Do regression homework
Regression takes the ideas developed in the Correlation Lecture and
refines them.
Week 5
Interactions
Get
Knowledge
Do
Interactions homework
This lecture begins to look at cases where we are interested in how
two IV's affect a DV.
Regression (finish)
Do regression
variance homework
Practice (Recommended)
StatTool (optional)
In the second part of the Regression Lecture you will learn about prediction
errors, prediction error variance, and the idea of least squared error.
These are important and deep concepts which underlie the philosophy
of statistics. Consequently they are a bit harder to learn. Expect that
it is normal to have to study this material over a few times to get
a good sense of it.
Interact
and Integrate: Virtual Lab, Assignment #1
Get Knowledge: Virtual Lab
Tutorial
Make Notes (No Notes are available for this material)
Do Virtual Lab Assignment #1
Do Homework (Homework is built into Virtual Lab: No other homework)
Virtual Lab is a highly innovative program that lets you simulate the
whole scientific problem solving process from theories and hypotheses
to designing research studies to collecting and analyzing data to making
conclusions and writing up reports.
This is Assignment #1 for Virtual Labs. Please choose only Bot
Research Volume 4: "Explorations"
as
your book to read for Assignment #1. Also, you must do three different
research projects (Chapters) to complete Assignment #1. Read "Get
Knowledge: Virtual Lab Tutorial" for more details.
Gain
Experience for future theory
Play Difference
to Inference
Get
Knowledge: Difference to Inference Tutorial
"Difference to Inference" is a game that brings together
many threads of learning that you've encountered up to this point. More
importantly, it provides you will experiences that will greatly help
in understanding theoretical concepts that we will develop later. "Difference
to Inference" builds on your experience with "Double Sample"
and "Detect Difference." It gives you an opportunity to use
Sample Data drawn from Normal Distributions to make Scientific Inferences
about which of several theories is the most scientifically viable.
Difference to Inference Grade: At this time your assignment
is to play the EASY and the MEDIUM levels of the Difference to Inference
Game. (Later, after we learn about t-tests, you will be required to
play the HARD level.) You must earn 2000 or more Grant Bucks on each
game level (Easy or Medium) to get to get a grade of 100%. If you get
less than 2000 grant bucks, your grade will be the percentage of 2000
that you earn. If you get more than 2000 grant bucks, you still only
get 100%. But there is a list of the top 10 researchers in the class
available to look at; so there is prestige (such as it is) attached
to earning more grant bucks.
Week 6
Sampling
Distributions
Get
Knowledge
Make
notes
Do
Binomial Sampling Distribution homework
Do Sampling Distribution of the Mean homework
Use Sampling Distribution of the
Mean Tool
Practice (Recommended)
Sampling Distributions are a pivotal concept in the true understanding
of statistical theory. The lectures, homeworks, and tools developed
for this course are holistically integrated to provide you with the
direct kind of experiences that enable you to understand these elusive
ideas.
Estimating
population parameters
Get Knowledge
Make notes
Do estimating parameters homework
Practice (Recommended)
We have established the distinction between populations and samples.
In the mathematical-statistical model, that data we collect in a research
is a sample from a probability distribution (which is called a population).
We are now going to learn how to make guesses (estimates) about the
parameters of a populations from sample data.
You have now completed all the material tested on the midterm exam.
You should continue to learn new material at the beginning of Week7.
This new material will not be covered on the Midterm but it is crucial
that you keep up with the pace of the course.
Online Students: Sign up for Midterm Exams.
Week 7
Midterm
Exam Form 1
Online: Register for Section 90 Midterm Exam Form 1
Sign up for
Midterm Exam Form 1NOW!
The links listed above allow you to sign up for midterm exams.
Classroom: Midterm Form 1 will given in the regular classroom
on the date listed in the syllabus.
Keep working on the new material listed for Week 7 as you
study for the Midterm.
Statistical
Conclusion Validity & Hypothesis Testing
Get Knowledge
Make notes
Do
Statistical Conclusion Validity--Coins homework
Do Statistical Conclusion Validity--Vaccine homework
Practice (Recommended)
Hypothesis Testing is a set of concepts in the formal mathematical-statistical
model. Statistical Conclusion Validity is a logical issue in the philosophy
of science and research methods. Statistical Conclusion Validity deals
with the question, "Could my results (data) have occurred by chance
alone?" Scientists use the formal mathematical model to evaluate
the role of chance in determining the outcome of their research.
Week 8
t
for independent means
Get Knowledge
Make notes
Do t for independent means homework
Practice (Recommended)
StatTool (optional)
In the Sampling Distributions, Estimating Parameters, and Hypothesis
Testing Lectures we laid out the theoretical foundations of inferential
statistics. The t-independent Lecture develops a powerful inferential
statistic with wide applicability.
t
for correlated means
Get Knowledge
Make notes
Do t for correlated means homework
Practice (Recommended)
StatTool (optional)
The t-correlated Lecture continues the development of common uses of
the the t statistic. It also introduces an important measurement distinction--are
the measures independent of each other or are they correlated with each
other? Consider one simple example. Suppose you are evaluating the effectiveness
of a Psychotherapy. Case #1: You could have two (independent) groups
of participants. One group would receive Psychotherapy and then be measured
for mental health. The other group would receive a Placebo Control and
then be measured for mental health. In other words, you have two groups,
and each group is measured only once. In contrast is Case #2. You could
have only one group of participants and measure them twice for mental
health, once before Psychotherapy and once after Psychotherapy. Case
#1 has two groups, each measured once. Case #2 has one group, measured
twice. The measurements in Case #1 are consdered independent and the
appropriate t-test is t-independent. The measurements in Case #2 are
correlated with each other and the appropriate t-test is t-correlated.
There is more to say on this matter, and you will find a more extensive
discussion in the t-correlated Lecture.
Quiz
1.
The first of two online quizzes will be offered during week 8. See
the syllabus for details. The format for quizzes will differ for classroom
and online students. Classroom students will be informed about quiz
format during their labs.
Online students: A Quiz will be just like the web homework you
have been doing. When you are doing a quiz it will look identical to
web homework. But you will not receive the correct answers nor feedback
on how to do the problem on quizzes. (You will see the thumbs up or
thumbs down symbol, so you will know immediately if you were correct
or not.) You will be allowed to do a quiz only in a given three day
window (whereas homeworks can be done over long periods of time). A
quiz grade will count much more toward your course grade than does a
homework (see syllabus). During the three day window, you will be allowed
to take the same quiz over as many times as you want. Your quiz score
will be immediately reported below your other web homework grades. So
you should be able to get %100.
All students. The purpose of the quizzes is to test your ability
to use online tools and games. (We cannot test those parts of the class
on the midterm and final because there are next to no testing centers
that have computers available for so many people.) So take the quizzes
in the same way you do for web homework, using your usual computer.
Expect Quiz 1 to focus on questions about the Normal Tool, the Binomial
Tool, the Sample from Normal Tool, the Double Sample Tool, and the Detect
Difference Game. You should also be able to answer questions from the
Estimating Paramters and Sampling Distributions web homeworks.
The quizzes should be straightforward and simple if you have been using
the tools and games and have been doing your homework. Our goal is to
get you to focus on the ideas and learn them well (not to penalize you
for making a mistake).
Online
Students--Take Quiz 1 (This
link takes you to the web homework. The quiz won't be there until Thursday,
Friday, and Saturday of Week 8.)
Use Normal Tool
Use Binomial Tool
Use Sampling Distribution of the
Mean Tool
Week 9
t
for a single mean
Get
Knowledge
Make notes
Do t for a single mean homework
Practice (Recommended)
The t-for a single mean is not very commonly used. It allows you to
evaluate the probability that a single sample mean is different from
some arbitrary number by chance alone.
t
for r
Get Knowledge
Make notes
Do t for r homework
Practice (Recommended)
StatTool (optional)
The t for r allows you evaluate whether a correlation coefficient (r)
is significantly different than 0.
Midterm
Form 2
Midterm Form 2 is optionally available at the end of Week 9. Take Form
2 only if you want to improve your grade. If you take both forms you
will automatically receive the higher of the two grades.
Online students: (optional) Register for Section 90 Midterm
Exam Form 2
Sign up for Midterm
Exam Form 2
Classroom: The second form will be offered in the classroom
at the normal time on the date listed in the syllabus.
Week 10
t
for b
Get Knowledge
Make notes
Do t for b homework
Practice (Recommended)
StatTool (optional)
The t for b statistic allows you to evaluate whether or not a regression
slope (b) is significantly different than 0. The t for b and the t for
r tests are formally the same test. If calculated on the same data,
they will give you the same value.
Interact
and Integrate
Use Virtual Lab
Virtual Lab Assignment #2: In the first Virtual Lab assignment
you only used descriptive statistics. Now you have learned enough to
do a more sophisticated Virtual Lab assignment. This assignment will
allow you to practice using all the t-tests in an open-ended context.
You will have to decide which of the t-tests to use and demonstrate
your ability to use them properly. You will also be required to make
statistical conclusions about the "significance" (statistical
conclusion validity) of your results. The most difficult discrimination
is when to use t-independent versus t-correlated. In fact, one of the
motivating reasons for developing Virtual Lab was because students demanded
lots of open-ended practice in telling when to use t-correlated and
when to use t-independent so they would be ready for the test and so
they would really understand the research issue involved. Please read
only Bot Res Vol 5 for this assignment.
You must do three research puzzles from Bot Res Vol 5. (It is good practice
for the final exam to do more puzzles; but only three count for a grade.)
StatTool. StatTool is a simple online data analysis program.
You may want to use it for Virtual Lab Assignment #2 because the data
you get in lab will require you to report correlations, regression lines,
and t-tests. The data from the Virtual Lab is automatically
imported into StatTool where the computer will do all the
analyses for you. So use StatTool unless you want to do the analyses
by hand.
Getting to StatTool. Once you have collected data in Virtual
lab, just close the data clipboard and you will see a button that says
"stat tool." Press that button. A page will come up (sometimes
slowly) with an overview of instructions for using StatTool on it. It
also has a large "Analyze Data" button. Look over (or print)
the instructions and then press "Analyze Data." You will see
a pale yellow "Raw Data" window with your Virtual Lab data
in it. Next to the raw data window is a blank white "Statistical
Results" window; later, when you do a data analysis the results
of you statistical analysis will appear in this white window. Both the
white and the pale yellow windows can be resized in case all the data
or all the statistical results don't fit the default window sizes.
Analyzing Data with StatTool. At the top of the pale yellow
raw data window is a series of menus (File, Des Stat, Cor Stat, Exp-Inf
Stat, Cor-Inf Stat, Graph). The File menu has the data for all the Practice
Homeworks. The Des Stat menu has descriptive statistics such as mean,
standard deviation, variance and z scores. The Cor-Stat menu has correlation
and regression statistics. The Exp-Inf Stat menu has the statistical
analyses used in experimental research such as t and F. The Cor-Inf
Stat menu has statistical analyses for correlation and regression. The
Graph menu will graph your data for you.
Take notes. Take notes on the statistical results that appear
in the white Statistical Results window. These will not import back
into Virtual Lab. So you will need to jot down the analyses so that
you can use them when you make a conclusion for your Virtual Lab research
project.
Chi-squared
Goodness of Fit
Get Knowledge
Make notes
Chi-Square Goodness of Fit homework (Web Homework not available)
Practice (Recommended)
Here we introduce another common and useful inferential statistic.
Chi-Square in widely used to evaluate the PCH of Chance when we have
categorical frequency data. Therefore, in this lecture, we introduce
an important distinction--the difference between measurement data and
frequency data.
Chi-squared
Test of Association
We are skipping the second chi-square to that you will have sufficient
time to study and learn the one-way ANOVA lecture before the final exam.
The one-way ANOVA is the longest, most complicated topic in the course.
So we highly recommend that you get started studying ANOVA right
away.
Get
Knowledge
Make notes
Do Chi-square Association homework
Practice (Recommended)
StatTool (optional)
The Chi-Square Test of Association allows you to determine if there
is a significant relationship between two categories such as Politcal
Party Affiliation and Enviromental Attitudes.
Week 11
Degrees
of Freedom
Get Knowledge
Make notes
Do Degrees of Freedom homework
Practice (Not Available)
The Degrees of Freedom Lecture examines the theoretical meaning of
the degrees of freedom concept in some rigor using the binomial distribution
and the Binomial Tool. Up to this point we have gained experience in
the t and Chi-Square lectures and in Virtual Lab with the practical
importance of degrees of freedom when using inferential statistics.
Building on that experience base, we now turn back to a theoretical
examination of the binomial distribution to see how changing the number
of observations does indeed change the shape of the sampling distribution
of the test statistic.
One of the great insights that Gosset (Student) had when he invented
the t-distribution was the first really clever use of degrees of freedom.
Interact
and Integrate
Use Virtual Lab
Virtual Lab Assignment #3. This assignment continues your
experiences with learning to use statistics in applied settings. In
Assignment #3, you now will have to discriminate when to use statistics
appropriate for measurement data (t-tests) from those appropriate
for categorical frequency data (chi-square).
Week 12
One
way ANOVA independent measures
Get Knowledge
Make notes
Do 1-ANOVA Independent homework
Practice (Recommended)
StatTool (optaional)
Visual ANOVA
People speak of "one-way" or "one-factor" ANOVA's.
ANOVA is short or "Analysis of Variance." "One-factor"
or "one-way" simply mean "one independent variable."
ANOVA is a very flexible system that can analyze many IV's at once,
We begin with the simplest case: The one-way ANOVA for independent groups.
The one factor Analysis of Variance (ANOVA) for independent groups
extends the t-independent statistical procedure from two groups to any
number of groups.
Week 13
One
way ANOVA Correlated DV measures
Get Knowledge
Make notes
Do 1-ANOVA Correlated homework
Practice (Recommended)
StatTool (optional)
The one-factor ANOVA for correlated DV measures generalizes the t for
correlated means from two groups to any number of groups.
Two
way ANOVA
Get Knowledge
Make notes
Do 2-ANOVA Independent homework
Practice (Recommended)
StatTool (optional)
The two way ANOVA for independent groups allows us to analyze research
projects that manipulate two IV's at the same time.
An important new concept introduced in these lectures is the idea of
an interaction between two IV's.
Week 14
Continue to work on the material two-way ANOVA for independent groups.
Especially focus on the concept of interaction.
Interact
and Integrate
Use Virtual Lab
Virtual Lab Assignment #4 requires that you solve research puzzles
that might require any of the statistics learned throughout the course.
TAKE
QUIZ 2
Classroom students take quiz 2 in lab.
Online students--Take
Quiz 2. (Available only Thursday through Saturday of Week 14)
Use Normal Tool
Use Binomial Tool
Use Sampling Distribution of the
Mean Tool
Quiz 2 , like Quiz 1, will be very much like a web homework. It will
cover material from Sampling Distributions, Estimating Parameters,
and Hypothesis Testing (Statistical Conclusion Validity). It will
cover Degrees of Freedom, only if that topic has been covered in the
course. It may also ask you to do a Virtual Lab research project or
play the Difference to Inference game. In other words, it is designed
to test your competency with computer-based, online learning tools
which cannot be tested in the hand written exams.
Interact
and Integrate
Use Virtual Lab
Virtual Lab Assignment #4. This assignment completes your
experiences with learning to use statistics in applied settings. In
Assignment #4, you now will have to discriminate when to use statistics
appropriate for all contexts we have learned about in this course.
Week 15
Review and prepare for the exam. Complete all coursework.
Online: Register for Section 90 Final Exam Form 1
Sign up for Final
Exam Form 1
Classroom: Final Form 1 will be offered in the classroom in
the normal classroom at the normal time on the date listed in the syllabus.
Final
Exam Week
Final Exam Form 2 (Optional)
Online: Register for Section 90 Final Exam Form 2
Sign up for
Final Exam Form 2
Classroom: Final Form 1 will be given in the classroom on
the date listed in the syllabus.
|
