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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 (Not Available)
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 and 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 (Not Available)
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 (Not Available)
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 (Not Available)
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.
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
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.
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.
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