Introduction to Statistics

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.

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 | Current Score: N/A
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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. (1) Click on "Do Homework" on the list above to open the Web Homework. Select Binomial Distribution from the web homework menu. (2) 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. (3) 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. (4) 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 bout 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.

Central Tendency | Current Score: N/A
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Do homework
Practice (Recommended)

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.

Variability | Current Score: N/A
Standard Scores | Current Score: N/A
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Do variability homework
Do standard scores homework
Practice (Recommended)

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 (Can be played multiple times)
Get Knowledge: 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.

Correlation (Concepts) | Current Score: N/A
Correlation (Calculations) | Current Score: N/A
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Do correlation concepts homework
Do correlation calculations homework
Practice (Recommended)

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.

Linear Functions | Current Score: N/A
Regression | Current Score: N/A
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Do linear functions homework
Do regression homework

Regression takes the ideas developed in the Correlation Lecture and refines them.

Interactions | Current Score: 1%
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Do Interactions homework

This lecture begins to look at ca ses where we are interested in how two IV's affect a DV.

Regression Variance | Current Score: N/A
Do regression variance homework
Practice (Recommended)

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
               Virtual Lab, Assignment #1 Chapter #1: | Current Score: N/A
               Virtual Lab, Assignment #1 Chapter #2: | Current Score: N/A
                Virtual Lab, Assignment #1 Chapter #3: | Current Score: N/A
Get Knowledge: Virtual Lab Tutorial
Make Notes (Not Available)
Do Virtual Lab Assignment #1 (Three Chapters Required, Each Lab can be repeated multiple times)
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 Volume 4: "Explorations" as your book to read for Assignment #1. Also, you must do three (3) 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 (Can be played multiple times)

"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.

Sampling Distributions | Current Score: N/A
Sampling Distributions of the Mean | Current Score: N/A
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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 | Current Score: N/A

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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 the next week. 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.

Midterm Exam Form 1 | Current Score: N/A

Online: Register for Section 90 Midterm Exam Form 1

You are required to make arrangements to find and coordinate with an approved proctor (a university or college testing center) to administrate your exam(s). To take an exam, you will need to submit an Exam Request Form through the Distance Education office. Keep in mind that this coordination between Distance Education and your approved proctor could take time, so proper planning is essential. In addition, there are costs associated with proctors and amounts vary depending on the institution. If you have any questions regarding exams, including approved proctors, please contact the Distance Education office at (800) 467-8839 or email at distance@aoce.utah.edu.

NOTE: You must pass the final exam in order to pass the course. If you fail this exam you will fail the course. This is a requirement of all U of U Distance Education courses.

Sign up for Out are Area Midterm Exam Form 1

Questions and Answers about Distance Education Exams

Keep working on the new material listed for this week as you study for the Midterm.

Statistical Conclusion Validity & Hypothesis Testing (Coins) | Current Score: N/A
Statistical Conclusion Validity & Hypothesis Testing (Vaccine) | Current Score: N/A
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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.

t for independent means | Current Score: N/A
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Do t for independent means homework
Practice (Recommended)

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 | Current Score: N/A
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Do t for correlated means homework
Practice (Recommended)

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.

t for r | Current Score: N/A
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Do t for r homework
Practice (Recommended)

The t for r allows you evaluate whether a correlation coefficient (r) is significantly different than 0.

Midterm Form 2 | Current Score: N/A
Midterm Form 2 is optionally available at the end of this week. 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

You are required to make arrangements to find and coordinate with an approved proctor (a university or college testing center) to administrate your exam(s). To take an exam, you will need to submit an Exam Request Form through the Distance Education office. Keep in mind that this coordination between Distance Education and your approved proctor could take time, so proper planning is essential. In addition, there are costs associated with proctors and amounts vary depending on the institution. If you have any questions regarding exams, including approved proctors, please contact the Distance Education office at (800) 467-8839 or email at distance@aoce.utah.edu.

NOTE: You must pass the final exam in order to pass the course. If you fail this exam you will fail the course. This is a requirement of all U of U Distance Education courses.

Sign up for Out of Area Midterm Exam Form 2
Questions and Answers about Distance Education Exams

t for b | Current Score: N/A
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Do t for b homework
Practice (Recommended)

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 (Three Chapters Required, Each Lab can be repeated multiple times)

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 Volume 5 for this assignment. You must do three (3) research puzzles from Volume 5. (It is good practice for the final exam to do more puzzles; but only three count for a grade.)

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.

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
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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 | Current Score: N/A
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Do Chi-square Association homework
Practice (Recommended)

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.

One way ANOVA independent measures | Current Score: N/A

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Do 1-ANOVA Independent homework
Practice (Recommended)
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.

One way ANOVA Correlated DV measures | Current Score: N/A
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Make notes
Do 1-ANOVA Correlated homework
Practice (Recommended)

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 (Optional, this material will not be on the exam.)
Make notes
Practice (Recommended)

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. Continue to work on the material two-way ANOVA for independent groups. Especially focus on the concept of interaction.

Review and prepare for the exam. Complete all coursework
Online: Register for Final Exam Form 1

You are required to make arrangements to find and coordinate with an approved proctor (a university or college testing center) to administrate your exam(s). To take an exam, you will need to submit an Exam Request Form through the Distance Education office. Keep in mind that this coordination between Distance Education and your approved proctor could take time, so proper planning is essential. In addition, there are costs associated with proctors and amounts vary depending on the institution. If you have any questions regarding exams, including approved proctors, please contact the Distance Education office at (800) 467-8839 or email at distance@aoce.utah.edu.

NOTE: You must pass the final exam in order to pass the course. If you fail this exam you will fail the course. This is a requirement of all U of U Distance Education courses.

Sign up for Out of Area Final Exam Form 1

Questions and Answers about Distance Education Exams

Final Exam Week
Final Exam Form 2 (Optional)

Online: Register for Final Exam Form 2

You are required to make arrangements to find and coordinate with an approved proctor (a university or college testing center) to administrate your exam(s). To take an exam, you will need to submit an Exam Request Form through the Distance Education office. Keep in mind that this coordination between Distance Education and your approved proctor could take time, so proper planning is essential. In addition, there are costs associated with proctors and amounts vary depending on the institution. If you have any questions regarding exams, including approved proctors, please contact the Distance Education office at (800) 467-8839 or email at distance@aoce.utah.edu.

NOTE: You must pass the final exam in order to pass the course. If you fail this exam you will fail the course. This is a requirement of all U of U Distance Education courses.

Sign up for Out of Area Final Exam Form 2

Questions and Answers about Distance Education Exams