Math 146 Introduction to StatisticsMath 146 Online Help

All course materials are available on CANVAS.

There are several excellent sources of online help for math concepts and problems.

Here are some sites:

https://www.khanacademy.org/math/statistics-probability

many short how to do it videos

https://www.wolframalpha.com/examples/mathematics/statistics/

advanced problem solver

http://www.mathsisfun.com/links/curriculum-high-school-statistics.html

organized approach, lots of interactivity

http://www.statsci.org/teaching.html

many pointers to teaching and learning materials

http://www.onlinemathlearning.com/statistics.html

lots of stat videos

https://phet.colorado.edu/en/search?q=statistics

good simulations for a couple of important topics

https://www.homeschoolmath.net/online/statistics.php

plenty of online simulations

Flu and Other Emergencies

This class is set up so that you can continue to make progress on the course

materials even if you cannot make it to class. In such circumstances, you will

probably need to supplement your learning with other resources, such as

— talking with classmates, friends and family

— studying the text book and its video support materials

— using online help

The instructor is always available via email if you have questions or concerns.

Math 146 Introduction to Statistics

Project 1 — Explore Public Data

Project 1 is to explore some of the large online databases. Introductory statistics

has not changed much over the last forty years. What has changed is

1) the accumulation of huge databases of public and private information,

2) public access over the internet to much of this data, and

3) descriptive statistical tools built into web pages for accessing data visually

Your assignment is to

— look at several of the data sources listed below

— choose a particular content area that you are interested in

— learn how to use the display tools in one source to access this data

— prepare a brief report to class members that includes

— the topic you chose to explore

— what you learned

— what surprised you

— the statistical techniques you learned to use

— the questions you have that remained unanswered.

Some public databases with built-in descriptive statistical tools:

Google Public Data

http://www.google.com/publicdata/directory

The U.S. Government’s open data resource

http://www.data.gov/

Similar government open data resources from

England

http://data.gov.uk/

India

http://data.gov.in/

US Census Bureau

https://www.census.gov/data.html

http://www.censusscope.org/

Tableau Public Data

https://public.tableau.com/en-us/gallery

CIA World Facebook

https://www.cia.gov/the-world-factbook/

Federal Health Data

https://www.healthdata.gov/

World Health Organization

https://www.who.int/en/

Math 146 Introduction to Statistics

Project 2 — Using Software Tools

Project 2 is to use a software statistical tool to generate descriptive information about some

data. Your task is to explore and use statistical software. There is some class descriptive

data on Canvas, as well some of the tools have pre-loaded data available, or you can find

interesting real data on the web, or even make up your own. The goal is to find a tool set that you

are comfortable to use for the rest of the course.

We are currently exploring some tools for descriptive data (histograms, scatter plots, etc).

Later we will explore the rest of the available tools, including regression analysis, inferential

statistics, and analysis of distributions. Try out tools that you do not yet understand. Discuss how to

use these tools with others.

You should freely explore all resources. Many of the larger collections of tools have dozens

(hundreds) of specialized tools. Your job is to try to figure out what some of them are doing.

It’s a good idea to work with another person if that is feasible. It’s also a good idea for now to

concentrate on descriptive statistics.

Widely used free statistical tools:

https://www.mathsisfun.com/data/index.html

clear and easy

https://www.makeuseof.com/tag/excel-basic-statistics/

excel spreadsheet

Comprehensive free statistical tools:

https://www.wolframalpha.com/examples/mathematics/statistics/

interactive website

https://www.graphpad.com/quickcalcs/

statistical calculators

https://www.r-project.org/

the R statistical program

http://www.shodor.org/interactivate/lessons/

search: statistics

http://www.sofastatistics.com/home.php

opensource download

Other free options:

applet collection

http://www.rossmanchance.com/applets/index.html

Descriptive Statistics

One proportion inference

support tools

https://www.geogebra.org/search/statistics

Binomial and Normal

Correlation

Statistics Activities

applets

https://onlinestatbook.com/rvls.html

Case Studies

Simulations

https://www.quantitativeskills.com/sisa/

interactive statistical analysis

https://www.danielsoper.com/statcalc/default.aspx

statistics calculators

Bricken

Math 146 Introduction to Statistics

2022

Project 3 — Reading Statistics

Project 3 is to find a technical report or article that includes statistics and describe

the statistics in the article.

The report or article can be a newspaper article, a published technical article, part

of a book, a web page, an online discussion, etc. Any source and any content that

applies statistics to data is appropriate. It’s better if you are interested in the topic,

but you do not need to understand the statistics in the article (that’s part of the

learning). I’ll be using your project report as a teaching opportunity.

The focus is on your description of the statistics used, not on the content (or the

controversy) of the article itself. Do not spend a lot of time searching through

articles to find one you like. The project is not about searching, it is about trying to

figure out what the reported statistics is saying.

Bring your selected article to class before the due date. Have your working group

(your table) verify that the article you chose

— has statistics that can be described

— is something that you can talk about for a couple of minutes

— is possible to understand.

This is an individual project (each student will select one article) with group

vetting (i.e. sanity checking) and group guidance.

On the project day, each student will describe what he/she found. You will have to

be succinct, you have no more than three minutes to describe the statistics in the

article.

Recommendations:

— The guidelines below (How to Read Statistics) are relevant.

— Write a one or two sentence summary of the content of your selected article.

— Make a bulleted list of the points you want to tell the class.

— Describe the data and the type of statistics in a few short sentences.

— Choose a small article with statistics you have seen in class.

Bricken

Math 146 Introduction to Statistics

2022

How to Read Statistics

Here are some guidelines:

1. What is the name the statistical technique?

2. Is it descriptive or analytic statistics?

3. Is the technique standard (common) or is it specialized (unusual)?

4. Is the technique intended for a professional or a general audience?

5. What is the question being asked (and answered)? Does the data technique

address the question? Does it answer the question?

6. What is the sample size and what is the population being generalized to?

7. How similar (or diverse) is the sample?

8. If the statistics is analytic, what is the significance level?

9. What is the measurement accuracy?

10. What is the exact definition of the units or data being reported? What exactly

is being measured?

11. What is the relation between the data that is gathered and the conclusions that

are reported?

12. If the data is reported as percentages or ratios or rates, what is being

compared? What is the relationship between the numerator and the denominator?

Bricken

Math 146 Introduction to Statistics

2022

Project 4 — Analyzing Statistics

Project 4 is to find a technical report or article that includes statistics and analyze

the statistics in the article.

The report or article can be a newspaper article, a published technical article, part

of a book, a web page, an online discussion, etc. Any source and any content that

applies statistics to data is appropriate. It’s better if you are interested in the topic,

but you do not need to understand the statistics in the article (that’s part of the

learning). I’ll be using your project report as a teaching opportunity.

The focus is on your opinion and commentary about the statistics used, not on the

content (or the controversy) of the article itself. Do not spend a lot of time

searching through articles to find one you like. The project is not about searching,

it is about trying to figure out what the reported statistics is saying and whether or

not the analysis is credible.

Bring your selected article to class before the due data. Have your working group

(your table) verify that the article you chose

— has statistics that can be discussed and critiqued

— is something that you can talk about for a couple of minutes

— is possible to understand.

This is an individual project (each student will select and discuss one article) with

group vetting (i.e. sanity checking) and group guidance.

On the last day of class, each student will describe what they found. You will have

to be succinct, you have no more than five minutes to share your opinions about the

statistics in the article.

Recommendations:

— The guidelines below (How to Analyze Statistics) are relevant.

— Write a one or two sentence summary of the content of your selected article.

— Make a bulleted list of the points you want to tell the class.

— Describe the data and the type of statistics in a few short sentences.

— Choose a small article with statistics you have seen in class.

Bricken

Math 146 Introduction to Statistics

2022

How to Analyze Statistics

“It is never safe to take published statistics at their face value, without knowing their

meaning and limitations, and it is always necessary to criticize arguments that are based

on statistics.”

L. Bowley

Here are some guidelines:

1. What is the question being asked (and answered)? Is the data technique

appropriate to answer the question?

2. What exactly is being measured?

3. How similar (or diverse) is the sample? How different is the sample from the

population that the data is claimed to represent?

4. What is the relation between the data that is gathered and the conclusions that

are reported?

5. What data or information should have been collected and reported? What is

missing from the data that is being analyzed?

6. If quantities are being compared, are they actually comparable?

7. What is the measurement accuracy? Does it align with the accuracy of the

reported statistics?

8. Is the time scope being reported sufficient to avoid fluctuation of daily

circumstances? What the time interval can the results be generalized to?

9. Are the article’s conclusions supported by the reported statistics? Does the data

directly support the conclusions?

10. Are the statistics being used to convince or to describe or to deceive?

11. What are the author’s vested interests or personal biases or professional

credibility?

12. Do you find the article’s use of statistics convincing?

Math 146 Introduction to Statistics

Project 2 — Using Software Tools

Project 2 is to use a software statistical tool to generate descriptive information about some

data. Your task is to explore and use statistical software. There is some class descriptive

data on Canvas, as well some of the tools have pre-loaded data available, or you can find

interesting real data on the web, or even make up your own. The goal is to find a tool set that you

are comfortable to use for the rest of the course.

We are currently exploring some tools for descriptive data (histograms, scatter plots, etc).

Later we will explore the rest of the available tools, including regression analysis, inferential

statistics, and analysis of distributions. Try out tools that you do not yet understand. Discuss how to

use these tools with others.

You should freely explore all resources. Many of the larger collections of tools have dozens

(hundreds) of specialized tools. Your job is to try to figure out what some of them are doing.

It’s a good idea to work with another person if that is feasible. It’s also a good idea for now to

concentrate on descriptive statistics.

Widely used free statistical tools:

https://www.mathsisfun.com/data/index.html

clear and easy

https://www.makeuseof.com/tag/excel-basic-statistics/

excel spreadsheet

Comprehensive free statistical tools:

https://www.wolframalpha.com/examples/mathematics/statistics/

interactive website

https://www.graphpad.com/quickcalcs/

statistical calculators

https://www.r-project.org/

the R statistical program

http://www.shodor.org/interactivate/lessons/

search: statistics

http://www.sofastatistics.com/home.php

opensource download

Other free options:

applet collection

http://www.rossmanchance.com/applets/index.html

Descriptive Statistics

One proportion inference

support tools

https://www.geogebra.org/search/statistics

Binomial and Normal

Correlation

Statistics Activities

applets

https://onlinestatbook.com/rvls.html

Case Studies

Simulations

https://www.quantitativeskills.com/sisa/

interactive statistical analysis

https://www.danielsoper.com/statcalc/default.aspx

statistics calculators

Bricken

Math 146 Introduction to Statistics

2022

Project 3 — Reading Statistics

Project 3 is to find a technical report or article that includes statistics and describe

the statistics in the article.

The report or article can be a newspaper article, a published technical article, part

of a book, a web page, an online discussion, etc. Any source and any content that

applies statistics to data is appropriate. It’s better if you are interested in the topic,

but you do not need to understand the statistics in the article (that’s part of the

learning). I’ll be using your project report as a teaching opportunity.

The focus is on your description of the statistics used, not on the content (or the

controversy) of the article itself. Do not spend a lot of time searching through

articles to find one you like. The project is not about searching, it is about trying to

figure out what the reported statistics is saying.

Bring your selected article to class before the due date. Have your working group

(your table) verify that the article you chose

— has statistics that can be described

— is something that you can talk about for a couple of minutes

— is possible to understand.

This is an individual project (each student will select one article) with group

vetting (i.e. sanity checking) and group guidance.

On the project day, each student will describe what he/she found. You will have to

be succinct, you have no more than three minutes to describe the statistics in the

article.

Recommendations:

— The guidelines below (How to Read Statistics) are relevant.

— Write a one or two sentence summary of the content of your selected article.

— Make a bulleted list of the points you want to tell the class.

— Describe the data and the type of statistics in a few short sentences.

— Choose a small article with statistics you have seen in class.

Bricken

Math 146 Introduction to Statistics

2022

How to Read Statistics

Here are some guidelines:

1. What is the name the statistical technique?

2. Is it descriptive or analytic statistics?

3. Is the technique standard (common) or is it specialized (unusual)?

4. Is the technique intended for a professional or a general audience?

5. What is the question being asked (and answered)? Does the data technique

address the question? Does it answer the question?

6. What is the sample size and what is the population being generalized to?

7. How similar (or diverse) is the sample?

8. If the statistics is analytic, what is the significance level?

9. What is the measurement accuracy?

10. What is the exact definition of the units or data being reported? What exactly

is being measured?

11. What is the relation between the data that is gathered and the conclusions that

are reported?

12. If the data is reported as percentages or ratios or rates, what is being

compared? What is the relationship between the numerator and the denominator?

Bricken

Math 146 Introduction to Statistics

2022

Project 4 — Analyzing Statistics

Project 4 is to find a technical report or article that includes statistics and analyze

the statistics in the article.

The report or article can be a newspaper article, a published technical article, part

of a book, a web page, an online discussion, etc. Any source and any content that

applies statistics to data is appropriate. It’s better if you are interested in the topic,

but you do not need to understand the statistics in the article (that’s part of the

learning). I’ll be using your project report as a teaching opportunity.

The focus is on your opinion and commentary about the statistics used, not on the

content (or the controversy) of the article itself. Do not spend a lot of time

searching through articles to find one you like. The project is not about searching,

it is about trying to figure out what the reported statistics is saying and whether or

not the analysis is credible.

Bring your selected article to class before the due data. Have your working group

(your table) verify that the article you chose

— has statistics that can be discussed and critiqued

— is something that you can talk about for a couple of minutes

— is possible to understand.

This is an individual project (each student will select and discuss one article) with

group vetting (i.e. sanity checking) and group guidance.

On the last day of class, each student will describe what they found. You will have

to be succinct, you have no more than five minutes to share your opinions about the

statistics in the article.

Recommendations:

— The guidelines below (How to Analyze Statistics) are relevant.

— Write a one or two sentence summary of the content of your selected article.

— Make a bulleted list of the points you want to tell the class.

— Describe the data and the type of statistics in a few short sentences.

— Choose a small article with statistics you have seen in class.

Bricken

Math 146 Introduction to Statistics

2022

How to Analyze Statistics

“It is never safe to take published statistics at their face value, without knowing their

meaning and limitations, and it is always necessary to criticize arguments that are based

on statistics.”

L. Bowley

Here are some guidelines:

1. What is the question being asked (and answered)? Is the data technique

appropriate to answer the question?

2. What exactly is being measured?

3. How similar (or diverse) is the sample? How different is the sample from the

population that the data is claimed to represent?

4. What is the relation between the data that is gathered and the conclusions that

are reported?

5. What data or information should have been collected and reported? What is

missing from the data that is being analyzed?

6. If quantities are being compared, are they actually comparable?

7. What is the measurement accuracy? Does it align with the accuracy of the

reported statistics?

8. Is the time scope being reported sufficient to avoid fluctuation of daily

circumstances? What the time interval can the results be generalized to?

9. Are the article’s conclusions supported by the reported statistics? Does the data

directly support the conclusions?

10. Are the statistics being used to convince or to describe or to deceive?

11. What are the author’s vested interests or personal biases or professional

credibility?

12. Do you find the article’s use of statistics convincing?

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