To view this presentation, you'll need to enable Flash.

Show me how

After you enable Flash, refresh this webpage and the presentation should play.

Loading...

PPT – Association Between Two Variables PowerPoint presentation | free to view - id: 146498-OWM2N

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Chapter 3

- Association Between Two Variables

True Interest of Statistics

- Examine relationship between two or more

variables. - Does an association exist? Does the value of one

variable relate to an other?

Terms

- Dependent (or response) variable
- Independent (or explanatory) variable

I) Two Categorical Variables

- Describe relationship using Contingency Table
- Each cell records the number of observations

meeting criteria set by variables.

Example Contingency Table

- Question Are pesticides less likely in organic

food (p. 95)? - 1) Identify explanatory and response variables.
- 2) Make a Table
- What do cell values represent?
- 3) Sum totals of each explanatory variable. WHY?

Example Contingency Table

- 4) Conditional upon being a certain type of

produce (Type X), what is the chance of finding

pesticides? - 5) Conclude

Excel Example Contingency Table

Other Examples of Two Categorical Variables

- Condition of Home vs. Home Ownership
- Gender vs. Smoking
- Others?

Identifying Explanatory and Response Variables

- THINK of cause and effect Response variable is

the effect - Direction of arrow
- Income Political ID
- Greenhouse Gas Global Temperature

But

- CORRELATION (ASSOCIATION) DOES NOT IMPLY

CAUSATION. - Reverse Causality (Feedback Loop)
- Omitted Variables
- This course Association/Correlation
- Advanced course Causation
- Be careful about language
- Side note Time component helps est. causation

II) Comparing a Categorical and a Quantitative

Variable

- Easier to analyze if the categorical variable is

the explanatory variable. - Conditional upon being in group X, what are the

characteristics of Y? - Gender and height
- Race and income

Options for Comparing

- 1) Compare summary statistics for two groups.

- 2) Recode categorical data as zeros and ones,

then draw a scatterplot.

Excel Example Ch3-1.xls

- 1) Sort data
- 2) Create table
- 3) Since womens heights are in Column B, Rows

2-263, type average(B2B263) in the table.

For men, type average(B264 B382).

Excel Example Ch3-1.xls

- 4) Standard deviation (of a sample) is

stdev(B2B263). To find this formula - Excel 2007 Formulas ? More Functions ?

Statistical ? stdev - ALL Excel Go to Function Wizard ? More Functions

? Standard Deviation, then select one of the

possibilities. - 5) Coefficient of Variation?
- Advantage of CV over s?

Excel Example Ch3-1.xls

- 6) Scatterplot
- i) Type if(A2Female,1,0) in Female

Column. Why? - ii) Double click crosshair on lower-right corner

of the cell. Why? - iii) Make Chart
- Excel 2007 Highlight Female and Height Data, Go

to Insert ? Chart ? Scatter - Old Excel Chart Wizard ? XY(Scatter) ? Finish
- What is true of all observations at X 0 ?
- What can we learn from this chart?

III) Comparing Two Quantitative Variables

- Examples?

Options for Comparing

- Correlation, r
- A single number (numerical summary) describing

the strength of a linear relationship between X

and Y. - Range of values
- Strong Positive Relationship r
- Strong Negative Relationship r
- Insensitive to which of the two variables is X

and which is Y. - Unit-Free (Insensitive to units of measurement)

Options for Comparing

- Correlation, r
- Where ZX deviations from the mean

Options for Comparing

- Correlation, r
- Correlation does not imply causation
- Reverse Causality
- Omitted (Lurking) Variables
- Scatterplot
- Does a relationship exist?
- Is the relationship linear?
- Is the relationship positive or negative?

Options for Comparing

- Scatterplot
- Example

Options for Comparing

- Scatterplot
- Example r

Options for Comparing

- Scatterplot
- Example r

Options for Comparing

- Scatterplot
- Example r

Options for Comparing

- Scatterplot
- Example Most of the time, when X is above its

mean, Y is above its mean, so ZX ZY gt 0 most of

the time. - This implies that r gt 0
- See Correlation by Eye applet for more

correlation examples.

Options for Comparing

- REGRESSION (Line of Best Fit)
- Suppose we believe a linear relationship between

X and Y exists such that - Y a bX error
- We can develop statistics (a b) to estimate

population parameters (a b) that predict Y

values given particular X values.

Options for Comparing

- REGRESSION (Line of Best Fit)

Excel Example Ch3-3.xls

- 3rd Party Votes in Florida, 1996 vs. 2000.
- What is X What is Y?
- Why is this interesting?
- 1) Correlation
- i) correl(B2B68, C2C68)
- ii) Tools ? Data Analysis ? Correlation

Excel Example Ch3-3.xls

- 2) Scatterplot
- i) Highlight columns
- ii) Choose Insert ? Chart ? Scatter (or Chart

Wizard ? XY(Scatter)) - 3) Regression / Line of Best Fit (all XLS

versions) - i) Right-Click scatterplot data
- ii) Choose Add Trendline, Select Display

equation on chart option. - iii) Interpretation of coefficients?
- iv) Much more on this later

Regression Intuition

- We observe Y, but develop statistics to predict Y

for given X values. - The difference (Y Y) is called a residual
- A regression line of best fit minimizes the sum

of squared residuals. That is, it makes the

errors associated with our predictions as small

as possible.

Regression Intuition

- What do residuals look like?
- Least squares regressions find a b values that

minimize the sum of squared residuals.

Regression Notes

- Size of b says nothing about the strength of the

statistical relationship. If you change the units

of X, you will change the size of b, but not r. - Although b r (SY/SX), you can have r 1 but

still find b to be meaningless. - A regression of Annual Wages on Number of

Children for men earning 20,000 to 40,000

reveals - Wage 29600 178 Children
- What does this mean?

Regression Potential Problems

- Extrapolation
- Previous example What about men who earn more

than 100,000 per year? - Time Series ESPNs Sports Figures episode

starring Marion Jones. Let the Y-variable

represent Ms. Joness fastest time in the 100m

Dash. Let X Years Since 1989, the year she

started competing. What will happen 120 years

after her first race?

Regression Potential Problems

- Correlation does not imply causation.
- Reverse Causality
- Omitted Variables
- Book Example A study found that, over a three

year period, the proportion of smokers who died

was less than the proportion of non-smokers who

died. Is smoking good for you?

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Association Between Two Variables" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!