Cancer:A Global View

Gretchen A. KochGoucher CollegePEER UTK 2011

Special Thanks To:• Dr. Claudia Neuhauser

o University of Minnesota – Rochestero Author and creator of modules

Learning ObjectivesAfter completion of this module, the student will be able to:1. Explore “social, economic and

environmental development at local, national and global levels” with Gapminder.

2. Perform and interpret logarithmic transformations for graphical display.

3. Download global health data from Gapminder and WHOSIS.

Prerequisites1. Calculating percent changes2. Straight lines3. Natural logarithm, exponential

function4. Graphing in Excel5. Fitting a straight line to data points

in Excel and displaying the equation

Knowledge Gained1. Logarithmic transformations2. Continuous time population models3. Fitting a straight line to data

Teaching Style1.See It2.Do It3.Teach It

Learning Objective 1: Gapminder

• A visualization tool to animate statistics and data to see trends over time

• Downloadable data sets• Interactive graphical resources• Unique visualization techniques

o Ex: Size and color of each country’s circle are significant.

• Video #1: Breast Cancer Statistics• Video #2: Lung Cancer Statistics

Think, Pair, Share• What features about Gapminder were

most intriguing? • What, if anything, confused you about

Gapminder?• What relationships would you like to

explore with respect to breast cancer and lung cancer in Gapminder?

Time to Share

Think, Pair, Share• Complete In-Class Activity #2 in the Cancer

Global View document • Pay special attention to what happens when you

change the scale of the graph

Time to Share

Summarizing

Learning Objective 2: Logarithmic

Transformations• Gapminder World:

o Lung cancer, new cases per 100,000 men versus Income per Capita • Linear y-axis with linear x-axis• Logarithmic y-axis with linear x-axis• Linear y-axis with logarithmic x-axis• Logarithmic y-axis with logarithmic x-axis

Learning Objective 2: Logarithmic

TransformationsSame data – different visualizations:

0 50 100 150 200 2500

2000

4000

6000

8000

10000

12000

14000

Plantain Data

Seeds planted per sqmAvg #

of

seeds

per

repro

duc-

ing i

ndiv

idual

1 10 100 100010

100

1000

10000

100000

Plantain Data

Seeds planted per sqmAvg #

of

seeds

per

repro

duc-

ing i

ndiv

idual

Linear versus Linear

Logarithmic versus

Logarithmic

Learning Objective 2: Logarithmic

TransformationsSame data – different visualizations:

76 78 80 82 84 86 88 90 92 94 960

0.1

0.2

0.3

0.4

0.5

0.6

Parakeet Data

Year

# M

onk P

ara

keets

per

Part

y

Hour

76 78 80 82 84 86 88 90 92 94 960.01

0.1

1

Parakeet Data

Year

# M

onk P

ara

keets

per

Part

y

Hour

Linear versus Linear

Logarithmic versus Linear

Learning Objective 2: Logarithmic

Transformations

(a)On the axes above, find the following numbers: x=0.05, 0.2, 8, 15, 750.

(b)Why do you think we choose logarithms to base 10, instead of some other base?

(c) Can you plot negative numbers on a logarithmic scale?

(d)As x approaches 0, where would you find x on a logarithmic scale?

So what is really happening?

• Case 1: Both axes are logarithmic.

Log/Log Graphs• Log/Log transformation = straight

line

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• Applying our rules for logarithms:

Log/Log Graphs• If we substitute in a constant, we find

Log/Log Graphs• If both axes are transformed logarithmically,

producing a straight line, then the relationship between x and y is that of a power function:

Case 2: Semi-log Graphs• In this case, the x-axis remains

linear, while the y-axis is transformed logarithmically.

Case 2: Semi-log Graphs• Again, let us assume that a straight

line results from this transformation.

Case 2: Semi-log Graphs• If we transform the y-axis

logarithmically, leave the x-axis linear, and a straight line results, what is the relationship between the data points?

Time’s Up!

Case 2: Semi-log Graphs

Case 2: Semi-log Graphs• If we transform the y-axis

logarithmically, leave the x-axis linear, and a straight line results, then the relationship between x and y is an exponential function.

Exploring Data in Excel1. Download the Excel data file from the Schedule page2. Click on the Parakeet tab. Highlight both columns of

data.3. Choose Charts Scatter Marked Scatter.4. Click on the legend and delete it.5. Click on the title and change it.6. Choose Chart Layout Axis Titles Horizontal Title

Below the Axis. Pick an appropriate name. Repeat the process for the Vertical Axis.

7. To make the horizontal axis start at 76 (not 0), right click on the horizontal axis. Select Format Axis. Uncheck the Minimum box, and put 76 in as the minimum.

8. Options for logarithmic transformations can be found under Chart Layout Axes Horizontal

9. If your axes do not look correct (i.e. the horizontal axis is not at the bottom of the graph), right click on the vertical axis. Select Format Axis. Ensure that the horizontal axis crosses at the minimum value of the vertical axis.

Fitting Data in Excel1. Graph your data on the scales desired.2. Select the graph. Choose Chart Layout

Trendline Trendline Options Options. Choose to display the equation on the chart, as well as displaying the R-squared value on the chart.

3. Select the graph. Choose Chart Layout Trendline Trendline Options Type. Try various options for the fit type, keeping in mind that the transformed graph should guide your decision. Note that an R-squared value closer to one indicates a stronger correlation between the two variables.

Group Activity• Fit an appropriate function to the Parakeet data.• Fit an appropriate function to the Plantain data.• Compare with your neighboring group.

Learning Objective 3: Downloading Data

• Follow the directions in the Cancer Global View pdf (starting on the bottom of page 6) to download data from Gapminder and WHO (links can be found on the schedule page).

• Complete the group project involving the mash-up data provided. Create a blog entry reflecting on your results.