1. Communicating Quantitative Information
Themes of course
Testing
Odds
Out-of-wedlock babies, census
Homework: Postings

2. Themes of course Meta level (over-arching) theme: ask questions
What is/are the definition(s)? To gather quantitative data, there needs to be an operational definition that may or may not be what you/the reader has in mind
What is the denominator (the base)?
absolute or relative
What is the … difference? the context? the relevant comparisons?
time (temporal) or space MAY be significant
data may be missing
What is the distribution?
The phenomenon may involve sets of numbers (test scores, infants who die before age 5, longevity, weight). The average (mean) is just one summary statistic. How are the values distributed: range, variance,quintile, etc.
What are the [critical] dimensions of the thing / phenomenon?
How to characterize something. How does a diagram represent information?

3. Recall "More women murdered"… What is the definition of 'on the job'?
For the comparison, the denominators/bases were… of the men who die and of the women who die
It probably was okay to talk relatively (without knowing absolute numbers) but needed to make the appropriate comparisons
What was killing the men was missing data.

4. gapminder.org Choose Wealth and Health of Nations
specific definitions of wealth and health
Shows what's the difference:
context over time
comparison between countries
Also:
distributions: comparisons within countries

5. Posting opportunity
Missing old people in Japan…..

6. Drinkers
Posting: CBS news story reported that death rates were non-drinkers, heavy drinkers and moderate drinkers… Population of non-drinkers had more deaths in a 20 year period.
This was a study of a specific set of 3 groups.
Definition of groups MAY be suspect
Prior work included previous heavy drinkers that had stopped in non-drinking category
Claim: other factors accounted for…
Comments?

7. Themes of course Be skeptical but do the math…arithmetic…
What is the story?

8. Today's topic Testing / screening
Can apply to HIV testing, mammograms, prostrate, security screen, scanning phone calls, etc.
There is a terminology of sensitivity and specificity ….

9. Testing for X Number with X Number without X Total Tests Positive
Tests Negative

10. Quality of test Two values (may not be the same) Suppose test is
99% accurate in predicting condition X (returning positive) when subject has X.
98% accurate in predicting the absence of X when subject does NOT have X.

11. Prevalence in population
Suppose population is 300,000 and 2% have condition X
How many have X?

12. How many?
* .02 = 6000
(How many is 1%: answer is % is twice that.)

13. Testing for X Number with X Number without X Total Tests Positive
Tests Negative
6000
294000

14. Testing for X Number with X Number without X Total Tests Positive
6000*.99
294000*.02
Tests Negative
6000*.01
294000*.98
6000
294000

15. Testing for X Number with X Number without X Total Tests Positive
6000*.99 =5940
294000*.02= 5880
= 11820
Tests Negative
6000*.01 = 60
294000*.98 =
=288180
6000
294000
300000

16. So….
Of the subjects given positive results (positive here may not be good!)
5940 really have X
5880 false positive—it was a mistake!
Procedure generally is to re-test all positives with same test or, mostly, a better (more expensive) test.

17. Which statement was correct?
For the situation just described: The test is 98 to 99% accurate. 2% of a population of have the condition X. If you get a positive result
there is 1 to 2% chance it is wrong.
there is around a 50% chance it is wrong.

18. Another example Make the 2x2 50000 in population 2000 have condition
Test is 95% accurate in finding condition when it is present. 98% accurate in NOT finding condition when it is absent.

19. Comments
Even with what appears to be an accurate test, there are many people told the wrong thing
Most especially, many False Positives. This is because the base for the potential false positives often is nearly the whole population.
There also are False Negatives, but much fewer.
Actual tests are somewhat more accurate, but still not absolutely accurate.

20. Testing
A test maker may prefer more false positives than false negatives because a process could be put in place to use a second test on all the positives.
However, false positives for conditions such as HIV make people very uncomfortable. BUT it could still be a good public health approach. (It may be that given this serious condition, the second test is performed on material from same person.)

21. General issue
Think of
testing for drugs
Mammograms
Screening phone calls
Cost of 'false positive', including the follow-up tests
for individual
shared health costs

22. Cancer biopsies May be follow-up treatment Not risk free
Treatment of early cancer is not risk free

23. Posting opportunity Do research to find out
Prevalence of HIV or something else in a typical population
Cancer screening
Recent reports on suggested policies regarding mammograms, other
Accuracy of typical tests
re-do calculation
make posting

24. Posting opportunity
Procedures and accuracies of tests done for Tour de France
Note: the AIDS/HIV example assumed that most people were not infected. What is the assumption (now) about cyclists? (SIGH)

25. Theme Questions
What is definition of accuracy for test and how does it work?
more complex (but understandable if you make the effort)
What is the difference/who cares: accuracy for general testing versus how someone should react to getting a notice….
Is value of test in scaring people…..

26. Out-of-wedlock births
Fairly frequent news story
One or more populations have increases in out-of-wedlock births
As previous situations
Definitions matter
Must make note of issues and terms such as percentages, rates, changing underlying population, absolute vs rates, rates of change, time interval under study

27. Posting opportunities
Story on chances of pregnancies of children of politicians in the news?
Success (define) rates of places with abstinence only versus more general sex education
Definitions of education
Definition of success

28.
Teenager births and unmarried births
(Data are for U.S. in 2006)
"Between 2005 and 2006, the birth rate for teenagers years rose 3 percent, from 40.5 live births per 1,000 females aged years in 2005 to 41.9 births per 1,000 in This follows a 14-year downward trend in which the teen birth rate fell by 34 percent from its recent peak of 61.8 births per 1,000 in 1991"

29. Source? I chose the CDC source. Let's look at others
What words do we put into google?
What about scholar.google.com
Posting opportunity: find out more exactly than I'm saying what scholar.google.com is
Note: data is somewhat older

30. Murphy Brown story
TV character!!! choosing to have child as a single mom. Criticized by VP Dan Quayle
News story: Murphy Brown was accurate Out-of-wedlock births by professional, well-off, non-minority women increasing at greater rate than other groups.
Be careful when comparing rates of change
If 1% goes to 2%, this is a doubling,100% increase
If 45% goes to 50%, this is increase of 11.1%

31. Homework
Postings
Note: any posting topic (that you or any classmate does or that no one does) could be a topic for one of the presentations.
Next class: measures of centrality:
Mean, median, mode, range, variance, standard deviation