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

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?

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.

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

Posting opportunity Missing old people in Japan…..

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?

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

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 ….

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

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.

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

How many? 300000 * .02 = 6000 (How many is 1%: answer is 3000. 2% is twice that.)

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

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

Testing for X Number with X Number without X Total Tests Positive 6000*.99 =5940 294000*.02= 5880 5940+5880 = 11820 Tests Negative 6000*.01 = 60 294000*.98 = 288120 60+288120=288180 6000 294000 300000

So…. Of the 11820 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.

Which statement was correct? For the situation just described: The test is 98 to 99% accurate. 2% of a population of 300000 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.

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.

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.

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.)

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

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

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

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)

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…..

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

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

http://www.cdc.gov/nchs/pressroom/07newsreleases/teenbirth.htm Teenager births and unmarried births (Data are for U.S. in 2006) "Between 2005 and 2006, the birth rate for teenagers 15-19 years rose 3 percent, from 40.5 live births per 1,000 females aged 15-19 years in 2005 to 41.9 births per 1,000 in 2006. 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"

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

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%

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