Some very cautionary statistics

by Dr Gavin Hitchcock


This article was sent to all Zimbabwean schools receiving Zimaths. We are still awaiting their response on this possibly contreversial article. The contreversy not being the article itself but the fact that a mathematics magazine had somehow decided to tell people facts that few others seemed to be mentioning. Your comments will also be appreciated.

Here are some statistical figures which are vitally relevant to everyone --- and some ideas for discussing them critically, and deducing consequences from them, which should bring every classroom to vibrant life. For what follows is, quite simply and bluntly, about matters of life and death.

Statistics can be boring --- these are not! Statistics can be meaningless, misleading, or downright deceitful. We have taken care to select and cite our references; that does not mean we think they're crystal-clear or infallible, nor do we endorse them, but we have chosen reasonably trustworthy sources. Graphs, charts and histograms can be abused, for alarmist or cover-up motives; we would encourage you to make diagrams to help understand what the figures really do mean. We urge our readers to be critical --- don't swallow anything based on statistics without careful scrutiny:

Are they well-referenced? Are the cited references reputable? Do the different sources agree within limits of error? Are these limits specified? Do they supply dates? Are they taken out of context? Have they been correctly reported? Watch for vagueness, ambiguities, apparent contradictions...the watchword with all such figures is: "Statistics change daily and should never be assumed to be up-to-date or complete."

With all that, we suggest that the overall message of the statistics we are about to quote is inescapable and urgent. We believe it is our duty and the duty of school and government authorities to bring these figures and their possible implications to the attention of all Zimbabweans.

  1. Trouble brewing in Africa

  2. Zimbabwe now in big trouble

  3. A major epidemic of STD in the USA

  4. What about a cure?

  5. What about condoms?

  6. Is there any way of ensuring I am safe? "Postponing sexual activity until marriage with an uninfected mate is the only way for adolescents to be 100% sure of avoiding STD infection and pregnancy. Most of them can accomplish this if properly instructed and encouraged....Likewise, single adults, including those with previous sexual experience, would be wise to save sex for a mutually monogamous lifetime partner. It is unrealistic to expect people to use condoms consistently and correctly with every act of intercourse for a long period of time. Delaying sex until marriage is the most medically sound advice we can give people in today's environment." (The Facts About STD Epidemic, Medical Institute for Sexual Health, ibid.)

Questions:

[Assume populations in millions: Zimbabwe 12, Harare 2, USA 250]

  1. Can you see any ambiguities or apparent contradictions in the first Herald report (item 1 of section 2) on death statistics? How might they be explained? Assuming the weekly AIDS related deaths are correctly reported for January 1998, and that it doesn't get better or worse, how old will you be when 1 million people have died of Aids in Harare? Will you still be alive?

  2. How many STD's are mentioned in the text above? Which are viral, so untreatable by antibiotics? Which was (at the time of reporting) the major cause of infertility among young people in the USA? Which was the fastest growing? Which was a major cause of cancer? Which is not protected against by condoms at all? Are these statements likely to be transferable to 1998 and to Zimbabwe?

  3. What is the definition of `failure-rate'? Could the 13% in item 1 of section 5 mean (and why are we left to guess?!):

  4. What does `most rapidly increasing cause' mean (in item 3 of section 3)?

  5. How do the Zimbabwe statistics (for HIV prevalence, STD prevalence, condom failure etc.) compare with those from other countries at similar times (Uganda, USA)?

  6. Do the statistics quoted in items 1 and 4 of section 3 correlate well? If not, what possible reasons are there? [Look at the difference in estimated numbers of people in the USA contracting an STD per year, over the period separating the two dated references.]

  7. If the population of USA was 240 million in 1993, how many under 25's in the USA in 1993 were likely to be infected with a viral STD? How many were likely to be ignorant of the fact? What are the figures likely to be now?

  8. How many under 25's in the US are HIV positive or have AIDS? [Use the estimates given in item 5 of section 3, and assume that the age distribution is similar to that for STD's reported in item 1 of section 3.] Compare the figure you get with your estimate in question 7, and draw some possible conclusions for Zimbabwe.

  9. If the probability is f of catching a virus in each sexual encounter, then the probability of doing so in 2 encounters is 1 minus the probability of 2 successes = 1-(1-f)^2, in 3 encounters is 1-(1-f)^3 , and in n encounters is 1-(1-f)^n. If f=1/1000, how many people out of 100 will contract the virus over a year? [Assume 50 encounters.] How many in the (very) long run? [Let n run to infinity.]

  10. Suppose that 13% of women (using new condoms regularly) fall pregnant every year, and that the fertile period for a woman is 3 days per month --- or approximately 10% of the time. Suppose also that HIV prevalence rate for men is 25%. What estimate can we make of the percentage of women (using new condoms regularly) who will contract the virus in the next year? [You need to make a similar assumption to that for the previous question, but it turns out that the number of encounters does not matter very much!] How does your answer compare with the figure given in item 1 of section 5?

  11. What does "safe'' mean in such widely advertised statements as `No condom --- no sex. Play safe --- use a condom.' Is safety from financial, social, moral, emotional, psychological or spiritual dangers (or `scars') included? What do you think of such statements in the light of the statistics?

  12. Is it possible to be 100% physically safe? Is it worth it?

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