1Stat 13, UCLA, Ivo DinovSlide 1UCLA STAT 13Introduction toStatistical Methods for the Life and Health ScienceszInstructor: Ivo Dinov, Asst. Prof. In Statistics and NeurologyzTeaching Assistants: Tom Daula and Ming ZhengUCLA StatisticsUniversity of California, Los Angeles, Winter 2003http://www.stat.ucla.edu/~dinov/courses_students.htmlStat 13, UCLA, Ivo DinovSlide 2UCLA STAT 10Introduction toStatistical ReasoningCourse Description, Class homepage, online supplements, VOH’s etc.http://www.stat.ucla.edu/~dinov/courses_students.htmlStat 13, UCLA, Ivo DinovSlide 3UCLA STAT 13to just hear is to forgetto see is to rememberto do it yourself is to understand …Stat 13, UCLA, Ivo DinovSlide 4What is Statistics? A practical examplezDemography: Uncertain population forecastsby Nico Keilman, Nature 412, 490 - 491 (2001) zTraditional population forecasts made by statistical agencies do not quantify uncertainty. But demographers and statisticians have developed methods to calculate probabilistic forecasts. zThe demographic future of any human population is uncertain, but some of the many possible trajectoriesare more probable than others. So, forecast demographics of a population, e.g., sizeby 2100, should include two elements: a range of possible outcomes, and a probability attached to that range. Stat 13, UCLA, Ivo DinovSlide 5What is Statistics?zTogether, ranges/probabilities constitute a prediction interval for the population. There are trade-offs between greater certainty (higher odds) and better precision (narrower intervals). Why?zFor instance, the next table shows an estimate that the odds are 4 to 1 (an 80% chance) that the world's population, now at 6.1 billion, will be in the range [5.6 : 12.1] billion in the year 2100. Odds of 19 to 1 (a 95% chance) result in a widerinterval: [4.3 : 14.4] billion.Stat 13, UCLA, Ivo DinovSlide 6What is Statistics?2Stat 13, UCLA, Ivo DinovSlide 7What is Statistics?LargeviewStat 13, UCLA, Ivo DinovSlide 8What is Statistics?zDemography: Uncertain population forecastsby Nico Keilman, Nature 412, ,2001zTraditional population forecastsmade by statistical agencies do not quantify uncertainty. But lately demographers and statisticians have developed methods to calculate probabilistic forecasts. zProportion of population over 60yrs.Stat 13, UCLA, Ivo DinovSlide 9What is Statistics?Stat 13, UCLA, Ivo DinovSlide 10What is Statistics?zThere is concern about the accuracy of population forecasts, in part because the rapid fall in fertility in Western countries in the 1970s came as a surprise. Forecasts made in those years predicted birth rates that were up to 80% too high. zThe rapid reduction in mortality after the Second World War was also not foreseen; life-expectancy forecasts were too low by 1–2 years; and the predicted number of elderly, particularly the oldest people, was far too low.Stat 13, UCLA, Ivo DinovSlide 11What is Statistics?zSo, during the 1990s, researchers developed methods for making probabilistic population forecasts, the aim of which is to calculate prediction intervals for every variable of interest. Examples include population forecasts for the USA, AU, DE, FIN and the Netherlands; these forecasts comprised prediction intervals for variablessuch as age structure, average number of children per woman, immigration flow, disease epidemics. zWe need accurate probabilistic population forecasts for the whole world, and its 13 large division regions (see Table). The conclusionis that there is an estimated 85% chance that the world's population will stop growing before 2100. Accurate?Stat 13, UCLA, Ivo DinovSlide 12What is Statistics?zThere are three main methods of probabilistic forecasting:time-series extrapolation; expert judgement; and extrapolation of historical forecast errors.zTime-series methods rely on statistical models that are fitted to historical data. These methods, however, seldom give an accurate description of the past. If many of the historical facts remain unexplained, time-series methods result in excessively wide prediction intervals when used for long-term forecasting.zExpert judgement is subjective, and historic-extrapolation alone may be near-sighted.3Stat 13, UCLA, Ivo DinovSlide 13Chapter 1: What is Statistics?zPolls and surveys – we’re all different; It’s impossible or expensive to investigate every single person.zExperimentation – sample vs. populationzObservational Studies – selection and non-response biaszStatistics -- What is it and who uses it?zSummary TextbookChris Wild & George SeberStat 13, UCLA, Ivo DinovSlide 14Newtonial science vs. chaotic sciencezArticle by Robert May, Nature, vol. 411, June 21, 2001zScience we encounter at schools deals with crisp certainties(e.g., prediction of planetary orbits, the periodic table as a descriptor of all elements, equations describing area, volume, velocity, position, etc.)zAs soon as uncertainty comes in the picture it shakes the foundation of the deterministic science, because only probabilistic statements can be made in describing a phenomenon (e.g., roulette wheels, chaotic dynamic weather predictions, Geiger counter, earthquakes, etc.)zWhat is then science all about – describing absolutely certain events and laws alone, or describing more general phenomena in terms of their behavior and chance of occurring? Or may be both!Stat 13, UCLA, Ivo DinovSlide 1550 60 70 80 90Samples of 20 peopleSamples of 500 peopleSample percentageTarget: True populationpercentage = 69%Figure 1.1.1Comparing percentages from 10 different surveys each of20 people with those from 10 surveys each of500 people (all surveys from same population).From Chance Encounters by C.J. Wild and G.A.F. Seber, © John Wiley & Sons, 2000.Variation in sample percentagesPoll: Do you consider yourselfoverweight? 1010We are getting closer toThe population mean, asis this a coincidence?∞→nStat 13, UCLA, Ivo DinovSlide 16Errors in Samples …z Selection bias: Sampled population is not a representative subgroup of the population really investigated.z Non-response bias: If a particular subgroup of the population studied does not respond, the resulting responses may be skewed.z Question effects: Survey questions may be slanted or loaded to influence the result of the sampling.z Is quota sampling reliable? Each interviewer is assigned a fixed quotaof subjects (subjects district, sex, age, income exactly specified, so investigator can select those people as they liked).z Target
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