- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Behind the headlines (Sol Garfunkel) 0:40 Have you ever noticed how much statistics there is in the news? The headline announces: Nations unemployment rate just dropped at 7.4\%. Inside Gallup poll said: 45\% Americans are afraid to go out at night because of crime. 1:00 Medical feature report claims: Taking aspirins may reduce the rate of hearth disease by 20\%. Back here in the business section there is a column on a new computer assembly line and how much are they increasing the quality and productivity of American industry. Not to mention all the statistics on the sport page. Thanks! Like to order? Yeah, I like to have two eggs over easy and bacon please. Thank you! 1:30 The numerical facts making the increasing part of the information that we need in order to understand our world. I call data like this statistics and there is a branch of mathematics that is also called statistics, that helps us to interpret and use these data. But where did the numbers come from? The Gallup poll did not ask me if I was afraid to go out at night for the fear of crime. In fact Gallup interviewed only 15,055 people. It says so right here at the end of the article. 2:00 How can information that is based on such a small number of people justify conclusions about a much larger group? It is the business of statistics to draw conclusions from partial numerical information, and to say how trustworthy these conclusions are. But it is a business not without controversy. The search in generals reports about smoking and health says that cigarette smoking is the largest avoidable cause of death and disability in United States. Most medical experts believe that tobacco accounts for 85-90\% of the over 95.000 of the lung cancer deaths in the country each year. But the tobacco industry says that the evidence linking smoking and lung cancer is weak, because it is only statistical. 3:00 How does statistics arrive to conclusions and how accurate is the statistical evidence? Well, as in any other science, the foundation is accurate observations. In statistics this means properly collecting the data. If this is not done correctly, then the short?? of conclusion ???? the result. Suppose that I wanted to figure out the unemployment rate, for example. I can go to a convenient busy street, stop people passing by and ask them if they are employed or not. 3:30 But would you tell the stranger with the clip board that you have been just laid off? And how many people with jobs are likely to be out there on the street in the middle of the day? Where am I gone find a typical street - whatever that means? And how many typical streets am I gone need to visit before I get a decent cross section of the country? 3:45 Excuse me, I am taking the survey! Do you have a job? Yes! Even if I do pick a place, and start asking people wather they have jobs I am only going to approach people who are going to look harmless. That keeps me safe. But it also means my results are unrepresentative. My survey is biased. 4:00 The only way to collect accurate data is to follow procedures expressly designed to eliminate bias. The fist step is to state what group we want to gain information about. Statisticians call this group population. For example, if we want to measure unemployment rate, we have to answer certain questions. What age group are we talking about? What about illegal aliens, what about people in prisons. Just who is part of the population? In fact the official unemployment figures are compiled by the Bureau of the labor statistics. When the Biro announces the national unemployment rate each month, the population it is measuring is - All U.S. residents (citizens or not) - 16 years of age or older - who are Civilians and - not institutionalized Once the population is defined, the next step is to select a sample - a part of the population from which to draw a conclusion about the whole. To measure the unemployment rate the Bureau ob the labor statistics relies on the sample of 16,000 households. 5:08 Janet Norwood, Commissioner, Bureau of Labor Statistics The households survey is a basic labor force survey which provides us with an enormous amount of data, providing information on a demographic characteristics of people and about their labor force status: the unemployment, the length of time they are employed, wather the are job seekers, employed part time and so on. That survey is conducted for us on contract by the bureau of the census. Interviewers go out to sample 16,000 households, which is spread throughout the country and more the 400 areas around the country. 5:51 How can we avoid bias in a selection of such a sample? A statistician's answer is to eliminate personal choice, by allowing chance to select that sample. 6:02 Now these beads are all identical, except for the fact that some of them are light and some of them are dark. Let us say I wanted to figure out what percentage of this beads is dark without counting each of them individually. To make things a little bit more interesting imagine that this box represents working age Americans and the dark beads represent those who are unemployed. Now I got a scoop here, with a 50 recess in it. So if I am gonna mix up all of these in this box and blanch a scoop, every bead would have the same chances as every other bead of being selected. Moreover, every group of 50 beads would have the same chances as every other group of 50 beads. That is a sattle point but it is important. Let us try. OK I got 12 dark beads. 12 out of 50 is the same as 24 out of a 100 or 24\%. 7:00 So this is an example of a simple random sample. I have drawn the sample of the population and I estimated a number. I am gonna use this number to guess what is going on for the entire population. But what would happen if I do it again. Am I likely to get the same 12 beads. Well probably not. Ou, I got 8 dark beads. Now 8 out of 50 is 16\%. So I got two different numbers. That is a little scary. Does this mean that if would take the monthly unemployment survey twice, I have to announce two different unemployment rates. It is holly?? the basis for the sound economic policy. Now what is going on here is that random sampling has eliminated bias, but it did not eliminate variability. Fortunately, there is a theorem ....... in the mathematics of probability, that describes this kind of variability when we have several repeated random samples. So while each individual outcome is unpredictable like the toose of a coin, in the long run a definite pattern emerges. Now, earlier I took 80 samples of this beads and I counted how many dark beads were in each sample. 8:12 My first sample of 50 beads had 12 dark ones or 24\%, the second sample contained 8 dark beads or 16\%, and the third sample had 26\% dark beads. Now after scooping 30 times, I round up with 8 dark beads, that is 16\%, had the total of four times. There were 5 samples that contain each contain 12 dark beads. When I put all my samples together like this, the display looks something like a bar graph? In fact it is a histogram. The graph that measures frequencies. 10 dark beads in a sample or 20 percent happen 6 times and the histogram shows that frequency. In the same way you can read the totals I got before directly of the graph. 9:00 It appears to be quite a beads of scattering around results. But most results clustered around 20\% and I know, because I counted them before I put them in, that exactly 20 beads in the container are dark one. Only 6 of my samples contained exactly 20\%. But you can see that about 2/3 were pretty close. The results of sampling are usually close to the population truth. Now the rules of probability enable us to make exact statements about what happens when we have many repetitions of a random sampling. And what we get is a definite pattern of variability, which allows us to compare the results of the sample with the truth about population. 9:45 So how does the bureau of labor statistics get those unemployment figures. Certainly they do not use beads in a box to determine who is gone be interviewed, in fact random selection is done by the computer. The census bureau does this job, first selecting at random a sample of contagious geographic areas, called primary sampling units. 10:03 Then smaller areas of about 500 inhabitants each, called census in a relation district, are chosen. Then again at random individual households within those districts are chosen. This procedure is a multistage probability sample. Far removed from a joint beads from the box. But it is still a random sample. The use of chance eliminates bias in choosing those interviewed, How many hours did you work last week at all jobs? 35, 37. Did you lose any time ... The bureau visits approximately 16,000 households each month. At home with a trained interviewer? people speak more freely. Although participation is not required by law, over 95\% of those contacted agree with the interview. A number of questions determine if each person is in a labor force. The survey also collect other important social and economic data. What were the most important activities or duties on you job? Speaking English, that is what I teach. But just as with beads the variability of the sample does not disappear even with the most careful choice of the sample. But the mathematics of probability enables the bureau of labor statistics to state pretty accurately what that probability is and what are the margins of error are within which most results are bound to fall. 11:30 Janet Norwood: Commissioner, Bureau of Labor Statistics Everyone, but everyone wants to live in a world of certainty. Even the statistician wants to live in a world of certainty. I think that our job is to explain to people that there is no such thing as absolute certainty. And that what we can do is to provide a set of statistics which have some error surrounding them, something that we often call sampling error or variance, which will tell them what the basic tolerances are. 12:13 The unemployment rate for example if it is moved by 1/10 of a point we in the bureau of labor statistics and all our releases/everything, will say that it is about the same. If it goes up or down 2/10 of a point, this is overall rate, we will say that there has been a change?. 12:30 Let us take another look at the arguments linking cigarette smoking and lung cancer. Let us see how confident can we be with statements that are made there. Several major medical studies show a very strong connection between cigarette smoking and incidents of lung cancer. Smokers are more likely, 20 times more likely in one study, than nonsmokers, to get the disease. Such a strong correlation is very unlikely due to chance alone. 13:00 We can actually say from just looking at samples that cigarette smoking causes lung cancer. Is not it possible that third factor might be involved? For example, it could be that cigarette smokers have genetic predisposition to both nicotine addiction and lung cancer. If that was the case, we would still see the strong connection, even if the cigarette smoke would have no effect on the lungs whatsoever. In order to prove the cause in that relationship, we have to conduct an experiment. Now for example, we can take two groups of children and require one group to smoke 2 packs of cigarettes every day of their life, while not allowing other group so much as the single puff? Then if the groups have been selected at random any difference in incidence of lung cancer could be confidently attributed to smoking cigarettes. But that is an experiment that we could not do for ethical reason. Although it is really no different in design from the way medical experiment are conducted ........ randomized comparative experiments, the main state? of research in medicine and agriculture and many other fields. 14:03 These experiments are comparative, because one group takes experimental treatment, while the second, the controlled group is given an alternative treatment. The subject are assigned to these groups at random, in order to eliminate bias, to insure that groups are comparable. Now in medicine a randomized experiment is called a randomized clinical trial. 14:25 On of the largest such trials ever undertaken is the physicians health study, which is investigating the effect of taking aspirin and reducing heart disease. And the same study investigating the effect of taking the beta carootin, which is the form of vitamin A, on prevention of cancer. The cardiovascular disease and cancer are responsible for 2/3 of the death in US each year. So work on their prevention is one of the most important challenges facing the epidemiology, the study of disease. 14:56 What is that about what we do, what we eat, what our environment is, our our occupations are, something about our history, medical history, our family history, that leads one group of people to be more or less likely to develop the disease than another group of people. Julie Buring, Physicians' Health Study and these factors we are trying to identify. We go at them a couple different ways. One is, what is called descriptive epidemiology, looking at trends of diseases over time, trends of diseases in one population relative to another population. We do not interfear in the process, we observe it. But the second type of the epidemiology, which is, as an example of physicians health study, is experimental epidemiology, experimental study, interventional study. We take a group of people who have the treatment, that are exposed to the treatment, the group of people who are not. The difference is that we, the investigators, determine who will be in what treatment group, who receives the treatment and the placebo, who will be exposed and who will not be exposed. 16:00 Charles Hennekens, Physicians' Health Study We would hope to either provide fair? medical evidence on which public policy can bit? days with regards to aspirin and beta carootin or alternatively if in fact we find no association between these treatments and the outcome of the study, than we could safely permit rechanneling of existing funds to other areas of research, rather than providing inconclusive results that really leave us in a quandary? of wether there is, there is not something going on here. 16:30 A physicians' Health Study is an experiment, because of the effects of certain treatments. just take the aspirin, the beta carrots is being compared to the effect of the identical but inactive pill, called placebo. It is a randomized experiment, a randomized clinical trial, because who gets which pills is determined by random assignment. Here is the design of the assignment. 16:55 Almost 22,000 physicians agreed to participate. Although the random assignments were actually made all at once by a computer, you can think of the design this way: first, after the physicians are randomly selected to use aspirin of aspirin placebo, then each of these groups are further split into beta carootin and beta carootin placebo groups. That makes 4 experimental conditions: aspirin and beta carootin aspirin and a placebo aspirin placebo and beta carootin two placebos All four groups, of course the doctors do not know what group they are in, since the placebos are filled with They mail them into the physicians There are the reports that are filled by staff members, who also do not know what doctors they had been assigned to. 17:48 People who are gathering this information do not know That is called blindness, of the interviewers or the people who are gathering information do not have knowledge of the different group. That is just one half of it. The another half would be the people who are receiving the treatment. 20:40 Let us be very careful here. Any significant difference between these two groups it is almost certainly due to the drugs. That is because the random assignment 21:52 The distinction is 22:00 22:56 But does the randomized experiment always required to large sample size? That depends on a lot of factors. If we think we know all the variables are, then there is some really lovely mathematical techniques, which can help us reduce the sample size and hence the cost of the experimentation. Let me show you what I mean. Todays cars ... 25:55 Remember, what we are really asking comparison of the different motor oils and gas usage consumption different kinds of cars, different types of drivers. Now, in the more complicated cases cardiovascular diseases, we do not even know ... might be. So, though Latin square design might be economical it is not always applicable. To decide when it is applicable and it the statisticians most important job. Whatever we want information about after data collection there is more than just a series of now it is crucial that we have accurate measurements but we have to know what we want to measure, why we want to measure it, we have to be able to do something with these measurements Next time we are going to look organizing data we will see how to convert what arrays of numbers striking visual images. 27:02 END