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1: CHAPTER INTRODUCTION 1.1 What is Statistics? Questions to explore: 1. What is the population of Canada? What is the population of Alberta? Canada: 31,612,897, Alberta: 3,306, 359 (2006). Census (every member of the population counted). Also data collected about the number of people in the household, age, sex, education, income, etc. 2. What is the crime rate (number of crimes per 100,000) in Canada in 2006? Rates (number of criminal code offences per 100,000) are based on counts obtained from police records. 1 Homicide rates: Toronto (1.8), Montreal (1.8), Vancouver (2.5), Edmonton (3.7). 2. Are Albertans receiving a fair share of wealth being generated by developing the province's oil sands? According to Probe Research Corp. 56 per cent of Albertans feel that citizens are not receiving a fair share of the wealth being generated by developing the province's oil sands. The study was conducted via telephone interviews between April 3 and 16, 2007 of a random and representative sampling of 500 adults from across the province of Alberta. With this sample size it can be concluded with 95 per cent certainty that the results are within plus or minus 4.4 percentage points of what they would have been if all qualifying Albertans had been interviewed. 3. Is echinacea effective as a treatment for a common cold? How would you conduct a study to test the claim? The study conducted in 1999 by researchers from the University of Wisconsin used a group of 148 cold-suffering college students as test subjects. Researchers randomly administered echinacea pills and a placebo to the students who, in turn, reported on the duration and severity of their 2 symptoms. In their report, the researchers concluded that, "compared with placebo, unrefined echinacea provided no detectable benefit or harm in these college students who had the common cold." The results fly in the face of marketing claims that echinacea is an effective treatment for colds. Echinacea was the most popular herbal remedy in Canada in 1999, with sales of $19.5 million and growing. Missing information: What specie of Echinacea was used? Was the entire plant or just root used? What was the dosage administered? Was echinacea administered immediately after infection? 4. Pesticides use and cancer. Pesticides have been blamed for rising incidence of some cancers, infertility and birth defects (higher rate of some cancers among people who have come into contact with pesticides). Pesticide producers say there is no proven cancer link. Who is right? 5. Do you always believe what you read? News reports of statistical studies usually provide summarized information. Look at the source of the research and of the funding, how the individuals or objects studied were selected, and the exact nature of measurements made or questions asked. 3 Statistics is the science of designing studies, collecting data, analyzing data, and drawing conclusions from data. Statistics provides support for inference from specific to general, from sample to population. Problem Study Design Data Collection Data Analysis Decisions Data Analysis Components: Description: Summarizing patterns in the data Inference: Making decisions based on the data generalizations to a wider group of subjects or objects) 1.2 What will you learn in this class? Learn how to carry out simple statistical analyses Learn appropriate methods for data collection Be able to follow basic statistical arguments 4 (i.e. Develop a critical attitude toward quantitative claims Get familiar with statistical software (StatCrunch) 1.3 Applications of Statistics Pharmaceuticals (pharmaceutical companies must demonstrate that new drugs are effective and safe, public good vs. commercial interests) Politics (polls, i.e. which of two candidates is favored by the voters) Environment (effect of pollution on health, water quality) Marketing (will the product sell? letting a sample of consumers try a new product; which marketing strategies: newspaper advertising, television commercials, flyers are most cost effective) Quality control (monitoring the quality of product or process; adjustments can be made before the process creates a large number of defective products) Product design (making very strong materials, the effect of several factors on the material 1.4 strength) Misuses of Statistics Example 1: Loaded Questions (deliberate bias) Group Anti-abortion Pro-choice Question Do you agree that abortion, the murder of innocent beings, should be outlawed? Do you agree that there are circumstances under which abortion should be legal, to protect the rights of the mother? 5 "As the population ages and health care demands increase, there will be relatively fewer working Canadians paying taxes needed to fund social programs. Given this, would you support alternate sources of funding for health care? (Pollara Poll January 2000) 75% agreed. National Post conclusion: "75% of Canadians support health care user fees." Example 2: Little Sense Comparisons Are young people safer drivers? In 1989, 5326 drivers 65 years of age and over were involved in fatal accidents. In contrast, only 2900 drivers aged 16 and 17 had fatal accidents. Can we conclude that young people are safer drivers? Example 3: Manipulating Scale (University Budget) Claim: "The University is sufficiently funded" Univ. Budget 590 570 550 $M 530 510 490 470 450 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 6 86 87 89 88 91 85 92 93 95 90 96 98 97 94 99 The graph has been shrunk horizontally and stretched vertically to give the impression of the steep increase. Univ. Budget 1000 900 800 700 600 500 400 300 200 100 0 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 In this case the graph has been stretched horizontally and shrunk vertically. The vertical scale set to between 0 and $1B. These two measures mask the real increase. Spending per student data needed to answer the question. Example 4: Is health care sustainable? Claim: "It is not sustainable to have health care costs rising by seven and eight 8 percent a year and government revenues at half that rate". Year 1997 1998 1999 2000 2001 2002 2003 2004 $M Health spending ($ B) 4.2 4.6 5 5.9 6.3 7.3 7.9 8.5 7 Alberta Health Spending 1997-2004 9 8.5 8 7.5 $ Billions 7 6.5 6 5.5 5 4.5 4 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Year The numbers do not adjust for either inflation or population growth. The annual percentage increase based on 1997 as the baseline (final year of cuts, large infusions of cash after 1997 to catch-up). 8 Once adjusted for inflation and population growth and averaged over 1992-2004 timeframe, the average yearly increase was 1.6 per cent per year. 1.5 Populations and Samples Population the entire collection of individuals or objects about which information is desired Population parameter- a numerical summary of the population Example: Population Canada's population Parameter- proportion of the smokers Census a survey in which the entire population is measured (time consuming and expensive) Sample the collection of individuals or objects we will actually measure Generalization Sample Population Statistic a numerical summary of the sample taken from the population 9 Example: proportion of smokers in a particular sample is a statistic The value of the statistic varies from sample to sample. Inferences - statements about the population based on the sample data Valid inferences about population can be reached if sample is representative of the population. Larger samples give more accurate results than smaller samples (statistic values tend to better approximate the population parameter for larger samples). No inferences with absolute certainty (partial information about the population, unrepresentative samples) Random Sample each subject or object in the population has the same chance of being included in that sample. Example: Obtaining a sample of students in a class: place names in a hat (the population) and draw out a handful (sample). 1.6 StatCrunch Demonstration Data Load Data From Sample Data StatCrunch File: Body measurements of 48 female sparrows. Column total beak/head humerus Description total length of the bird length of beak and head length of humerus 10 Obtain 10 random samples of n=5 sparrows each and demonstrate the variation in the sample mean total length from sample to sample. Repeat the exercise for n=10. What do you conclude? Henryk Kolacz, September 2007 11
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Path: Bucknell >> EDUC >> 243 Winter, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> ENG >> 010 Fall, 2007
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> CRJ >> 101 Spring, 2008
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Path: Kutztown >> CRJ >> 101 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: Michigan >> HIST >> 443 Winter, 2008
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Path: UMass (Amherst) >> PHY >> 134 Fall, 2007
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Path: UMass (Amherst) >> PHY >> 134 Fall, 2007
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Path: UMass (Amherst) >> PHY >> 134 Fall, 2007
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Path: UMass (Amherst) >> PHY >> 134 Fall, 2007
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Path: Michigan >> HIST >> 443 Winter, 2008
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Path: Michigan >> HIST >> 443 Winter, 2008
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Path: Michigan >> HIST >> 443 Winter, 2008
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Path: Michigan >> HIST >> 443 Winter, 2008
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Path: Michigan >> HIST >> 443 Winter, 2008
Description: Ottoman Baghdad 1/29/2008 3:00:00 PM Baghdad as commercial center an eye witness wrote in 1774 \"this is the grand mart for the produce of India and Persia, Constantinople, Aleppo and Damascus; in short is the grand oriental depository\" Sulayman Pas...
