1. 1.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Lecture Slides Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola

2. 1.1 - 2 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Chapter 1 Introduction to Statistics 1-1Review and Preview 1-2Statistical Thinking 1-3Types of Data 1-4Critical Thinking 1-5Collecting Sample Data

3. 1.1 - 3 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 1-1 Review and Preview

4. 1.1 - 4 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Preview Polls, studies, surveys and other data collecting tools collect data from a small part of a larger group so that we can learn something about the larger group. This is a common and important goal of statistics: Learn about a large group by examining data from some of its members. If we could ask everybody in a large group (like whole US), we would not need statistics

5. 1.1 - 5 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Population  Population the complete collection of all individuals (scores, weights, heights, people, measurements, and so on) to be studied; Ex: population of US, population of all students in class, college, etc...

6. 1.1 - 6 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Census versus Sample  Census Collection of data from every member of a population (US census – familiar, but could be census for any population we study)  Sample Subcollection of members selected from a population ( most population studies are done via much smaller samples )

7. 1.1 - 7 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. The Infamous Literary Digest Poll, and the Election of 1936 In 1936, Franklin Delano Roosevelt (FDR) had been President for one term. The Literary Digest magazine predicted that Alf Landon would beat FDR in that year's election by 57 to 43 percent. The Digest mailed over 10 million questionnaires to names drawn from lists of automobile and telephone owners, and over 2.3 million people responded - a huge sample out of total population of 100 mil voters At the same time, George Gallup sampled only 50,000 people and predicted that Roosevelt would win. Gallup's prediction was ridiculed as naive. After all, the Digest had predicted the winner in every election since 1916, and had based its predictions on the largest response to any sample poll in history. But Roosevelt won with 62% of the vote. The size of the Digest's error is staggering. How could they have been so far off? The Great Depression had begun in 1929, and Roosevelt had attempted to mitigate its effects with then controversial policies like Social Security, large government "make-work" jobs programs, and other "socialistic" projects. The underlying economic condition was still that of widespread and deep depression The Literary Digest had made two fatal mistakes. 1) Their list of names was biased in favor of those with enough money to buy cars and phones (tend to be Republicans), a much smaller portion of the population in the thirties than it is today. 2) And, more seriously, the Digest had depended on voluntary response. FDR was the incumbent, and those who were unhappy with his administration were more likely to respond to the Digest survey. When a sample is biased, a large number of subjects can NOT correct for the error. Today’s scientific polls with proper randomization give good prediction based on only 1000-1200 sample out entire US population

8. 1.1 - 8 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Chapter Key Concepts  Sample data must be collected in an appropriate way, such as through a process of random selection.  Useless otherwise.

9. 1.1 - 9 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 1-2 Statistical Thinking

10. 1.1 - 10 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Context  What do the values represent?  Where did the data come from?  Why were they collected? x5561525149 y5160535049 Here is, say, a data set. By itself, it is meaningless! Need context! Context is: Weight loss in a clinical study of some drug. x – weights before drug (kg), y – weights after (kg). Drug manufacturer claims that a person should loose at least 2kg. Does the data support this claim???

11. 1.1 - 11 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Source of data  Is the source objective?  Is the source biased?  Is there some incentive to distort or spin results to support some self-serving position? Here the source is an objective medical study, not paid by manufacturer => expect it to be unbiased.

12. 1.1 - 12 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Sampling Method  Voluntary response (or self-selected) samples often have bias (those with special interest are more likely to participate). These samples’ results are not necessarily valid.  Other methods (random) are more likely to produce good results. Internet, TV, etc… polls are self-selected – not representative of entire population, only of those viewers who chose to respond. In drug studies, often double blind approach with placebo is used. The weights in the table above are from a much larger sample.

13. 1.1 - 13 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Conclusions  Make statements that are clear to those without an understanding of statistics and its terminology. In our example the conclusion was that only about 1kg weight loss on average is observed.

14. 1.1 - 14 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Practical Implications  State practical implications of the results. Drug may be used in conjunction with exercise.  There may exist some statistical significance yet there may be NO practical significance. 1kg weight loss may be statistically significant, but not practically significant to justify the use of these drug

15. 1.1 - 15 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 1-3 Types of Data

16. 1.1 - 16 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Parameter a numerical measurement describing some characteristic of entire population. population parameter Parameter

17. 1.1 - 17 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Statistic  Statistic a numerical measurement describing some characteristic of a sample. sample statistic

18. 1.1 - 18 Example There are 30 students in the class: 17Girls and 13Boys. 17/30 = 0.57  57% of girls – parameter (based on full population of the class) There is an opinion poll based on sample of 1200 people. 47% support the president – statistics (based on sample) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

19. 1.1 - 19 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Quantitative Data  Quantitative (or numerical) data consists of numbers representing counts or measurements. Examples: weights, ages, heights, blood cholesterol level, number of credit cards you own, salary, battery life…

20. 1.1 - 20 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Categorical Data  Categorical (or qualitative or nominal) data consists of names or labels (representing categories) Examples: gender (male/female), smoker (yes/no), political affiliation (Dem, Rep, Indep), car manufacturer, car model, blood type, hair color, ethnicity. Shirt numbers on professional athletes uniforms - substitutes for names, NOT quantitative.

21. 1.1 - 21 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Working with Quantitative Data Quantitative data can further be described by distinguishing between discrete and continuous types.

22. 1.1 - 22 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Discrete data - whole numbers 0, 1, 2, 3,... Examples: number of students in class, number of cars in a parking lot, number of stars in a galaxy… Discrete Data

23. 1.1 - 23 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Continuous (numerical) data some continuous scale that covers a range of values Continuous Data Example: weight, height, distance, temperatures, etc... It can be anything within some range.

24. 1.1 - 24 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 1-4 Critical Thinking

25. 1.1 - 25 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Correlation and Causality  Concluding that one variable causes the other variable when in fact the variables are linked Two variables may seemed linked, like high calorie diet is linked to obesity and diabetes - correlation. But we can NOT conclude the one causes the other. There are professional athlete in perfect health with high calorie diets and not all obese people have diabetes. Correlation does NOT imply causality.

26. 1.1 - 26 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Percentages Misleading or unclear percentages are sometimes used. For example, if you take 100% of a quantity, you take it all. If you have improved 100%, then are you perfect?! Continental airline once falsely claimed that it improved its handling of baggage by 110%. 110% of an effort does not make sense.

27. 1.1 - 27 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Loaded Questions Survey questions can be “loaded” or intentionally worded to elicit a desired response. Example: Too little money is being spent on “welfare” vs. too little money is being spent on “assistance to the poor.” Results: 19% versus 63% Do you support attempts by US to bring freedom and democracy around the world? VS Do you support unprovoked military action by US?

28. 1.1 - 28 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Self-Interest Study Some parties with interest to promote will sponsor studies. Be wary of a survey in which the sponsor can enjoy monetary gain from the results. Pharmaceutical companies pay millions to conduct studies that prove the effectiveness of their drugs, but they have self-interest. Really only independent studies can be trusted…

29. 1.1 - 29 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Cross sectional study data are observed, measured, and collected at one point in time In medicine, they are often used to assess the prevalence of acute or chronic conditions, or to answer questions about the causes of disease or the results of medical intervention. prevalence  Retrospective (or case control) study data are collected from the past by going back in time (examine records, interviews, …) Say compare the driving records of drivers who drink (moderately) and who do not.  Prospective (or longitudinal or cohort) study data are collected in the future from groups sharing common factors (called cohorts) There are have been a number of famous cohort studies over many years when life styles are compared with health and life length. Types of Studies

30. 1.1 - 30 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Double-Blind Blinding occurs at two levels: Double Blind (1)The subject doesn’t know whether he or she is receiving the treatment or a placebo (2)The experimenter does not know whether he or she is administering the treatment or placebo

31. 1.1 - 31 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.  Confounding occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors. Example: Studies have found that religious people live longer than nonreligious people. But, religious people also take better care of themselves and are less likely to smoke or be overweight - (confounding variables). Book Fig 1.4(a), p 33 shows experiment where the treatment group was just women and placebo were just men. Say, women showed much better results, but it was confounded on gender and we can NOT say if the treatment or gender had an effect. Confounding

32. 1.1 - 32 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Three very important considerations in the design of experiments are the following: Summary 1.Use randomization to assign subjects to different groups 2.Use replication by repeating the experiment on enough subjects so that effects of treatment or other factors can be clearly seen. 3.Control the effects of variables by using such techniques as blinding and a completely randomized experimental design