Statistics: The art and Science of Data

1.1 Where do data come from? What is data? Information We gain this information from Observations Counts Measurements responses

Data Good Data Products of intelligent human effort Bad Data Results from laziness Lack of understanding Even the desire to mislead others Where do the data come from? Should always be the first question you ask…

Data beats personal experience How will you get relevant data to help answer your questions? It’s very tempting to base conclusions on your experience. In fact, the incidents that stick in our memory are often unusual.

Example A In August 2000, Dr.Chris Newman appeared as a guest on CNN’s Larry King Live. Dr. Newman had developed brain cancer. He was also a frequent cell phone user. Dr. Newman’s physician suggested that the brain tumor may have been caused by cell phone use. So Dr. Newman decided to sue the cell phone make, Motorola, and the phone company that provided his service, Verizon. As people heard Dr. Newman’s sad story, they began to worry about whether their own cell phone use might lead to cancer. Since 2000, several statistical studies have investigated the link between cell phone use and brain cancer. One of the largest as conducted by the Danish Cancer Society. over 400,000 Denmark residents who regularly used cell phones were included in the study. Researchers compared the brain cancer rate for the cell phone users with the rate in the general population. The result: no difference. In fact, most studies have produced similar conclusions. In spite of the evidence, many people people are still convinced that Dr. Newman’s experience is typical.

Example B The American Cancer Society, in a booklet titled “The Hopeful side of Cancer,” claimed that about one in three cancer patients is now cured, while in 1930 only on in five patients was cured. That’s encouraging. But where does this encouraging estimate come from? From the state of Connecticut. Why Connecticut? Because it is the only stat that kept record of cancer patients in It is a matter of available data. But Connecticut is not typical of the entire nation. It is densely populated but has no large cities and has few blacks than the national average. Cancer deaths rates are higher in large cities than in rural locations, and higher among blacks than whites. Data from Connecticut alone do not necessarily mirror national trends.

Talking about data: individuals and variables Statistics: The art and science of dealing with data. Good judgement, good math, & even good taste make good statistics. Good judgement is deciding what to measure in order to produce data that helps answer your questions.

Measurements are made on individuals and organized in variables. Individuals: the objects described by a set of data, people, animals and things. Examples: company employee, student names Variables: Characteristics of an individual. A variable can take different values for different variables. Examples: eye color, race, gender, job type, salary, hair color, religion, height, marital status

Statistics deals with numbers: Quantitative Variables: numerical values for which arithmetic operations, add, subtract, multiply, averaging, make sense. Examples: height, weight, age

Not all variables are numbers: Categorical variables: Also called qualitative variables Places individuals into one of several groups or categories. Counts or percents to summarize the data Examples: name, state, eye color, city, hair color

Example C NameJob TypeAgeGenderRaceSalary Cedillo, Jose Technical27MaleWhile52300 Chambers, Tonia Management42FemaleBlack Childers, Amanda Clerical39FemaleWhite27500 Chen, Huabang Technical51MaleAsian83600

Measurements are made on individuals and organized in variables. In Super Bowl XXXVII, the Tampa Bay Buccaneers defeated the Oakland Raiders. Here is a portion of Tampa Bay’s team roster : Example D: NameNo.Pos.HtWtBirth dateExpCollege Brad Johnson 14QB /13/689Florida State Warren Sapp 99DT /06/728Miami Martin Gramatica 7K /27/754Kansas State Tom Tupa9P /06/6614Ohio

Observational Studies Observes individuals and measure variables of interest Does not attempt to influence the response Purpose is to describe some group or situation “Observe But Don’t Disturb” Using sampling: to gain information about the whole by examining only a part of the population.

Example E: An Associated Press news article begins, “people hurt in traffic accidents actually recover more quickly when they cannot collect money for their pain and suffering researchers say in a new study.” The Canadian province of Saskatchewan changed its insurance laws. The old system allowed lawsuits for “pain and suffering”. The new no-fault system paid for medical costs and lost work but not for subjective suffering. The study looked at insurance claims filed between July 1 of the year before the change and December 31 of the year after the change. Under the new system there were not just fewer claims of whiplash neck injuries but faster recovery with less pain for the people who filed claims.

Population: WHOLE Entire group of individuals about which we want information Example: MWHS student population Sample: PART A part of the population from which we actually collect information. Use to draw conclusions about the whole Example: Mrs Aitken’s Classes “THE DISTINCTION BETWEEN POPULATION & SAMPLE IS BASIC TO STATISTICS”

Example F: Government economic and social data come from large sample surveys of a nation’s individuals, households, or businesses. The monthly Current Population Survey (CPS) is the most important government sample survey in the United States. Many of the variables recorded by the CPS concern the employment or unemployment of everyone over 16 years old in a household. The government’s monthly unemployment rate comes from the CPS. The CPS also records many other economic and social variables.

Example G: Market research is designed to discover what consumers want and what products they use. One example of market research is the television-rating service of Nielson Media Research. The Nielson ratings influence how much advertisers will pay to sponsor a program and whether or not the program stays on the air.

Example H: Social science research makes heavy use of sampling. The General Social Survey (GSS), carried out every second year by the National Opinion Research Center at the University of Chicago, is the most important social science sample survey. The variables cover the participant’s personal and family background experiences and habits, and attitudes and opinions on subjects from abortion to war.

Characteristics of Data Populations Parameters: a number that describes a population characteristics Sample Statistics: a number that describes a sample characteristic

Venn Diagrams : show sample and population SamplePopulation

Sample

Population Sample SampleSample

Census A sample survey that attempts to include the entire population in the sample Is not foolproof Expensive Takes a long time Over count or under count the population Time and money favor samples over census Sample advantages Produce more accurate data than census Example: sampling inventory of spare parts than counting 500,000 parts in a warehouse

Example I: A census can only attempt to sample the entire population. The Census Bureau estimates that the 1990 census missed 1.6% of the American population. These missing persons included an estimated 4.4% of the black population, largely in inner cities. In 2000, the census overcounted the U.S. population by about 1.3million. Millions of people who live in two places – like college students– were counted twice. About 1.8% of blacks and 0.7% of Hispanics were not counted at all a census is not foolproof, even with the resources of the government behind it.

Experiments We want to CHANGE behaviors Deliberately impose some treatment on individuals in order to observe their responses. The purpose of an experiment is to study whether the treatment causes a change in the response. We don’t just observe individuals or ask questions, we actively impose some treatment in order to observe the response. In principle, experiments can give good evidence for cause and effect.

ExampleJ: There may be a “gender gap” in political part preference in the United States, with women more likely than men to prefer Democratic candidates. A political scientist interviews a large sample of registered voters, both men and women. She asks each voter whether they voted for the Democratic or the Republican candidate in the last congressional election. Is this study an experiment? Why or why not? What variables does the study measure?

Example K It has been claimed that large doses of vitamin C will prevent colds. An experiment to test this claim was performed in Toronto during the winter months. About 500 volunteer subjects were assigned “ at random” to each of two groups. Group 1 received 1 gram per day of vitamin C and 4 grams per day at the first sign of a cold. Group 2 served as a control group and received a placebo pill – identical in appearance to the vitamin C capsule but with no active ingredient. Both groups were regularly checked for illness during the winter. Groups 1 and 2 were very similar in age, occupation, smoking habits, and other background variables. At the end of the winter, 26% of the subjects in Group 1 had not had a cold, compared to 18% in Group 2

Example L Most adult recipients of welfare are mothers of young children. Observational studies of welfare mothers show that many are able to increase their earning and leave the welfare system. Some take advantage of voluntary job-training programs to improve their skills. Should participation in job-training and job- search programs be required of all able bodied welfare mothers?

1.2 Drawing Conclusions from DATA The Statistical Problem Solving Process 4 step process 1. As a question of interest. 2. Produce Data: methods of choice are observational studies and experiments 3. Analyze Data: tools for describing patterns, deviations(variations) from the patterns 4. Interpret the results; How does the data analysis answer the question of interest. Collect the Data Organize the Data Analyze the Data Interpret the Data

Example M: Who has tattoos? 1. Ask a question: What percent of U.S. adults have one or more tattoos? 2. Produce data 3. Analyze Data: 4. Interpret Results:

Sampling Variability A different samples of the same size taken in the same way from the same population will yield different results.

Example N: How prevalent is cheating on test? Representative from the Gallup Organization were determined to find out. They conducted an Internet survey of 1200 students, ages 13-17, between Jan. 23 and Feb. 10, The questions they posed was “Have you, yourself, ever cheated on a test or exam?” Forty-eight percent of those surveyed said “Yes”. If Gallup had asked the same questions of all year old students, would exactly 48% have answered “Yes”?