Statistics: The art and Science of Data Chapter 1 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 1.1a 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 one 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 1930. 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 judgment, good math, & even good taste make good statistics. Good judgment 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

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: In your notes tell me which is the categorical variables and which is the quatitative variables Name No. Pos. Ht Wt Birth date Exp College Brad Johnson 14 QB 77 224 09/13/68 9 Florida State Warren Sapp 99 DT 74 303 12/06/72 8 Miami Martin Gramatica 7 K 68 170 11/27/75 4 Kansas State Tom Tupa P 76 235 06/06/66 Ohio

Exercises Starting at page 5 Do questions: 1.1-1.5

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 1.3 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.

Sampling 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: Mr. Mylius’ Classes “THE DISTINCTION BETWEEN POPULATION & SAMPLE IS BASIC TO STATISTICS”

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

Multiple Samples Sample Sample Population

Multiple Samples with Intersection Population Sample Sample Sample

Exercise Starting on pg. 9 1.7 together On your own: 1.8-1.11

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 When would a Census be good to use?

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.

Question? 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?

Exercises Starting on pg. 14 Do question 1.13 as a class Do questions 1.14-1.16, 1.18

Review for Quiz To study for your quiz feel free to do problems on pg 17 Numbers 1.19-1.24 as practice

Activity 1.1 See no evil, Hear No Evil? With your partner do activity 1.2 as your success starter

1.2 Drawing Conclusions from DATA The Statistical Problem Solving Process 4 step process 1. Ask 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 1.10 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.